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3<title>Steel sheet gong: how the parameters shape the sound</title>
4<style>
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15svg.setup { display: block; max-width: 100%; height: auto; }
16</style></head><body>
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="70" y1="72" x2="70" y2="90" 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="70" cy="90" r="3" fill="#15171a" stroke="#c8cbd0"/>
27 <text x="80" y="106" 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="#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></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. 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 heavier stick carries more momentum, stays in contact longer, and pushes the sheet further, which favours the low modes; a light stick gives a short, bright tap.</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; a hard tip (dense wood, or a metal beater) has a high K and a sharp click.</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.</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.</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.</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; a release over tens of milliseconds excites only the lowest modes, as a fingertip does.</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.</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.</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.</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.</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, and the same push is a smaller multiple of the thickness, which weakens the nonlinear effects. 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.</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; it also radiates more efficiently.</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.</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="material">
944<h2>Sheet: material (push and release)</h2>
945<p>Stainless steel, aluminium, and brass at the same thickness. The mode frequencies scale with the square root of E over rho, which differs little between these metals; the loss parameters are kept fixed, although real materials differ there too.</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">stainless steel</div>
949 <audio controls preload="none" src="clips/material-0.wav"></audio>
950 <img src="clips/material-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">aluminium</div>
963 <audio controls preload="none" src="clips/material-1.wav"></audio>
964 <img src="clips/material-1.png" alt="spectrogram" width="640" height="200">
965 <div class="metrics">
966 <div>peak 0.050 Pa (68 dB SPL)</div>
967 <div>RMS 3.5 mPa</div>
968 <div>centroid 183 Hz</div>
969 <div>T60 100-500 Hz 4.6 s, 2-8 kHz 6.7 s</div>
971 <div class="dim">wav peak -6.0 dBFS</div>
972 </div>
973 <a href="../../?E=69000000000&nu=0.33&rho=2700">Open in simulator</a>
974</div>
975<div class="card">
976 <div class="label">brass</div>
977 <audio controls preload="none" src="clips/material-2.wav"></audio>
978 <img src="clips/material-2.png" alt="spectrogram" width="640" height="200">
979 <div class="metrics">
980 <div>peak 0.022 Pa (61 dB SPL)</div>
981 <div>RMS 1.4 mPa</div>
982 <div>centroid 126 Hz</div>
983 <div>T60 100-500 Hz 3.4 s, 2-8 kHz 7.2 s</div>
985 <div class="dim">wav peak -13.3 dBFS</div>
986 </div>
987 <a href="../../?E=100000000000&nu=0.34&rho=8500">Open in simulator</a>
988</div></div>
989</section>
990<section id="material-strike">
991<h2>Sheet: material (drumstick strike)</h2>
992<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push.</p>
993<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>
994<div class="cards"><div class="card">
995 <div class="label">stainless steel</div>
996 <audio controls preload="none" src="clips/material-strike-0.wav"></audio>
997 <img src="clips/material-strike-0.png" alt="spectrogram" width="640" height="200">
998 <div class="metrics">
999 <div>peak 2.552 Pa (102 dB SPL)</div>
1000 <div>RMS 10.9 mPa</div>
1001 <div>centroid 655 Hz</div>
1002 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1003 <div>contact force 195 N</div>
1004 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1005 </div>
1006 <a href="../../?excitation=strike">Open in simulator</a>
1007</div>
1008<div class="card">
1009 <div class="label">aluminium</div>
1010 <audio controls preload="none" src="clips/material-strike-1.wav"></audio>
1011 <img src="clips/material-strike-1.png" alt="spectrogram" width="640" height="200">
1012 <div class="metrics">
1013 <div>peak 3.361 Pa (105 dB SPL)</div>
1014 <div>RMS 19.2 mPa</div>
1015 <div>centroid 1280 Hz</div>
1016 <div>T60 100-500 Hz 4.1 s, 2-8 kHz 3.5 s</div>
1017 <div>contact force 106 N</div>
1018 <div class="dim">wav peak 30.5 dBFS (soft-clipped)</div>
1019 </div>
1020 <a href="../../?excitation=strike&E=69000000000&nu=0.33&rho=2700">Open in simulator</a>
1021</div>
1022<div class="card">
1023 <div class="label">brass</div>
1024 <audio controls preload="none" src="clips/material-strike-2.wav"></audio>
1025 <img src="clips/material-strike-2.png" alt="spectrogram" width="640" height="200">
1026 <div class="metrics">
1027 <div>peak 3.476 Pa (105 dB SPL)</div>
1028 <div>RMS 13.6 mPa</div>
1029 <div>centroid 366 Hz</div>
1030 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 5.4 s</div>
1031 <div>contact force 199 N</div>
1032 <div class="dim">wav peak 30.8 dBFS (soft-clipped)</div>
1033 </div>
1034 <a href="../../?excitation=strike&E=100000000000&nu=0.34&rho=8500">Open in simulator</a>
1035</div></div>
1036</section>
1037<section id="damping-sigma0">
1038<h2>Damping: frequency-independent loss (push and release)</h2>
1039<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.</p>
1040<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>
1041<div class="cards"><div class="card">
1042 <div class="label">0.4 1/s</div>
1043 <audio controls preload="none" src="clips/damping-sigma0-0.wav"></audio>
1044 <img src="clips/damping-sigma0-0.png" alt="spectrogram" width="640" height="200">
1045 <div class="metrics">
1046 <div>peak 0.047 Pa (67 dB SPL)</div>
1047 <div>RMS 3.7 mPa</div>
1048 <div>centroid 287 Hz</div>
1049 <div>T60 100-500 Hz 7.8 s, 2-8 kHz 6.6 s</div>
1051 <div class="dim">wav peak -6.6 dBFS</div>
1052 </div>
1053 <a href="../../?sigma0=0.4">Open in simulator</a>
1054</div>
1055<div class="card">
1056 <div class="label">1.15 1/s</div>
1057 <audio controls preload="none" src="clips/damping-sigma0-1.wav"></audio>
1058 <img src="clips/damping-sigma0-1.png" alt="spectrogram" width="640" height="200">
1059 <div class="metrics">
1060 <div>peak 0.046 Pa (67 dB SPL)</div>
1061 <div>RMS 3.3 mPa</div>
1062 <div>centroid 196 Hz</div>
1063 <div>T60 100-500 Hz 4.0 s, 2-8 kHz 7.7 s</div>
1065 <div class="dim">wav peak -6.7 dBFS</div>
1066 </div>
1067 <a href="../../?sigma0=1.15">Open in simulator</a>
1068</div>
1069<div class="card">
1070 <div class="label">3.5 1/s</div>
1071 <audio controls preload="none" src="clips/damping-sigma0-2.wav"></audio>
1072 <img src="clips/damping-sigma0-2.png" alt="spectrogram" width="640" height="200">
1073 <div class="metrics">
1074 <div>peak 0.046 Pa (67 dB SPL)</div>
1075 <div>RMS 2.5 mPa</div>
1076 <div>centroid 153 Hz</div>
1077 <div>T60 100-500 Hz 1.8 s, 2-8 kHz 13.7 s</div>
1079 <div class="dim">wav peak -6.8 dBFS</div>
1080 </div>
1081 <a href="../../?sigma0=3.5">Open in simulator</a>
1082</div></div>
1083</section>
1084<section id="damping-sigma0-strike">
1085<h2>Damping: frequency-independent loss (drumstick strike)</h2>
1086<p>The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the corner push.</p>
1087<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>
1088<div class="cards"><div class="card">
1089 <div class="label">0.4 1/s</div>
1090 <audio controls preload="none" src="clips/damping-sigma0-strike-0.wav"></audio>
1091 <img src="clips/damping-sigma0-strike-0.png" alt="spectrogram" width="640" height="200">
1092 <div class="metrics">
1093 <div>peak 2.552 Pa (102 dB SPL)</div>
1094 <div>RMS 11.2 mPa</div>
1095 <div>centroid 606 Hz</div>
1096 <div>T60 100-500 Hz 6.3 s, 2-8 kHz 4.0 s</div>
1097 <div>contact force 195 N</div>
1098 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1099 </div>
1100 <a href="../../?excitation=strike&sigma0=0.4">Open in simulator</a>
1101</div>
1102<div class="card">
1103 <div class="label">1.15 1/s</div>
1104 <audio controls preload="none" src="clips/damping-sigma0-strike-1.wav"></audio>
1105 <img src="clips/damping-sigma0-strike-1.png" alt="spectrogram" width="640" height="200">
1106 <div class="metrics">
1107 <div>peak 2.552 Pa (102 dB SPL)</div>
1108 <div>RMS 10.9 mPa</div>
1109 <div>centroid 655 Hz</div>
1110 <div>T60 100-500 Hz 4.2 s, 2-8 kHz 4.6 s</div>
1111 <div>contact force 195 N</div>
1112 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1113 </div>
1114 <a href="../../?excitation=strike&sigma0=1.15">Open in simulator</a>
1115</div>
1116<div class="card">
1117 <div class="label">3.5 1/s</div>
1118 <audio controls preload="none" src="clips/damping-sigma0-strike-2.wav"></audio>
1119 <img src="clips/damping-sigma0-strike-2.png" alt="spectrogram" width="640" height="200">
1120 <div class="metrics">
1121 <div>peak 2.552 Pa (102 dB SPL)</div>
1122 <div>RMS 10.6 mPa</div>
1123 <div>centroid 513 Hz</div>
1124 <div>T60 100-500 Hz 1.9 s, 2-8 kHz 5.9 s</div>
1125 <div>contact force 195 N</div>
1126 <div class="dim">wav peak 28.1 dBFS (soft-clipped)</div>
1127 </div>
1128 <a href="../../?excitation=strike&sigma0=3.5">Open in simulator</a>
1129</div></div>
1130</section>
1131<p class="dim">Generated by <code>steelsim gallery</code>; parameters not listed take the simulator defaults.</p>
1132</body></html>
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