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3<title>Steel sheet gong: how the parameters shape the sound</title>
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17<h1>Steel sheet gong: how the parameters shape the sound</h1>
18<div class="setup-wrap"><svg class="setup" viewBox="0 0 880 358.6" width="880" height="358.6" role="img" aria-label="Physical setup">
19 <defs><marker id="arrow" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="8" markerHeight="8" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" fill="#f0b429"/></marker></defs>
20 <g font-family="system-ui, sans-serif" font-size="12" fill="#c8cbd0">
21 <text x="60" y="38" font-weight="600">Front view</text>
22 <text x="60" y="56" fill="#9aa0a8">12 x 18 in, 0.79 mm stainless steel</text>
23 <!-- thread and hanging sheet -->
24 <line x1="66" y1="72" x2="66" y2="86" stroke="#c8cbd0" stroke-width="1" stroke-dasharray="3 2"/>
25 <rect x="60" y="80" width="152.39999999999998" height="228.6" fill="#2a3340" stroke="#c8cbd0" stroke-width="1.5"/>
26 <circle cx="66" cy="86" r="3" fill="#15171a" stroke="#c8cbd0"/>
27 <text x="76" y="102" fill="#9aa0a8">hangs from a thread through a hole</text>
28 <!-- strike point -->
29 <circle cx="166.67999999999998" cy="228.59" r="6" fill="none" stroke="#6fa8ea" stroke-width="2"/>
30 <line x1="173.67999999999998" y1="221.59" x2="224.67999999999998" y2="170.59" stroke="#b08050" stroke-width="5" stroke-linecap="round"/>
31 <text x="234.67999999999998" y="168.59" fill="#6fa8ea">drumstick strike</text>
32 <text x="234.67999999999998" y="182.59" fill="#9aa0a8">70% of width, 35% of height</text>
33 <!-- pushed corner -->
34 <circle cx="212.39999999999998" cy="308.6" r="7" fill="none" stroke="#f0b429" stroke-width="2"/>
35 <text x="60" y="332.6" fill="#f0b429">finger pushes this corner 10 mm toward the listener,</text>
36 <text x="60" y="346.6" fill="#9aa0a8">holds it until the sheet settles, then lets go</text>
37 <!-- top view -->
38 <text x="430" y="38" font-weight="600">Top view</text>
39 <text x="430" y="56" fill="#9aa0a8">the sheet seen from above</text>
40 <path d="M 430 90 Q 506.2 110 582.4 90" fill="none" stroke="#c8cbd0" stroke-width="3"/>
41 <text x="594.4" y="94" fill="#9aa0a8">bow of 3 mm across the width</text>
42 <text x="594.4" y="108" fill="#9aa0a8">(exaggerated), bulging toward the listener</text>
43 <line x1="582.4" y1="96" x2="582.4" y2="134" stroke="#f0b429" stroke-width="2" marker-end="url(#arrow)"/>
44 <text x="594.4" y="136" fill="#f0b429">push</text>
45 <line x1="506.2" y1="108" x2="506.2" y2="276" stroke="#9aa0a8" stroke-width="1" stroke-dasharray="4 3"/>
46 <text x="514.2" y="200" fill="#9aa0a8">1 m</text>
47 <circle cx="506.2" cy="290" r="8" fill="none" stroke="#6fa8ea" stroke-width="2"/>
48 <circle cx="506.2" cy="290" r="2" fill="#6fa8ea"/>
49 <text x="522.2" y="286" fill="#6fa8ea">listener</text>
50 <text x="522.2" y="302" fill="#9aa0a8">on the normal through the center</text>
51 </g>
52</svg></div>
53<p class="dim">The setup: the sheet hangs from a thread through a hole near one corner. It is either pushed at the opposite corner by a fingertip, held until it settles, and released, or struck with a wooden drumstick. It has a slight bow, and the sound is computed 1 m in front of its center.</p>
54<p>Each section varies one property of the simulated sheet or of the excitation while everything else stays at the simulator defaults: a 12 by 18 inch, 22 gauge (0.79 mm) stainless steel sheet hanging in portrait orientation with a 3 mm bow across its width, heard 1 m in front of its center, recorded for 4 s. The clips are computed with the simulator's default numerical settings (8 mm grid), so the 'Open in simulator' links reproduce them exactly. Click a player to hear a clip. Every clip is rendered at the simulator's default playback level (+20 dB relative to 1 Pa at full scale, with the same soft clipper), so loudness differences within and between sections are the ones the model predicts, and a clip sounds as it does in the app. The numbers under each clip are the peak pressure and sound pressure level at the listener, the RMS pressure over the clip, the spectral centroid of the sound between 0.2 and 1.2 s (a measure of brightness), and fitted 60 dB decay times of a low and a high band.</p>
55<ul class="toc"><li><a href="#strike-speed">Drumstick: stick speed</a></li><li><a href="#strike-mass">Drumstick: stick mass</a></li><li><a href="#strike-stiffness">Drumstick: tip hardness</a></li><li><a href="#strike-position">Drumstick: strike position</a></li><li><a href="#push-amount">Push and release: push amount</a></li><li><a href="#push-sign">Push and release: with or against the bow</a></li><li><a href="#push-release">Push and release: release time</a></li><li><a href="#bow-amplitude">Sheet: initial bow (push and release)</a></li><li><a href="#bow-amplitude-strike">Sheet: initial bow (drumstick strike)</a></li><li><a href="#bow-shape">Sheet: shape of the bow (push and release)</a></li><li><a href="#bow-shape-strike">Sheet: shape of the bow (drumstick strike)</a></li><li><a href="#thickness">Sheet: thickness (push and release)</a></li><li><a href="#thickness-strike">Sheet: thickness (drumstick strike)</a></li><li><a href="#size">Sheet: size (push and release)</a></li><li><a href="#size-strike">Sheet: size (drumstick strike)</a></li><li><a href="#outline">Sheet: outline at equal area (push and release)</a></li><li><a href="#outline-strike">Sheet: outline at equal area (drumstick strike)</a></li><li><a href="#ellipse-size">Ellipse: size (push and release)</a></li><li><a href="#ellipse-size-strike">Ellipse: size (drumstick strike)</a></li><li><a href="#material">Sheet: material (push and release)</a></li><li><a href="#material-strike">Sheet: material (drumstick strike)</a></li><li><a href="#damping-sigma0">Damping: frequency-independent loss (push and release)</a></li><li><a href="#damping-sigma0-strike">Damping: frequency-independent loss (drumstick strike)</a></li><li><a href="#damping-sigma1">Damping: frequency-dependent loss (push and release)</a></li><li><a href="#damping-sigma1-strike">Damping: frequency-dependent loss (drumstick strike)</a></li><li><a href="#damping-inplane">Damping: in-plane loss (push and release)</a></li><li><a href="#damping-inplane-strike">Damping: in-plane loss (drumstick strike)</a></li></ul>
56<section id="strike-speed">
57<h2>Drumstick: stick speed</h2>
58<p>A wooden stick tip (30 g effective mass) strikes the sheet at 70 percent of its width and 35 percent of its height. Speed sets both the loudness and the character: the contact force grows with speed, the contact shortens, and more energy reaches the high modes. In these clips the peak level rises from about 87 dB at 0.5 m/s to 109 dB at 6 m/s, and the spectral centroid from about 190 Hz to 1.6 kHz, so the sound grows brighter as well as louder.</p>
59<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
60<div class="cards"><div class="card">
61 <div class="label">0.5 m/s</div>
62 <audio controls preload="none" src="clips/strike-speed-0.wav"></audio>
63 <img src="clips/strike-speed-0.png" alt="spectrogram" width="640" height="200">
64 <div class="metrics">
65 <div>peak 0.435 Pa (87 dB SPL)</div>
66 <div>RMS 1.7 mPa</div>
67 <div>centroid 192 Hz</div>
68 <div>T60 100-500 Hz 4.8 s, 2-8 kHz 8.6 s</div>
69 <div>contact force 28 N</div>
70 <div class="dim">wav peak 12.8 dBFS (soft-clipped)</div>
71 </div>
72 <a href="../../?excitation=strike&strikeVelocity=0.5">Open in simulator</a>
73</div>
74<div class="card">
75 <div class="label">1 m/s</div>
76 <audio controls preload="none" src="clips/strike-speed-1.wav"></audio>
77 <img src="clips/strike-speed-1.png" alt="spectrogram" width="640" height="200">
78 <div class="metrics">
79 <div>peak 0.891 Pa (93 dB SPL)</div>
80 <div>RMS 3.6 mPa</div>
81 <div>centroid 259 Hz</div>
82 <div>T60 100-500 Hz 4.8 s, 2-8 kHz 6.8 s</div>
83 <div>contact force 58 N</div>
84 <div class="dim">wav peak 19.0 dBFS (soft-clipped)</div>
85 </div>
86 <a href="../../?excitation=strike&strikeVelocity=1">Open in simulator</a>
87</div>
88<div class="card">
89 <div class="label">2 m/s</div>
90 <audio controls preload="none" src="clips/strike-speed-2.wav"></audio>
91 <img src="clips/strike-speed-2.png" alt="spectrogram" width="640" height="200">
92 <div class="metrics">
93 <div>peak 1.676 Pa (98 dB SPL)</div>
94 <div>RMS 7.3 mPa</div>
95 <div>centroid 317 Hz</div>
96 <div>T60 100-500 Hz 3.9 s, 2-8 kHz 5.1 s</div>
97 <div>contact force 124 N</div>
98 <div class="dim">wav peak 24.5 dBFS (soft-clipped)</div>
99 </div>
100 <a href="../../?excitation=strike&strikeVelocity=2">Open in simulator</a>
101</div>
102<div class="card">
103 <div class="label">3 m/s</div>
104 <audio controls preload="none" src="clips/strike-speed-3.wav"></audio>
105 <img src="clips/strike-speed-3.png" alt="spectrogram" width="640" height="200">
106 <div class="metrics">
107 <div>peak 2.552 Pa (102 dB SPL)</div>
108 <div>RMS 10.9 mPa</div>
109 <div>centroid 655 Hz</div>
110 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
111 <div>contact force 195 N</div>
112 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
113 </div>
114 <a href="../../?excitation=strike&strikeVelocity=3">Open in simulator</a>
115</div>
116<div class="card">
117 <div class="label">4.5 m/s</div>
118 <audio controls preload="none" src="clips/strike-speed-4.wav"></audio>
119 <img src="clips/strike-speed-4.png" alt="spectrogram" width="640" height="200">
120 <div class="metrics">
121 <div>peak 4.114 Pa (106 dB SPL)</div>
122 <div>RMS 17.2 mPa</div>
123 <div>centroid 678 Hz</div>
124 <div>T60 100-500 Hz 4.4 s, 2-8 kHz 3.8 s</div>
125 <div>contact force 315 N</div>
126 <div class="dim">wav peak 32.3 dBFS (soft-clipped)</div>
127 </div>
128 <a href="../../?excitation=strike&strikeVelocity=4.5">Open in simulator</a>
129</div>
130<div class="card">
131 <div class="label">6 m/s</div>
132 <audio controls preload="none" src="clips/strike-speed-5.wav"></audio>
133 <img src="clips/strike-speed-5.png" alt="spectrogram" width="640" height="200">
134 <div class="metrics">
135 <div>peak 5.721 Pa (109 dB SPL)</div>
136 <div>RMS 24.9 mPa</div>
137 <div>centroid 1654 Hz</div>
138 <div>T60 100-500 Hz 3.9 s, 2-8 kHz 3.4 s</div>
139 <div>contact force 448 N</div>
140 <div class="dim">wav peak 35.1 dBFS (soft-clipped)</div>
141 </div>
142 <a href="../../?excitation=strike&strikeVelocity=6">Open in simulator</a>
143</div></div>
144</section>
145<section id="strike-mass">
146<h2>Drumstick: stick mass</h2>
147<p>The same speed with a lighter or heavier stick. A light stick gives a short contact and a bright tap. A heavier stick stays in contact longer, which by itself favours the low modes, but it also pushes the sheet further, and the extra energy reaches the high partials through the nonlinearity. In these clips the two effects roughly cancel between 10 and 60 g, and the 120 g stick is both the loudest and the brightest of the set. The peak contact force changes little with the mass (about 180 N at 10 g and 230 N at 120 g), because the local response of the sheet limits it.</p>
148<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
149<div class="cards"><div class="card">
150 <div class="label">10 g</div>
151 <audio controls preload="none" src="clips/strike-mass-0.wav"></audio>
152 <img src="clips/strike-mass-0.png" alt="spectrogram" width="640" height="200">
153 <div class="metrics">
154 <div>peak 2.452 Pa (102 dB SPL)</div>
155 <div>RMS 9.7 mPa</div>
156 <div>centroid 654 Hz</div>
157 <div>T60 100-500 Hz 4.3 s, 2-8 kHz 5.2 s</div>
158 <div>contact force 183 N</div>
159 <div class="dim">wav peak 27.8 dBFS (soft-clipped)</div>
160 </div>
161 <a href="../../?excitation=strike&stickMass=0.01">Open in simulator</a>
162</div>
163<div class="card">
164 <div class="label">30 g</div>
165 <audio controls preload="none" src="clips/strike-mass-1.wav"></audio>
166 <img src="clips/strike-mass-1.png" alt="spectrogram" width="640" height="200">
167 <div class="metrics">
168 <div>peak 2.552 Pa (102 dB SPL)</div>
169 <div>RMS 10.9 mPa</div>
170 <div>centroid 655 Hz</div>
171 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
172 <div>contact force 195 N</div>
173 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
174 </div>
175 <a href="../../?excitation=strike&stickMass=0.03">Open in simulator</a>
176</div>
177<div class="card">
178 <div class="label">60 g</div>
179 <audio controls preload="none" src="clips/strike-mass-2.wav"></audio>
180 <img src="clips/strike-mass-2.png" alt="spectrogram" width="640" height="200">
181 <div class="metrics">
182 <div>peak 2.578 Pa (102 dB SPL)</div>
183 <div>RMS 12.3 mPa</div>
184 <div>centroid 686 Hz</div>
185 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 3.8 s</div>
186 <div>contact force 205 N</div>
187 <div class="dim">wav peak 28.2 dBFS (soft-clipped)</div>
188 </div>
189 <a href="../../?excitation=strike&stickMass=0.06">Open in simulator</a>
190</div>
191<div class="card">
192 <div class="label">120 g</div>
193 <audio controls preload="none" src="clips/strike-mass-3.wav"></audio>
194 <img src="clips/strike-mass-3.png" alt="spectrogram" width="640" height="200">
195 <div class="metrics">
196 <div>peak 2.591 Pa (102 dB SPL)</div>
197 <div>RMS 17.0 mPa</div>
198 <div>centroid 1346 Hz</div>
199 <div>T60 100-500 Hz 3.5 s, 2-8 kHz 3.2 s</div>
200 <div>contact force 232 N</div>
201 <div class="dim">wav peak 28.3 dBFS (soft-clipped)</div>
202 </div>
203 <a href="../../?excitation=strike&stickMass=0.12">Open in simulator</a>
204</div></div>
205</section>
206<section id="strike-stiffness">
207<h2>Drumstick: tip hardness</h2>
208<p>The Hertz contact stiffness K stands for the hardness of the tip. A soft (rubber or felt) tip has a low K and a long, gentle contact that excites mainly the low modes: the softest tip here is about 17 dB quieter than the default and has almost no energy above 2 kHz. A hard tip (dense wood, or a metal beater) has a high K and a larger contact force, which makes the strike louder; in these clips the brightness does not increase further beyond the default value.</p>
209<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
210<div class="cards"><div class="card">
211 <div class="label">5000000 N/m^1.5</div>
212 <audio controls preload="none" src="clips/strike-stiffness-0.wav"></audio>
213 <img src="clips/strike-stiffness-0.png" alt="spectrogram" width="640" height="200">
214 <div class="metrics">
215 <div>peak 0.380 Pa (86 dB SPL)</div>
216 <div>RMS 5.1 mPa</div>
217 <div>centroid 375 Hz</div>
218 <div>T60 100-500 Hz 4.4 s, 2-8 kHz 4.7 s</div>
219 <div>contact force 113 N</div>
220 <div class="dim">wav peak 11.6 dBFS (soft-clipped)</div>
221 </div>
222 <a href="../../?excitation=strike&contactStiffness=5000000">Open in simulator</a>
223</div>
224<div class="card">
225 <div class="label">50000000 N/m^1.5</div>
226 <audio controls preload="none" src="clips/strike-stiffness-1.wav"></audio>
227 <img src="clips/strike-stiffness-1.png" alt="spectrogram" width="640" height="200">
228 <div class="metrics">
229 <div>peak 1.436 Pa (97 dB SPL)</div>
230 <div>RMS 7.9 mPa</div>
231 <div>centroid 677 Hz</div>
232 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 4.4 s</div>
233 <div>contact force 148 N</div>
234 <div class="dim">wav peak 23.1 dBFS (soft-clipped)</div>
235 </div>
236 <a href="../../?excitation=strike&contactStiffness=50000000">Open in simulator</a>
237</div>
238<div class="card">
239 <div class="label">500000000 N/m^1.5</div>
240 <audio controls preload="none" src="clips/strike-stiffness-2.wav"></audio>
241 <img src="clips/strike-stiffness-2.png" alt="spectrogram" width="640" height="200">
242 <div class="metrics">
243 <div>peak 2.552 Pa (102 dB SPL)</div>
244 <div>RMS 10.9 mPa</div>
245 <div>centroid 655 Hz</div>
246 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
247 <div>contact force 195 N</div>
248 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
249 </div>
250 <a href="../../?excitation=strike&contactStiffness=500000000">Open in simulator</a>
251</div>
252<div class="card">
253 <div class="label">5000000000 N/m^1.5</div>
254 <audio controls preload="none" src="clips/strike-stiffness-3.wav"></audio>
255 <img src="clips/strike-stiffness-3.png" alt="spectrogram" width="640" height="200">
256 <div class="metrics">
257 <div>peak 3.469 Pa (105 dB SPL)</div>
258 <div>RMS 15.5 mPa</div>
259 <div>centroid 563 Hz</div>
260 <div>T60 100-500 Hz 3.8 s, 2-8 kHz 4.5 s</div>
261 <div>contact force 532 N</div>
262 <div class="dim">wav peak 30.8 dBFS (soft-clipped)</div>
263 </div>
264 <a href="../../?excitation=strike&contactStiffness=5000000000">Open in simulator</a>
265</div></div>
266</section>
267<section id="strike-position">
268<h2>Drumstick: strike position</h2>
269<p>Where the sheet is struck decides which modes are excited: a strike at the center excites only modes that are symmetric about both axes, while a strike near an edge or a corner excites the twisting and edge modes as well. The central strike is the loudest and the lowest of the four, since it drives the low symmetric modes that radiate best; the off-center default is the brightest.</p>
270<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
271<div class="cards"><div class="card">
272 <div class="label">center</div>
273 <audio controls preload="none" src="clips/strike-position-0.wav"></audio>
274 <img src="clips/strike-position-0.png" alt="spectrogram" width="640" height="200">
275 <div class="metrics">
276 <div>peak 4.090 Pa (106 dB SPL)</div>
277 <div>RMS 17.4 mPa</div>
278 <div>centroid 449 Hz</div>
279 <div>T60 100-500 Hz 4.7 s, 2-8 kHz 3.9 s</div>
280 <div>contact force 195 N</div>
281 <div class="dim">wav peak 32.2 dBFS (soft-clipped)</div>
282 </div>
283 <a href="../../?excitation=strike&strikeFracX=0.5&strikeFracY=0.5">Open in simulator</a>
284</div>
285<div class="card">
286 <div class="label">off-center (default)</div>
287 <audio controls preload="none" src="clips/strike-position-1.wav"></audio>
288 <img src="clips/strike-position-1.png" alt="spectrogram" width="640" height="200">
289 <div class="metrics">
290 <div>peak 2.552 Pa (102 dB SPL)</div>
291 <div>RMS 10.9 mPa</div>
292 <div>centroid 655 Hz</div>
293 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
294 <div>contact force 195 N</div>
295 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
296 </div>
297 <a href="../../?excitation=strike&strikeFracX=0.7&strikeFracY=0.35">Open in simulator</a>
298</div>
299<div class="card">
300 <div class="label">near the right edge</div>
301 <audio controls preload="none" src="clips/strike-position-2.wav"></audio>
302 <img src="clips/strike-position-2.png" alt="spectrogram" width="640" height="200">
303 <div class="metrics">
304 <div>peak 2.026 Pa (100 dB SPL)</div>
305 <div>RMS 9.8 mPa</div>
306 <div>centroid 457 Hz</div>
307 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.5 s</div>
308 <div>contact force 190 N</div>
309 <div class="dim">wav peak 26.1 dBFS (soft-clipped)</div>
310 </div>
311 <a href="../../?excitation=strike&strikeFracX=0.95&strikeFracY=0.5">Open in simulator</a>
312</div>
313<div class="card">
314 <div class="label">near a corner</div>
315 <audio controls preload="none" src="clips/strike-position-3.wav"></audio>
316 <img src="clips/strike-position-3.png" alt="spectrogram" width="640" height="200">
317 <div class="metrics">
318 <div>peak 2.641 Pa (102 dB SPL)</div>
319 <div>RMS 13.0 mPa</div>
320 <div>centroid 540 Hz</div>
321 <div>T60 100-500 Hz 4.7 s, 2-8 kHz 4.4 s</div>
322 <div>contact force 197 N</div>
323 <div class="dim">wav peak 28.4 dBFS (soft-clipped)</div>
324 </div>
325 <a href="../../?excitation=strike&strikeFracX=0.92&strikeFracY=0.08">Open in simulator</a>
326</div></div>
327</section>
328<section id="push-amount">
329<h2>Push and release: push amount</h2>
330<p>The corner is pushed by a given amount, held until the sheet settles, and released over 20 ms. A larger push stores more energy and, because the stiffness rises with deflection, produces a stronger pitch glide and a stronger transfer of energy to the higher partials. The 2 and 5 mm pushes are nearly linear and very quiet, with most of their sound below 100 Hz; the 20 mm push is about 10 dB louder than the default and has far more energy above 500 Hz.</p>
331<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
332<div class="cards"><div class="card">
333 <div class="label">2 mm</div>
334 <audio controls preload="none" src="clips/push-amount-0.wav"></audio>
335 <img src="clips/push-amount-0.png" alt="spectrogram" width="640" height="200">
336 <div class="metrics">
337 <div>peak 0.012 Pa (56 dB SPL)</div>
338 <div>RMS 0.1 mPa</div>
339 <div>centroid 427 Hz</div>
340 <div>T60 100-500 Hz 4.8 s, 2-8 kHz 17.5 s</div>
342 <div class="dim">wav peak -18.2 dBFS</div>
343 </div>
344 <a href="../../?pushAmount=0.002">Open in simulator</a>
345</div>
346<div class="card">
347 <div class="label">5 mm</div>
348 <audio controls preload="none" src="clips/push-amount-1.wav"></audio>
349 <img src="clips/push-amount-1.png" alt="spectrogram" width="640" height="200">
350 <div class="metrics">
351 <div>peak 0.018 Pa (59 dB SPL)</div>
352 <div>RMS 0.4 mPa</div>
353 <div>centroid 179 Hz</div>
354 <div>T60 100-500 Hz 4.7 s, 2-8 kHz 10.7 s</div>
356 <div class="dim">wav peak -14.7 dBFS</div>
357 </div>
358 <a href="../../?pushAmount=0.005">Open in simulator</a>
359</div>
360<div class="card">
361 <div class="label">10 mm</div>
362 <audio controls preload="none" src="clips/push-amount-2.wav"></audio>
363 <img src="clips/push-amount-2.png" alt="spectrogram" width="640" height="200">
364 <div class="metrics">
365 <div>peak 0.046 Pa (67 dB SPL)</div>
366 <div>RMS 3.3 mPa</div>
367 <div>centroid 196 Hz</div>
368 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
370 <div class="dim">wav peak -6.7 dBFS</div>
371 </div>
372 <a href="../../?pushAmount=0.01">Open in simulator</a>
373</div>
374<div class="card">
375 <div class="label">20 mm</div>
376 <audio controls preload="none" src="clips/push-amount-3.wav"></audio>
377 <img src="clips/push-amount-3.png" alt="spectrogram" width="640" height="200">
378 <div class="metrics">
379 <div>peak 0.147 Pa (77 dB SPL)</div>
380 <div>RMS 6.8 mPa</div>
381 <div>centroid 411 Hz</div>
382 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.2 s</div>
384 <div class="dim">wav peak 3.3 dBFS (soft-clipped)</div>
385 </div>
386 <a href="../../?pushAmount=0.02">Open in simulator</a>
387</div></div>
388</section>
389<section id="push-sign">
390<h2>Push and release: with or against the bow</h2>
391<p>The sheet has a 3 mm bow across its width. Pushing the corner in the direction of the bow and against it are not equivalent: the shell stiffness is asymmetric, so the two cases have different low-mode frequencies and a different wobble. Here the push against the bow gives a quieter and lower sound, with about 20 dB less energy between 500 Hz and 2 kHz.</p>
392<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
393<div class="cards"><div class="card">
394 <div class="label">+10 mm (with the bow)</div>
395 <audio controls preload="none" src="clips/push-sign-0.wav"></audio>
396 <img src="clips/push-sign-0.png" alt="spectrogram" width="640" height="200">
397 <div class="metrics">
398 <div>peak 0.046 Pa (67 dB SPL)</div>
399 <div>RMS 3.3 mPa</div>
400 <div>centroid 196 Hz</div>
401 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
403 <div class="dim">wav peak -6.7 dBFS</div>
404 </div>
405 <a href="../../?pushAmount=0.01">Open in simulator</a>
406</div>
407<div class="card">
408 <div class="label">-10 mm (against the bow)</div>
409 <audio controls preload="none" src="clips/push-sign-1.wav"></audio>
410 <img src="clips/push-sign-1.png" alt="spectrogram" width="640" height="200">
411 <div class="metrics">
412 <div>peak 0.021 Pa (61 dB SPL)</div>
413 <div>RMS 2.0 mPa</div>
414 <div>centroid 114 Hz</div>
415 <div>T60 100-500 Hz 5.1 s, 2-8 kHz 7.6 s</div>
417 <div class="dim">wav peak -13.5 dBFS</div>
418 </div>
419 <a href="../../?pushAmount=-0.01">Open in simulator</a>
420</div></div>
421</section>
422<section id="push-release">
423<h2>Push and release: release time</h2>
424<p>How fast the finger lets go. An instantaneous release is a step in force and excites every mode, giving a click that is about 24 dB louder at its peak than the default; a release over tens of milliseconds excites only the lowest modes, as a fingertip does, and the 50 ms release brings the centroid down to about 100 Hz.</p>
425<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
426<div class="cards"><div class="card">
427 <div class="label">0 ms</div>
428 <audio controls preload="none" src="clips/push-release-0.wav"></audio>
429 <img src="clips/push-release-0.png" alt="spectrogram" width="640" height="200">
430 <div class="metrics">
431 <div>peak 0.764 Pa (92 dB SPL)</div>
432 <div>RMS 9.0 mPa</div>
433 <div>centroid 227 Hz</div>
434 <div>T60 100-500 Hz 4.5 s, 2-8 kHz 4.8 s</div>
436 <div class="dim">wav peak 17.7 dBFS (soft-clipped)</div>
437 </div>
438 <a href="../../?releaseTime=0">Open in simulator</a>
439</div>
440<div class="card">
441 <div class="label">5 ms</div>
442 <audio controls preload="none" src="clips/push-release-1.wav"></audio>
443 <img src="clips/push-release-1.png" alt="spectrogram" width="640" height="200">
444 <div class="metrics">
445 <div>peak 0.052 Pa (68 dB SPL)</div>
446 <div>RMS 3.8 mPa</div>
447 <div>centroid 225 Hz</div>
448 <div>T60 100-500 Hz 4.6 s, 2-8 kHz 5.4 s</div>
450 <div class="dim">wav peak -5.7 dBFS</div>
451 </div>
452 <a href="../../?releaseTime=0.005">Open in simulator</a>
453</div>
454<div class="card">
455 <div class="label">20 ms</div>
456 <audio controls preload="none" src="clips/push-release-2.wav"></audio>
457 <img src="clips/push-release-2.png" alt="spectrogram" width="640" height="200">
458 <div class="metrics">
459 <div>peak 0.046 Pa (67 dB SPL)</div>
460 <div>RMS 3.3 mPa</div>
461 <div>centroid 196 Hz</div>
462 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
464 <div class="dim">wav peak -6.7 dBFS</div>
465 </div>
466 <a href="../../?releaseTime=0.02">Open in simulator</a>
467</div>
468<div class="card">
469 <div class="label">50 ms</div>
470 <audio controls preload="none" src="clips/push-release-3.wav"></audio>
471 <img src="clips/push-release-3.png" alt="spectrogram" width="640" height="200">
472 <div class="metrics">
473 <div>peak 0.030 Pa (64 dB SPL)</div>
474 <div>RMS 2.1 mPa</div>
475 <div>centroid 103 Hz</div>
476 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 13.6 s</div>
478 <div class="dim">wav peak -10.4 dBFS</div>
479 </div>
480 <a href="../../?releaseTime=0.05">Open in simulator</a>
481</div></div>
482</section>
483<section id="bow-amplitude">
484<h2>Sheet: initial bow (push and release)</h2>
485<p>Real sheet metal has a bow of a few millimetres, which makes it a shallow shell with an asymmetric stiffness. A flat plate has a symmetric, purely hardening nonlinearity; the bowed sheet moves energy out of the inaudible sub-50 Hz range into the audible partials and produces the slow wobble of a real sheet. In these clips the flat plate and the 1.5 mm bow are about 8 dB quieter than the 3 mm bow, and the centroid rises with the bow.</p>
486<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
487<div class="cards"><div class="card">
488 <div class="label">0 mm</div>
489 <audio controls preload="none" src="clips/bow-amplitude-0.wav"></audio>
490 <img src="clips/bow-amplitude-0.png" alt="spectrogram" width="640" height="200">
491 <div class="metrics">
492 <div>peak 0.019 Pa (59 dB SPL)</div>
493 <div>RMS 1.4 mPa</div>
494 <div>centroid 139 Hz</div>
495 <div>T60 100-500 Hz 3.8 s, 2-8 kHz 5.7 s</div>
497 <div class="dim">wav peak -14.6 dBFS</div>
498 </div>
499 <a href="../../?bowAmplitude=0">Open in simulator</a>
500</div>
501<div class="card">
502 <div class="label">1.5 mm</div>
503 <audio controls preload="none" src="clips/bow-amplitude-1.wav"></audio>
504 <img src="clips/bow-amplitude-1.png" alt="spectrogram" width="640" height="200">
505 <div class="metrics">
506 <div>peak 0.020 Pa (60 dB SPL)</div>
507 <div>RMS 1.9 mPa</div>
508 <div>centroid 151 Hz</div>
509 <div>T60 100-500 Hz 3.9 s, 2-8 kHz 5.8 s</div>
511 <div class="dim">wav peak -13.8 dBFS</div>
512 </div>
513 <a href="../../?bowAmplitude=0.0015">Open in simulator</a>
514</div>
515<div class="card">
516 <div class="label">3 mm</div>
517 <audio controls preload="none" src="clips/bow-amplitude-2.wav"></audio>
518 <img src="clips/bow-amplitude-2.png" alt="spectrogram" width="640" height="200">
519 <div class="metrics">
520 <div>peak 0.046 Pa (67 dB SPL)</div>
521 <div>RMS 3.3 mPa</div>
522 <div>centroid 196 Hz</div>
523 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
525 <div class="dim">wav peak -6.7 dBFS</div>
526 </div>
527 <a href="../../?bowAmplitude=0.003">Open in simulator</a>
528</div>
529<div class="card">
530 <div class="label">6 mm</div>
531 <audio controls preload="none" src="clips/bow-amplitude-3.wav"></audio>
532 <img src="clips/bow-amplitude-3.png" alt="spectrogram" width="640" height="200">
533 <div class="metrics">
534 <div>peak 0.051 Pa (68 dB SPL)</div>
535 <div>RMS 3.9 mPa</div>
536 <div>centroid 260 Hz</div>
537 <div>T60 100-500 Hz 4.7 s, 2-8 kHz 19.0 s</div>
539 <div class="dim">wav peak -5.8 dBFS</div>
540 </div>
541 <a href="../../?bowAmplitude=0.006">Open in simulator</a>
542</div></div>
543</section>
544<section id="bow-amplitude-strike">
545<h2>Sheet: initial bow (drumstick strike)</h2>
546<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. The trend reverses: struck, the flat plate rings brightest, and the 6 mm bow gives the dullest sound, with about 10 dB less energy above 2 kHz than the default, presumably because the curvature couples the bending motion to the in-plane motion and its loss. The peak pressure is the same in all four clips, since the impact itself sets it.</p>
547<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
548<div class="cards"><div class="card">
549 <div class="label">0 mm</div>
550 <audio controls preload="none" src="clips/bow-amplitude-strike-0.wav"></audio>
551 <img src="clips/bow-amplitude-strike-0.png" alt="spectrogram" width="640" height="200">
552 <div class="metrics">
553 <div>peak 2.552 Pa (102 dB SPL)</div>
554 <div>RMS 10.7 mPa</div>
555 <div>centroid 674 Hz</div>
556 <div>T60 100-500 Hz 3.6 s, 2-8 kHz 3.4 s</div>
557 <div>contact force 196 N</div>
558 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
559 </div>
560 <a href="../../?excitation=strike&bowAmplitude=0">Open in simulator</a>
561</div>
562<div class="card">
563 <div class="label">1.5 mm</div>
564 <audio controls preload="none" src="clips/bow-amplitude-strike-1.wav"></audio>
565 <img src="clips/bow-amplitude-strike-1.png" alt="spectrogram" width="640" height="200">
566 <div class="metrics">
567 <div>peak 2.552 Pa (102 dB SPL)</div>
568 <div>RMS 10.7 mPa</div>
569 <div>centroid 601 Hz</div>
570 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 3.3 s</div>
571 <div>contact force 195 N</div>
572 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
573 </div>
574 <a href="../../?excitation=strike&bowAmplitude=0.0015">Open in simulator</a>
575</div>
576<div class="card">
577 <div class="label">3 mm</div>
578 <audio controls preload="none" src="clips/bow-amplitude-strike-2.wav"></audio>
579 <img src="clips/bow-amplitude-strike-2.png" alt="spectrogram" width="640" height="200">
580 <div class="metrics">
581 <div>peak 2.552 Pa (102 dB SPL)</div>
582 <div>RMS 10.9 mPa</div>
583 <div>centroid 655 Hz</div>
584 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
585 <div>contact force 195 N</div>
586 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
587 </div>
588 <a href="../../?excitation=strike&bowAmplitude=0.003">Open in simulator</a>
589</div>
590<div class="card">
591 <div class="label">6 mm</div>
592 <audio controls preload="none" src="clips/bow-amplitude-strike-3.wav"></audio>
593 <img src="clips/bow-amplitude-strike-3.png" alt="spectrogram" width="640" height="200">
594 <div class="metrics">
595 <div>peak 2.552 Pa (102 dB SPL)</div>
596 <div>RMS 13.3 mPa</div>
597 <div>centroid 291 Hz</div>
598 <div>T60 100-500 Hz 4.6 s, 2-8 kHz 6.3 s</div>
599 <div>contact force 195 N</div>
600 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
601 </div>
602 <a href="../../?excitation=strike&bowAmplitude=0.006">Open in simulator</a>
603</div></div>
604</section>
605<section id="bow-shape">
606<h2>Sheet: shape of the bow (push and release)</h2>
607<p>The same 3 mm sag as a bow across the width, across the height, or as a dish curved both ways. With the push at a corner, the bow across the width gives the loudest and brightest sound and the bow across the height the lowest.</p>
608<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
609<div class="cards"><div class="card">
610 <div class="label">across the width</div>
611 <audio controls preload="none" src="clips/bow-shape-0.wav"></audio>
612 <img src="clips/bow-shape-0.png" alt="spectrogram" width="640" height="200">
613 <div class="metrics">
614 <div>peak 0.046 Pa (67 dB SPL)</div>
615 <div>RMS 3.3 mPa</div>
616 <div>centroid 196 Hz</div>
617 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
619 <div class="dim">wav peak -6.7 dBFS</div>
620 </div>
621 <a href="../../?bowShape=width">Open in simulator</a>
622</div>
623<div class="card">
624 <div class="label">across the height</div>
625 <audio controls preload="none" src="clips/bow-shape-1.wav"></audio>
626 <img src="clips/bow-shape-1.png" alt="spectrogram" width="640" height="200">
627 <div class="metrics">
628 <div>peak 0.030 Pa (63 dB SPL)</div>
629 <div>RMS 2.0 mPa</div>
630 <div>centroid 141 Hz</div>
631 <div>T60 100-500 Hz 4.9 s, 2-8 kHz 7.8 s</div>
633 <div class="dim">wav peak -10.5 dBFS</div>
634 </div>
635 <a href="../../?bowShape=height">Open in simulator</a>
636</div>
637<div class="card">
638 <div class="label">dish</div>
639 <audio controls preload="none" src="clips/bow-shape-2.wav"></audio>
640 <img src="clips/bow-shape-2.png" alt="spectrogram" width="640" height="200">
641 <div class="metrics">
642 <div>peak 0.037 Pa (65 dB SPL)</div>
643 <div>RMS 2.7 mPa</div>
644 <div>centroid 155 Hz</div>
645 <div>T60 100-500 Hz 4.7 s, 2-8 kHz 6.6 s</div>
647 <div class="dim">wav peak -8.7 dBFS</div>
648 </div>
649 <a href="../../?bowShape=dish">Open in simulator</a>
650</div></div>
651</section>
652<section id="bow-shape-strike">
653<h2>Sheet: shape of the bow (drumstick strike)</h2>
654<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. The bow across the height again gives the lowest sound (a centroid near 460 Hz against 650 Hz for the bow across the width), while the peak pressure is the same for all three.</p>
655<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
656<div class="cards"><div class="card">
657 <div class="label">across the width</div>
658 <audio controls preload="none" src="clips/bow-shape-strike-0.wav"></audio>
659 <img src="clips/bow-shape-strike-0.png" alt="spectrogram" width="640" height="200">
660 <div class="metrics">
661 <div>peak 2.552 Pa (102 dB SPL)</div>
662 <div>RMS 10.9 mPa</div>
663 <div>centroid 655 Hz</div>
664 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
665 <div>contact force 195 N</div>
666 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
667 </div>
668 <a href="../../?excitation=strike&bowShape=width">Open in simulator</a>
669</div>
670<div class="card">
671 <div class="label">across the height</div>
672 <audio controls preload="none" src="clips/bow-shape-strike-1.wav"></audio>
673 <img src="clips/bow-shape-strike-1.png" alt="spectrogram" width="640" height="200">
674 <div class="metrics">
675 <div>peak 2.552 Pa (102 dB SPL)</div>
676 <div>RMS 10.9 mPa</div>
677 <div>centroid 464 Hz</div>
678 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.2 s</div>
679 <div>contact force 195 N</div>
680 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
681 </div>
682 <a href="../../?excitation=strike&bowShape=height">Open in simulator</a>
683</div>
684<div class="card">
685 <div class="label">dish</div>
686 <audio controls preload="none" src="clips/bow-shape-strike-2.wav"></audio>
687 <img src="clips/bow-shape-strike-2.png" alt="spectrogram" width="640" height="200">
688 <div class="metrics">
689 <div>peak 2.552 Pa (102 dB SPL)</div>
690 <div>RMS 10.9 mPa</div>
691 <div>centroid 618 Hz</div>
692 <div>T60 100-500 Hz 4.6 s, 2-8 kHz 4.1 s</div>
693 <div>contact force 195 N</div>
694 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
695 </div>
696 <a href="../../?excitation=strike&bowShape=dish">Open in simulator</a>
697</div></div>
698</section>
699<section id="thickness">
700<h2>Sheet: thickness (push and release)</h2>
701<p>Bending stiffness grows with the cube of the thickness while mass grows linearly, so a thicker sheet has higher mode frequencies. The same 10 mm push, however, is a smaller multiple of the thickness, which weakens the nonlinear transfer of energy to the higher partials, and in these clips this effect wins: the sound becomes lower and purer with thickness even though the individual modes rise. Gauges 24, 22, 18 and 14.</p>
702<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
703<div class="cards"><div class="card">
704 <div class="label">0.6 mm</div>
705 <audio controls preload="none" src="clips/thickness-0.wav"></audio>
706 <img src="clips/thickness-0.png" alt="spectrogram" width="640" height="200">
707 <div class="metrics">
708 <div>peak 0.027 Pa (63 dB SPL)</div>
709 <div>RMS 2.1 mPa</div>
710 <div>centroid 188 Hz</div>
711 <div>T60 100-500 Hz 3.4 s, 2-8 kHz 7.9 s</div>
713 <div class="dim">wav peak -11.4 dBFS</div>
714 </div>
715 <a href="../../?h=0.0006">Open in simulator</a>
716</div>
717<div class="card">
718 <div class="label">0.79 mm</div>
719 <audio controls preload="none" src="clips/thickness-1.wav"></audio>
720 <img src="clips/thickness-1.png" alt="spectrogram" width="640" height="200">
721 <div class="metrics">
722 <div>peak 0.046 Pa (67 dB SPL)</div>
723 <div>RMS 3.3 mPa</div>
724 <div>centroid 196 Hz</div>
725 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
727 <div class="dim">wav peak -6.7 dBFS</div>
728 </div>
729 <a href="../../?h=0.00079">Open in simulator</a>
730</div>
731<div class="card">
732 <div class="label">1.2 mm</div>
733 <audio controls preload="none" src="clips/thickness-2.wav"></audio>
734 <img src="clips/thickness-2.png" alt="spectrogram" width="640" height="200">
735 <div class="metrics">
736 <div>peak 0.069 Pa (71 dB SPL)</div>
737 <div>RMS 5.9 mPa</div>
738 <div>centroid 120 Hz</div>
739 <div>T60 100-500 Hz 4.9 s, 2-8 kHz 7.4 s</div>
741 <div class="dim">wav peak -3.2 dBFS</div>
742 </div>
743 <a href="../../?h=0.0012">Open in simulator</a>
744</div>
745<div class="card">
746 <div class="label">2 mm</div>
747 <audio controls preload="none" src="clips/thickness-3.wav"></audio>
748 <img src="clips/thickness-3.png" alt="spectrogram" width="640" height="200">
749 <div class="metrics">
750 <div>peak 0.052 Pa (68 dB SPL)</div>
751 <div>RMS 7.7 mPa</div>
752 <div>centroid 97 Hz</div>
753 <div>T60 100-500 Hz 5.2 s, 2-8 kHz 7.3 s</div>
755 <div class="dim">wav peak -5.6 dBFS</div>
756 </div>
757 <a href="../../?h=0.002">Open in simulator</a>
758</div></div>
759</section>
760<section id="thickness-strike">
761<h2>Sheet: thickness (drumstick strike)</h2>
762<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. Struck, the trend is the opposite: the stick meets a stiffer sheet with a shorter, harder contact (the peak contact force rises from about 170 N at 0.6 mm to 700 N at 2 mm), so the thick sheets are louder and much brighter.</p>
763<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
764<div class="cards"><div class="card">
765 <div class="label">0.6 mm</div>
766 <audio controls preload="none" src="clips/thickness-strike-0.wav"></audio>
767 <img src="clips/thickness-strike-0.png" alt="spectrogram" width="640" height="200">
768 <div class="metrics">
769 <div>peak 2.616 Pa (102 dB SPL)</div>
770 <div>RMS 10.5 mPa</div>
771 <div>centroid 634 Hz</div>
772 <div>T60 100-500 Hz 4.5 s, 2-8 kHz 5.0 s</div>
773 <div>contact force 168 N</div>
774 <div class="dim">wav peak 28.4 dBFS (soft-clipped)</div>
775 </div>
776 <a href="../../?excitation=strike&h=0.0006">Open in simulator</a>
777</div>
778<div class="card">
779 <div class="label">0.79 mm</div>
780 <audio controls preload="none" src="clips/thickness-strike-1.wav"></audio>
781 <img src="clips/thickness-strike-1.png" alt="spectrogram" width="640" height="200">
782 <div class="metrics">
783 <div>peak 2.552 Pa (102 dB SPL)</div>
784 <div>RMS 10.9 mPa</div>
785 <div>centroid 655 Hz</div>
786 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
787 <div>contact force 195 N</div>
788 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
789 </div>
790 <a href="../../?excitation=strike&h=0.00079">Open in simulator</a>
791</div>
792<div class="card">
793 <div class="label">1.2 mm</div>
794 <audio controls preload="none" src="clips/thickness-strike-2.wav"></audio>
795 <img src="clips/thickness-strike-2.png" alt="spectrogram" width="640" height="200">
796 <div class="metrics">
797 <div>peak 3.749 Pa (105 dB SPL)</div>
798 <div>RMS 15.9 mPa</div>
799 <div>centroid 1009 Hz</div>
800 <div>T60 100-500 Hz 4.4 s, 2-8 kHz 3.3 s</div>
801 <div>contact force 348 N</div>
802 <div class="dim">wav peak 31.5 dBFS (soft-clipped)</div>
803 </div>
804 <a href="../../?excitation=strike&h=0.0012">Open in simulator</a>
805</div>
806<div class="card">
807 <div class="label">2 mm</div>
808 <audio controls preload="none" src="clips/thickness-strike-3.wav"></audio>
809 <img src="clips/thickness-strike-3.png" alt="spectrogram" width="640" height="200">
810 <div class="metrics">
811 <div>peak 3.795 Pa (106 dB SPL)</div>
812 <div>RMS 22.2 mPa</div>
813 <div>centroid 2181 Hz</div>
814 <div>T60 100-500 Hz 5.0 s, 2-8 kHz 2.5 s</div>
815 <div>contact force 699 N</div>
816 <div class="dim">wav peak 31.6 dBFS (soft-clipped)</div>
817 </div>
818 <a href="../../?excitation=strike&h=0.002">Open in simulator</a>
819</div></div>
820</section>
821<section id="size">
822<h2>Sheet: size (push and release)</h2>
823<p>Plate dimensions (width by height) at the same thickness. Mode frequencies scale with the inverse square of the size, so a larger sheet is lower and slower, and under the same 10 mm push it also stores less energy and sounds quieter. The 24 by 36 inch sheet is an extreme case: its lowest modes lie near 10 Hz, below hearing, and most of its peak pressure is this infrasound, so it sounds much fainter than its sound pressure level suggests.</p>
824<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
825<div class="cards"><div class="card">
826 <div class="label">8 x 12 in</div>
827 <audio controls preload="none" src="clips/size-0.wav"></audio>
828 <img src="clips/size-0.png" alt="spectrogram" width="640" height="200">
829 <div class="metrics">
830 <div>peak 0.064 Pa (70 dB SPL)</div>
831 <div>RMS 3.6 mPa</div>
832 <div>centroid 300 Hz</div>
833 <div>T60 100-500 Hz 4.4 s, 2-8 kHz 6.5 s</div>
835 <div class="dim">wav peak -3.8 dBFS</div>
836 </div>
837 <a href="../../?Lx=0.2032&Ly=0.3048">Open in simulator</a>
838</div>
839<div class="card">
840 <div class="label">12 x 18 in (default)</div>
841 <audio controls preload="none" src="clips/size-1.wav"></audio>
842 <img src="clips/size-1.png" alt="spectrogram" width="640" height="200">
843 <div class="metrics">
844 <div>peak 0.046 Pa (67 dB SPL)</div>
845 <div>RMS 3.3 mPa</div>
846 <div>centroid 196 Hz</div>
847 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
849 <div class="dim">wav peak -6.7 dBFS</div>
850 </div>
851 <a href="../../?">Open in simulator</a>
852</div>
853<div class="card">
854 <div class="label">18 x 24 in</div>
855 <audio controls preload="none" src="clips/size-2.wav"></audio>
856 <img src="clips/size-2.png" alt="spectrogram" width="640" height="200">
857 <div class="metrics">
858 <div>peak 0.029 Pa (63 dB SPL)</div>
859 <div>RMS 2.3 mPa</div>
860 <div>centroid 122 Hz</div>
861 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 7.3 s</div>
863 <div class="dim">wav peak -10.8 dBFS</div>
864 </div>
865 <a href="../../?Lx=0.4572&Ly=0.6096">Open in simulator</a>
866</div>
867<div class="card">
868 <div class="label">24 x 36 in</div>
869 <audio controls preload="none" src="clips/size-3.wav"></audio>
870 <img src="clips/size-3.png" alt="spectrogram" width="640" height="200">
871 <div class="metrics">
872 <div>peak 0.256 Pa (82 dB SPL)</div>
873 <div>RMS 2.2 mPa</div>
874 <div>centroid 532 Hz</div>
875 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 6.2 s</div>
877 <div class="dim">wav peak 8.2 dBFS (soft-clipped)</div>
878 </div>
879 <a href="../../?Lx=0.6096&Ly=0.9144">Open in simulator</a>
880</div></div>
881</section>
882<section id="size-strike">
883<h2>Sheet: size (drumstick strike)</h2>
884<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. Struck, the larger sheets are louder and lower, the 18 by 24 inch sheet reaching about 105 dB at its peak against 100 dB for the smallest; the 24 by 36 inch sheet again puts much of its energy below 100 Hz.</p>
885<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
886<div class="cards"><div class="card">
887 <div class="label">8 x 12 in</div>
888 <audio controls preload="none" src="clips/size-strike-0.wav"></audio>
889 <img src="clips/size-strike-0.png" alt="spectrogram" width="640" height="200">
890 <div class="metrics">
891 <div>peak 1.956 Pa (100 dB SPL)</div>
892 <div>RMS 8.8 mPa</div>
893 <div>centroid 968 Hz</div>
894 <div>T60 100-500 Hz 4.4 s, 2-8 kHz 4.7 s</div>
895 <div>contact force 196 N</div>
896 <div class="dim">wav peak 25.8 dBFS (soft-clipped)</div>
897 </div>
898 <a href="../../?excitation=strike&Lx=0.2032&Ly=0.3048">Open in simulator</a>
899</div>
900<div class="card">
901 <div class="label">12 x 18 in (default)</div>
902 <audio controls preload="none" src="clips/size-strike-1.wav"></audio>
903 <img src="clips/size-strike-1.png" alt="spectrogram" width="640" height="200">
904 <div class="metrics">
905 <div>peak 2.552 Pa (102 dB SPL)</div>
906 <div>RMS 10.9 mPa</div>
907 <div>centroid 655 Hz</div>
908 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
909 <div>contact force 195 N</div>
910 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
911 </div>
912 <a href="../../?excitation=strike">Open in simulator</a>
913</div>
914<div class="card">
915 <div class="label">18 x 24 in</div>
916 <audio controls preload="none" src="clips/size-strike-2.wav"></audio>
917 <img src="clips/size-strike-2.png" alt="spectrogram" width="640" height="200">
918 <div class="metrics">
919 <div>peak 3.582 Pa (105 dB SPL)</div>
920 <div>RMS 14.4 mPa</div>
921 <div>centroid 397 Hz</div>
922 <div>T60 100-500 Hz 3.8 s, 2-8 kHz 4.6 s</div>
923 <div>contact force 195 N</div>
924 <div class="dim">wav peak 31.1 dBFS (soft-clipped)</div>
925 </div>
926 <a href="../../?excitation=strike&Lx=0.4572&Ly=0.6096">Open in simulator</a>
927</div>
928<div class="card">
929 <div class="label">24 x 36 in</div>
930 <audio controls preload="none" src="clips/size-strike-3.wav"></audio>
931 <img src="clips/size-strike-3.png" alt="spectrogram" width="640" height="200">
932 <div class="metrics">
933 <div>peak 2.823 Pa (103 dB SPL)</div>
934 <div>RMS 17.4 mPa</div>
935 <div>centroid 453 Hz</div>
936 <div>T60 100-500 Hz 3.9 s, 2-8 kHz 4.5 s</div>
937 <div>contact force 167 N</div>
938 <div class="dim">wav peak 29.0 dBFS (soft-clipped)</div>
939 </div>
940 <a href="../../?excitation=strike&Lx=0.6096&Ly=0.9144">Open in simulator</a>
941</div></div>
942</section>
943<section id="outline">
944<h2>Sheet: outline at equal area (push and release)</h2>
945<p>Four outlines cut from the same amount of steel (216 square inches, the area of the default 12 by 18 inch sheet): the rectangle, a square, the ellipse of the same 2:3 proportions, and a circle. Everything else is held at the defaults, including the 3 mm bow across the width. The push acts at a corner for the rectangle and the square and at the rim point opposite the hole for the ellipse and the circle, so part of the difference is the excitation itself: a rim point of an ellipse is stiffer than the corner of a rectangle, and the same 10 mm push deforms the whole sheet rather than bending a corner.</p>
946<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
947<div class="cards"><div class="card">
948 <div class="label">rectangle 12 x 18 in</div>
949 <audio controls preload="none" src="clips/outline-0.wav"></audio>
950 <img src="clips/outline-0.png" alt="spectrogram" width="640" height="200">
951 <div class="metrics">
952 <div>peak 0.046 Pa (67 dB SPL)</div>
953 <div>RMS 3.3 mPa</div>
954 <div>centroid 196 Hz</div>
955 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
957 <div class="dim">wav peak -6.7 dBFS</div>
958 </div>
959 <a href="../../?">Open in simulator</a>
960</div>
961<div class="card">
962 <div class="label">square 14.7 x 14.7 in</div>
963 <audio controls preload="none" src="clips/outline-1.wav"></audio>
964 <img src="clips/outline-1.png" alt="spectrogram" width="640" height="200">
965 <div class="metrics">
966 <div>peak 0.042 Pa (67 dB SPL)</div>
967 <div>RMS 2.9 mPa</div>
968 <div>centroid 154 Hz</div>
969 <div>T60 100-500 Hz 3.8 s, 2-8 kHz 9.8 s</div>
971 <div class="dim">wav peak -7.5 dBFS</div>
972 </div>
973 <a href="../../?Lx=0.37338&Ly=0.37338">Open in simulator</a>
974</div>
975<div class="card">
976 <div class="label">ellipse 13.5 x 20.3 in</div>
977 <audio controls preload="none" src="clips/outline-2.wav"></audio>
978 <img src="clips/outline-2.png" alt="spectrogram" width="640" height="200">
979 <div class="metrics">
980 <div>peak 0.148 Pa (77 dB SPL)</div>
981 <div>RMS 6.3 mPa</div>
982 <div>centroid 151 Hz</div>
983 <div>T60 100-500 Hz 3.6 s, 2-8 kHz 5.0 s</div>
985 <div class="dim">wav peak 3.4 dBFS (soft-clipped)</div>
986 </div>
987 <a href="../../?shape=ellipse&Lx=0.34392&Ly=0.51587">Open in simulator</a>
988</div>
989<div class="card">
990 <div class="label">circle 16.6 in</div>
991 <audio controls preload="none" src="clips/outline-3.wav"></audio>
992 <img src="clips/outline-3.png" alt="spectrogram" width="640" height="200">
993 <div class="metrics">
994 <div>peak 0.158 Pa (78 dB SPL)</div>
995 <div>RMS 5.8 mPa</div>
996 <div>centroid 204 Hz</div>
997 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 5.9 s</div>
999 <div class="dim">wav peak 4.0 dBFS (soft-clipped)</div>
1000 </div>
1001 <a href="../../?shape=ellipse&Lx=0.42113&Ly=0.42113">Open in simulator</a>
1002</div></div>
1003</section>
1004<section id="outline-strike">
1005<h2>Sheet: outline at equal area (drumstick strike)</h2>
1006<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the push. The strike point is at the same fraction of the width and height in every case.</p>
1007<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1008<div class="cards"><div class="card">
1009 <div class="label">rectangle 12 x 18 in</div>
1010 <audio controls preload="none" src="clips/outline-strike-0.wav"></audio>
1011 <img src="clips/outline-strike-0.png" alt="spectrogram" width="640" height="200">
1012 <div class="metrics">
1013 <div>peak 2.552 Pa (102 dB SPL)</div>
1014 <div>RMS 10.9 mPa</div>
1015 <div>centroid 655 Hz</div>
1016 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1017 <div>contact force 195 N</div>
1018 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1019 </div>
1020 <a href="../../?excitation=strike">Open in simulator</a>
1021</div>
1022<div class="card">
1023 <div class="label">square 14.7 x 14.7 in</div>
1024 <audio controls preload="none" src="clips/outline-strike-1.wav"></audio>
1025 <img src="clips/outline-strike-1.png" alt="spectrogram" width="640" height="200">
1026 <div class="metrics">
1027 <div>peak 2.443 Pa (102 dB SPL)</div>
1028 <div>RMS 10.3 mPa</div>
1029 <div>centroid 458 Hz</div>
1030 <div>T60 100-500 Hz 4.8 s, 2-8 kHz 4.6 s</div>
1031 <div>contact force 194 N</div>
1032 <div class="dim">wav peak 27.8 dBFS (soft-clipped)</div>
1033 </div>
1034 <a href="../../?excitation=strike&Lx=0.37338&Ly=0.37338">Open in simulator</a>
1035</div>
1036<div class="card">
1037 <div class="label">ellipse 13.5 x 20.3 in</div>
1038 <audio controls preload="none" src="clips/outline-strike-2.wav"></audio>
1039 <img src="clips/outline-strike-2.png" alt="spectrogram" width="640" height="200">
1040 <div class="metrics">
1041 <div>peak 2.461 Pa (102 dB SPL)</div>
1042 <div>RMS 10.0 mPa</div>
1043 <div>centroid 602 Hz</div>
1044 <div>T60 100-500 Hz 3.6 s, 2-8 kHz 4.4 s</div>
1045 <div>contact force 195 N</div>
1046 <div class="dim">wav peak 27.8 dBFS (soft-clipped)</div>
1047 </div>
1048 <a href="../../?excitation=strike&shape=ellipse&Lx=0.34392&Ly=0.51587">Open in simulator</a>
1049</div>
1050<div class="card">
1051 <div class="label">circle 16.6 in</div>
1052 <audio controls preload="none" src="clips/outline-strike-3.wav"></audio>
1053 <img src="clips/outline-strike-3.png" alt="spectrogram" width="640" height="200">
1054 <div class="metrics">
1055 <div>peak 2.487 Pa (102 dB SPL)</div>
1056 <div>RMS 10.0 mPa</div>
1057 <div>centroid 280 Hz</div>
1058 <div>T60 100-500 Hz 3.5 s, 2-8 kHz 4.5 s</div>
1059 <div>contact force 194 N</div>
1060 <div class="dim">wav peak 27.9 dBFS (soft-clipped)</div>
1061 </div>
1062 <a href="../../?excitation=strike&shape=ellipse&Lx=0.42113&Ly=0.42113">Open in simulator</a>
1063</div></div>
1064</section>
1065<section id="ellipse-size">
1066<h2>Ellipse: size (push and release)</h2>
1067<p>Elliptical sheets inscribed in the same bounding boxes as the rectangular size sweep above, pushed 10 mm at the rim.</p>
1068<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1069<div class="cards"><div class="card">
1070 <div class="label">8 x 12 in</div>
1071 <audio controls preload="none" src="clips/ellipse-size-0.wav"></audio>
1072 <img src="clips/ellipse-size-0.png" alt="spectrogram" width="640" height="200">
1073 <div class="metrics">
1074 <div>peak 0.064 Pa (70 dB SPL)</div>
1075 <div>RMS 4.7 mPa</div>
1076 <div>centroid 216 Hz</div>
1077 <div>T60 100-500 Hz 4.7 s, 2-8 kHz 5.1 s</div>
1079 <div class="dim">wav peak -3.9 dBFS</div>
1080 </div>
1081 <a href="../../?shape=ellipse&Lx=0.2032&Ly=0.3048">Open in simulator</a>
1082</div>
1083<div class="card">
1084 <div class="label">12 x 18 in</div>
1085 <audio controls preload="none" src="clips/ellipse-size-1.wav"></audio>
1086 <img src="clips/ellipse-size-1.png" alt="spectrogram" width="640" height="200">
1087 <div class="metrics">
1088 <div>peak 0.119 Pa (76 dB SPL)</div>
1089 <div>RMS 6.5 mPa</div>
1090 <div>centroid 528 Hz</div>
1091 <div>T60 100-500 Hz 3.7 s, 2-8 kHz 3.7 s</div>
1093 <div class="dim">wav peak 1.5 dBFS (soft-clipped)</div>
1094 </div>
1095 <a href="../../?shape=ellipse">Open in simulator</a>
1096</div>
1097<div class="card">
1098 <div class="label">18 x 24 in</div>
1099 <audio controls preload="none" src="clips/ellipse-size-2.wav"></audio>
1100 <img src="clips/ellipse-size-2.png" alt="spectrogram" width="640" height="200">
1101 <div class="metrics">
1102 <div>peak 0.145 Pa (77 dB SPL)</div>
1103 <div>RMS 6.6 mPa</div>
1104 <div>centroid 125 Hz</div>
1105 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 6.4 s</div>
1107 <div class="dim">wav peak 3.3 dBFS (soft-clipped)</div>
1108 </div>
1109 <a href="../../?shape=ellipse&Lx=0.4572&Ly=0.6096">Open in simulator</a>
1110</div>
1111<div class="card">
1112 <div class="label">24 x 36 in</div>
1113 <audio controls preload="none" src="clips/ellipse-size-3.wav"></audio>
1114 <img src="clips/ellipse-size-3.png" alt="spectrogram" width="640" height="200">
1115 <div class="metrics">
1116 <div>peak 0.130 Pa (76 dB SPL)</div>
1117 <div>RMS 3.3 mPa</div>
1118 <div>centroid 210 Hz</div>
1119 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 6.1 s</div>
1121 <div class="dim">wav peak 2.3 dBFS (soft-clipped)</div>
1122 </div>
1123 <a href="../../?shape=ellipse&Lx=0.6096&Ly=0.9144">Open in simulator</a>
1124</div></div>
1125</section>
1126<section id="ellipse-size-strike">
1127<h2>Ellipse: size (drumstick strike)</h2>
1128<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the push.</p>
1129<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1130<div class="cards"><div class="card">
1131 <div class="label">8 x 12 in</div>
1132 <audio controls preload="none" src="clips/ellipse-size-strike-0.wav"></audio>
1133 <img src="clips/ellipse-size-strike-0.png" alt="spectrogram" width="640" height="200">
1134 <div class="metrics">
1135 <div>peak 1.956 Pa (100 dB SPL)</div>
1136 <div>RMS 8.0 mPa</div>
1137 <div>centroid 513 Hz</div>
1138 <div>T60 100-500 Hz 4.8 s, 2-8 kHz 4.3 s</div>
1139 <div>contact force 198 N</div>
1140 <div class="dim">wav peak 25.8 dBFS (soft-clipped)</div>
1141 </div>
1142 <a href="../../?shape=ellipse&excitation=strike&Lx=0.2032&Ly=0.3048">Open in simulator</a>
1143</div>
1144<div class="card">
1145 <div class="label">12 x 18 in</div>
1146 <audio controls preload="none" src="clips/ellipse-size-strike-1.wav"></audio>
1147 <img src="clips/ellipse-size-strike-1.png" alt="spectrogram" width="640" height="200">
1148 <div class="metrics">
1149 <div>peak 2.218 Pa (101 dB SPL)</div>
1150 <div>RMS 8.9 mPa</div>
1151 <div>centroid 748 Hz</div>
1152 <div>T60 100-500 Hz 3.5 s, 2-8 kHz 4.0 s</div>
1153 <div>contact force 195 N</div>
1154 <div class="dim">wav peak 26.9 dBFS (soft-clipped)</div>
1155 </div>
1156 <a href="../../?shape=ellipse&excitation=strike">Open in simulator</a>
1157</div>
1158<div class="card">
1159 <div class="label">18 x 24 in</div>
1160 <audio controls preload="none" src="clips/ellipse-size-strike-2.wav"></audio>
1161 <img src="clips/ellipse-size-strike-2.png" alt="spectrogram" width="640" height="200">
1162 <div class="metrics">
1163 <div>peak 3.235 Pa (104 dB SPL)</div>
1164 <div>RMS 12.0 mPa</div>
1165 <div>centroid 438 Hz</div>
1166 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 4.3 s</div>
1167 <div>contact force 195 N</div>
1168 <div class="dim">wav peak 30.2 dBFS (soft-clipped)</div>
1169 </div>
1170 <a href="../../?shape=ellipse&excitation=strike&Lx=0.4572&Ly=0.6096">Open in simulator</a>
1171</div>
1172<div class="card">
1173 <div class="label">24 x 36 in</div>
1174 <audio controls preload="none" src="clips/ellipse-size-strike-3.wav"></audio>
1175 <img src="clips/ellipse-size-strike-3.png" alt="spectrogram" width="640" height="200">
1176 <div class="metrics">
1177 <div>peak 2.523 Pa (102 dB SPL)</div>
1178 <div>RMS 14.1 mPa</div>
1179 <div>centroid 306 Hz</div>
1180 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 4.4 s</div>
1181 <div>contact force 167 N</div>
1182 <div class="dim">wav peak 28.0 dBFS (soft-clipped)</div>
1183 </div>
1184 <a href="../../?shape=ellipse&excitation=strike&Lx=0.6096&Ly=0.9144">Open in simulator</a>
1185</div></div>
1186</section>
1187<section id="material">
1188<h2>Sheet: material (push and release)</h2>
1189<p>Stainless steel, aluminium, and brass at the same thickness. The mode frequencies scale with the square root of E over rho, which is nearly the same for steel and aluminium but about 30 percent lower for brass, so the brass sheet sounds lower and, under the same push, about 7 dB quieter. The loss parameters are kept fixed, although real materials differ there too.</p>
1190<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1191<div class="cards"><div class="card">
1192 <div class="label">stainless steel</div>
1193 <audio controls preload="none" src="clips/material-0.wav"></audio>
1194 <img src="clips/material-0.png" alt="spectrogram" width="640" height="200">
1195 <div class="metrics">
1196 <div>peak 0.046 Pa (67 dB SPL)</div>
1197 <div>RMS 3.3 mPa</div>
1198 <div>centroid 196 Hz</div>
1199 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
1201 <div class="dim">wav peak -6.7 dBFS</div>
1202 </div>
1203 <a href="../../?">Open in simulator</a>
1204</div>
1205<div class="card">
1206 <div class="label">aluminium</div>
1207 <audio controls preload="none" src="clips/material-1.wav"></audio>
1208 <img src="clips/material-1.png" alt="spectrogram" width="640" height="200">
1209 <div class="metrics">
1210 <div>peak 0.050 Pa (68 dB SPL)</div>
1211 <div>RMS 3.5 mPa</div>
1212 <div>centroid 183 Hz</div>
1213 <div>T60 100-500 Hz 4.6 s, 2-8 kHz 6.7 s</div>
1215 <div class="dim">wav peak -6.0 dBFS</div>
1216 </div>
1217 <a href="../../?E=69000000000&nu=0.33&rho=2700">Open in simulator</a>
1218</div>
1219<div class="card">
1220 <div class="label">brass</div>
1221 <audio controls preload="none" src="clips/material-2.wav"></audio>
1222 <img src="clips/material-2.png" alt="spectrogram" width="640" height="200">
1223 <div class="metrics">
1224 <div>peak 0.022 Pa (61 dB SPL)</div>
1225 <div>RMS 1.4 mPa</div>
1226 <div>centroid 126 Hz</div>
1227 <div>T60 100-500 Hz 3.4 s, 2-8 kHz 7.2 s</div>
1229 <div class="dim">wav peak -13.3 dBFS</div>
1230 </div>
1231 <a href="../../?E=100000000000&nu=0.34&rho=8500">Open in simulator</a>
1232</div></div>
1233</section>
1234<section id="material-strike">
1235<h2>Sheet: material (drumstick strike)</h2>
1236<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. Struck, the aluminium sheet, at about a third of the mass of the steel one, is the loudest and by far the brightest (a centroid near 1.3 kHz), and the brass sheet is the lowest.</p>
1237<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1238<div class="cards"><div class="card">
1239 <div class="label">stainless steel</div>
1240 <audio controls preload="none" src="clips/material-strike-0.wav"></audio>
1241 <img src="clips/material-strike-0.png" alt="spectrogram" width="640" height="200">
1242 <div class="metrics">
1243 <div>peak 2.552 Pa (102 dB SPL)</div>
1244 <div>RMS 10.9 mPa</div>
1245 <div>centroid 655 Hz</div>
1246 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1247 <div>contact force 195 N</div>
1248 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1249 </div>
1250 <a href="../../?excitation=strike">Open in simulator</a>
1251</div>
1252<div class="card">
1253 <div class="label">aluminium</div>
1254 <audio controls preload="none" src="clips/material-strike-1.wav"></audio>
1255 <img src="clips/material-strike-1.png" alt="spectrogram" width="640" height="200">
1256 <div class="metrics">
1257 <div>peak 3.361 Pa (105 dB SPL)</div>
1258 <div>RMS 19.2 mPa</div>
1259 <div>centroid 1280 Hz</div>
1260 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 3.5 s</div>
1261 <div>contact force 106 N</div>
1262 <div class="dim">wav peak 30.5 dBFS (soft-clipped)</div>
1263 </div>
1264 <a href="../../?excitation=strike&E=69000000000&nu=0.33&rho=2700">Open in simulator</a>
1265</div>
1266<div class="card">
1267 <div class="label">brass</div>
1268 <audio controls preload="none" src="clips/material-strike-2.wav"></audio>
1269 <img src="clips/material-strike-2.png" alt="spectrogram" width="640" height="200">
1270 <div class="metrics">
1271 <div>peak 3.476 Pa (105 dB SPL)</div>
1272 <div>RMS 13.6 mPa</div>
1273 <div>centroid 366 Hz</div>
1274 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 5.4 s</div>
1275 <div>contact force 199 N</div>
1276 <div class="dim">wav peak 30.8 dBFS (soft-clipped)</div>
1277 </div>
1278 <a href="../../?excitation=strike&E=100000000000&nu=0.34&rho=8500">Open in simulator</a>
1279</div></div>
1280</section>
1281<section id="damping-sigma0">
1282<h2>Damping: frequency-independent loss (push and release)</h2>
1283<p>sigma0 sets the decay of the lowest modes (T60 = 6.9 / sigma0). It stands in for everything that damps the sheet uniformly: the suspension, air drag, the material. In the clips the band below 100 Hz decays in roughly 12, 5 and 2 s (the 4 s clip cannot resolve the longest time well). A lower loss also leaves more time for the nonlinear transfer to the higher partials, so the less damped sheet is brighter as well as longer.</p>
1284<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1285<div class="cards"><div class="card">
1286 <div class="label">0.4 1/s</div>
1287 <audio controls preload="none" src="clips/damping-sigma0-0.wav"></audio>
1288 <img src="clips/damping-sigma0-0.png" alt="spectrogram" width="640" height="200">
1289 <div class="metrics">
1290 <div>peak 0.047 Pa (67 dB SPL)</div>
1291 <div>RMS 3.7 mPa</div>
1292 <div>centroid 287 Hz</div>
1293 <div>T60 100-500 Hz 7.8 s, 2-8 kHz 6.6 s</div>
1295 <div class="dim">wav peak -6.6 dBFS</div>
1296 </div>
1297 <a href="../../?sigma0=0.4">Open in simulator</a>
1298</div>
1299<div class="card">
1300 <div class="label">1.15 1/s</div>
1301 <audio controls preload="none" src="clips/damping-sigma0-1.wav"></audio>
1302 <img src="clips/damping-sigma0-1.png" alt="spectrogram" width="640" height="200">
1303 <div class="metrics">
1304 <div>peak 0.046 Pa (67 dB SPL)</div>
1305 <div>RMS 3.3 mPa</div>
1306 <div>centroid 196 Hz</div>
1307 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
1309 <div class="dim">wav peak -6.7 dBFS</div>
1310 </div>
1311 <a href="../../?sigma0=1.15">Open in simulator</a>
1312</div>
1313<div class="card">
1314 <div class="label">3.5 1/s</div>
1315 <audio controls preload="none" src="clips/damping-sigma0-2.wav"></audio>
1316 <img src="clips/damping-sigma0-2.png" alt="spectrogram" width="640" height="200">
1317 <div class="metrics">
1318 <div>peak 0.046 Pa (67 dB SPL)</div>
1319 <div>RMS 2.5 mPa</div>
1320 <div>centroid 153 Hz</div>
1321 <div>T60 100-500 Hz 1.8 s, 2-8 kHz 13.7 s</div>
1323 <div class="dim">wav peak -6.8 dBFS</div>
1324 </div>
1325 <a href="../../?sigma0=3.5">Open in simulator</a>
1326</div></div>
1327</section>
1328<section id="damping-sigma0-strike">
1329<h2>Damping: frequency-independent loss (drumstick strike)</h2>
1330<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. The decay of the low band follows the same rule, while the brightness changes less than it does under the push.</p>
1331<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1332<div class="cards"><div class="card">
1333 <div class="label">0.4 1/s</div>
1334 <audio controls preload="none" src="clips/damping-sigma0-strike-0.wav"></audio>
1335 <img src="clips/damping-sigma0-strike-0.png" alt="spectrogram" width="640" height="200">
1336 <div class="metrics">
1337 <div>peak 2.552 Pa (102 dB SPL)</div>
1338 <div>RMS 11.2 mPa</div>
1339 <div>centroid 606 Hz</div>
1340 <div>T60 100-500 Hz 6.3 s, 2-8 kHz 4.0 s</div>
1341 <div>contact force 195 N</div>
1342 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1343 </div>
1344 <a href="../../?excitation=strike&sigma0=0.4">Open in simulator</a>
1345</div>
1346<div class="card">
1347 <div class="label">1.15 1/s</div>
1348 <audio controls preload="none" src="clips/damping-sigma0-strike-1.wav"></audio>
1349 <img src="clips/damping-sigma0-strike-1.png" alt="spectrogram" width="640" height="200">
1350 <div class="metrics">
1351 <div>peak 2.552 Pa (102 dB SPL)</div>
1352 <div>RMS 10.9 mPa</div>
1353 <div>centroid 655 Hz</div>
1354 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1355 <div>contact force 195 N</div>
1356 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1357 </div>
1358 <a href="../../?excitation=strike&sigma0=1.15">Open in simulator</a>
1359</div>
1360<div class="card">
1361 <div class="label">3.5 1/s</div>
1362 <audio controls preload="none" src="clips/damping-sigma0-strike-2.wav"></audio>
1363 <img src="clips/damping-sigma0-strike-2.png" alt="spectrogram" width="640" height="200">
1364 <div class="metrics">
1365 <div>peak 2.552 Pa (102 dB SPL)</div>
1366 <div>RMS 10.6 mPa</div>
1367 <div>centroid 513 Hz</div>
1368 <div>T60 100-500 Hz 1.9 s, 2-8 kHz 5.9 s</div>
1369 <div>contact force 195 N</div>
1370 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1371 </div>
1372 <a href="../../?excitation=strike&sigma0=3.5">Open in simulator</a>
1373</div></div>
1374</section>
1375<section id="damping-sigma1">
1376<h2>Damping: frequency-dependent loss (push and release)</h2>
1377<p>sigma1 makes the high modes decay faster, in proportion to the square of their wavenumber; it stands mainly for radiation into the air. Too little and the highs ring like a cymbal; too much and the sheet sounds dull. At the lowest value here the band above 2 kHz decays about as slowly as the low modes; at the highest it sits more than 50 dB below the 100 to 500 Hz band.</p>
1378<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1379<div class="cards"><div class="card">
1380 <div class="label">0.0001 m^2/s</div>
1381 <audio controls preload="none" src="clips/damping-sigma1-0.wav"></audio>
1382 <img src="clips/damping-sigma1-0.png" alt="spectrogram" width="640" height="200">
1383 <div class="metrics">
1384 <div>peak 0.047 Pa (67 dB SPL)</div>
1385 <div>RMS 3.6 mPa</div>
1386 <div>centroid 238 Hz</div>
1387 <div>T60 100-500 Hz 4.8 s, 2-8 kHz 4.2 s</div>
1389 <div class="dim">wav peak -6.6 dBFS</div>
1390 </div>
1391 <a href="../../?sigma1=0.0001">Open in simulator</a>
1392</div>
1393<div class="card">
1394 <div class="label">0.0005 m^2/s</div>
1395 <audio controls preload="none" src="clips/damping-sigma1-1.wav"></audio>
1396 <img src="clips/damping-sigma1-1.png" alt="spectrogram" width="640" height="200">
1397 <div class="metrics">
1398 <div>peak 0.046 Pa (67 dB SPL)</div>
1399 <div>RMS 3.3 mPa</div>
1400 <div>centroid 196 Hz</div>
1401 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
1403 <div class="dim">wav peak -6.7 dBFS</div>
1404 </div>
1405 <a href="../../?sigma1=0.0005">Open in simulator</a>
1406</div>
1407<div class="card">
1408 <div class="label">0.0025 m^2/s</div>
1409 <audio controls preload="none" src="clips/damping-sigma1-2.wav"></audio>
1410 <img src="clips/damping-sigma1-2.png" alt="spectrogram" width="640" height="200">
1411 <div class="metrics">
1412 <div>peak 0.046 Pa (67 dB SPL)</div>
1413 <div>RMS 2.9 mPa</div>
1414 <div>centroid 118 Hz</div>
1415 <div>T60 100-500 Hz 2.9 s, 2-8 kHz 23.2 s</div>
1417 <div class="dim">wav peak -6.8 dBFS</div>
1418 </div>
1419 <a href="../../?sigma1=0.0025">Open in simulator</a>
1420</div></div>
1421</section>
1422<section id="damping-sigma1-strike">
1423<h2>Damping: frequency-dependent loss (drumstick strike)</h2>
1424<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. Struck, the difference is more audible: the lowest value gives a long metallic ring with a centroid near 3.8 kHz, and the highest a dull thud with a centroid near 220 Hz.</p>
1425<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1426<div class="cards"><div class="card">
1427 <div class="label">0.0001 m^2/s</div>
1428 <audio controls preload="none" src="clips/damping-sigma1-strike-0.wav"></audio>
1429 <img src="clips/damping-sigma1-strike-0.png" alt="spectrogram" width="640" height="200">
1430 <div class="metrics">
1431 <div>peak 2.552 Pa (102 dB SPL)</div>
1432 <div>RMS 13.5 mPa</div>
1433 <div>centroid 3839 Hz</div>
1434 <div>T60 100-500 Hz 5.6 s, 2-8 kHz 2.7 s</div>
1435 <div>contact force 195 N</div>
1436 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1437 </div>
1438 <a href="../../?excitation=strike&sigma1=0.0001">Open in simulator</a>
1439</div>
1440<div class="card">
1441 <div class="label">0.0005 m^2/s</div>
1442 <audio controls preload="none" src="clips/damping-sigma1-strike-1.wav"></audio>
1443 <img src="clips/damping-sigma1-strike-1.png" alt="spectrogram" width="640" height="200">
1444 <div class="metrics">
1445 <div>peak 2.552 Pa (102 dB SPL)</div>
1446 <div>RMS 10.9 mPa</div>
1447 <div>centroid 655 Hz</div>
1448 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1449 <div>contact force 195 N</div>
1450 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1451 </div>
1452 <a href="../../?excitation=strike&sigma1=0.0005">Open in simulator</a>
1453</div>
1454<div class="card">
1455 <div class="label">0.0025 m^2/s</div>
1456 <audio controls preload="none" src="clips/damping-sigma1-strike-2.wav"></audio>
1457 <img src="clips/damping-sigma1-strike-2.png" alt="spectrogram" width="640" height="200">
1458 <div class="metrics">
1459 <div>peak 2.554 Pa (102 dB SPL)</div>
1460 <div>RMS 10.0 mPa</div>
1461 <div>centroid 218 Hz</div>
1462 <div>T60 100-500 Hz 2.8 s, 2-8 kHz 35.6 s</div>
1463 <div>contact force 195 N</div>
1464 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1465 </div>
1466 <a href="../../?excitation=strike&sigma1=0.0025">Open in simulator</a>
1467</div></div>
1468</section>
1469<section id="damping-inplane">
1470<h2>Damping: in-plane loss (push and release)</h2>
1471<p>The stretching modes of the sheet lie at several kilohertz and, once the sheet is curved, couple to transverse motion. Without their own loss they ring for the whole low-frequency decay. Under the push the effect on the metrics is small (the band above 2 kHz is more than 40 dB down in every case); it is mainly audible as a faint high ring late in the decay when the loss is zero.</p>
1472<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1473<div class="cards"><div class="card">
1474 <div class="label">0 1/s</div>
1475 <audio controls preload="none" src="clips/damping-inplane-0.wav"></audio>
1476 <img src="clips/damping-inplane-0.png" alt="spectrogram" width="640" height="200">
1477 <div class="metrics">
1478 <div>peak 0.047 Pa (67 dB SPL)</div>
1479 <div>RMS 3.4 mPa</div>
1480 <div>centroid 198 Hz</div>
1481 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 14.7 s</div>
1483 <div class="dim">wav peak -6.6 dBFS</div>
1484 </div>
1485 <a href="../../?sigmaIn=0">Open in simulator</a>
1486</div>
1487<div class="card">
1488 <div class="label">20 1/s</div>
1489 <audio controls preload="none" src="clips/damping-inplane-1.wav"></audio>
1490 <img src="clips/damping-inplane-1.png" alt="spectrogram" width="640" height="200">
1491 <div class="metrics">
1492 <div>peak 0.046 Pa (67 dB SPL)</div>
1493 <div>RMS 3.3 mPa</div>
1494 <div>centroid 196 Hz</div>
1495 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
1497 <div class="dim">wav peak -6.7 dBFS</div>
1498 </div>
1499 <a href="../../?sigmaIn=20">Open in simulator</a>
1500</div>
1501<div class="card">
1502 <div class="label">100 1/s</div>
1503 <audio controls preload="none" src="clips/damping-inplane-2.wav"></audio>
1504 <img src="clips/damping-inplane-2.png" alt="spectrogram" width="640" height="200">
1505 <div class="metrics">
1506 <div>peak 0.047 Pa (67 dB SPL)</div>
1507 <div>RMS 3.3 mPa</div>
1508 <div>centroid 198 Hz</div>
1509 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 6.0 s</div>
1511 <div class="dim">wav peak -6.6 dBFS</div>
1512 </div>
1513 <a href="../../?sigmaIn=100">Open in simulator</a>
1514</div></div>
1515</section>
1516<section id="damping-inplane-strike">
1517<h2>Damping: in-plane loss (drumstick strike)</h2>
1518<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push. Struck, the difference is plain: with no in-plane loss the stretching modes ring at several kilohertz and pull the centroid up to about 5 kHz.</p>
1519<p class="dim">Playback gain +20 dB relative to 1 Pa = 0 dBFS (the simulator's default is +20 dB); loud onsets are soft-clipped. Spectrograms: 0 to 5 kHz over the clip, 80 dB range, one color scale per section.</p>
1520<div class="cards"><div class="card">
1521 <div class="label">0 1/s</div>
1522 <audio controls preload="none" src="clips/damping-inplane-strike-0.wav"></audio>
1523 <img src="clips/damping-inplane-strike-0.png" alt="spectrogram" width="640" height="200">
1524 <div class="metrics">
1525 <div>peak 2.552 Pa (102 dB SPL)</div>
1526 <div>RMS 11.3 mPa</div>
1527 <div>centroid 5040 Hz</div>
1528 <div>T60 100-500 Hz 4.3 s, 2-8 kHz 6.0 s</div>
1529 <div>contact force 195 N</div>
1530 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1531 </div>
1532 <a href="../../?excitation=strike&sigmaIn=0">Open in simulator</a>
1533</div>
1534<div class="card">
1535 <div class="label">20 1/s</div>
1536 <audio controls preload="none" src="clips/damping-inplane-strike-1.wav"></audio>
1537 <img src="clips/damping-inplane-strike-1.png" alt="spectrogram" width="640" height="200">
1538 <div class="metrics">
1539 <div>peak 2.552 Pa (102 dB SPL)</div>
1540 <div>RMS 10.9 mPa</div>
1541 <div>centroid 655 Hz</div>
1542 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1543 <div>contact force 195 N</div>
1544 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1545 </div>
1546 <a href="../../?excitation=strike&sigmaIn=20">Open in simulator</a>
1547</div>
1548<div class="card">
1549 <div class="label">100 1/s</div>
1550 <audio controls preload="none" src="clips/damping-inplane-strike-2.wav"></audio>
1551 <img src="clips/damping-inplane-strike-2.png" alt="spectrogram" width="640" height="200">
1552 <div class="metrics">
1553 <div>peak 2.552 Pa (102 dB SPL)</div>
1554 <div>RMS 10.9 mPa</div>
1555 <div>centroid 637 Hz</div>
1556 <div>T60 100-500 Hz 3.7 s, 2-8 kHz 3.9 s</div>
1557 <div>contact force 195 N</div>
1558 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1559 </div>
1560 <a href="../../?excitation=strike&sigmaIn=100">Open in simulator</a>
1561</div></div>
1562</section>
1563<p class="dim">Generated by <code>steelsim gallery</code>; parameters not listed take the simulator defaults.</p>
1564</body></html>