Steel sheet gong: how the parameters shape the sound
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Elliptical sheets inscribed in the same bounding boxes as the rectangular size sweep above, pushed 10 mm at the rim.
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.
The same sweep excited by the default drumstick strike (30 g at 3 m/s) instead of the push.
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.
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.
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.
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.
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.
Damping: frequency-independent loss (push and release)
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.
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.
Damping: frequency-independent loss (drumstick strike)
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.
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.
Damping: frequency-dependent loss (push and release)
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.
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.
Damping: frequency-dependent loss (drumstick strike)
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.
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.
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.
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.
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.
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.
