Membrane Sound Lab

What it is for

Why does a drum hit in the centre sound dull, and why does it ring with more overtones near the rim? Why do square drumheads sound different from long rectangular ones? This lab answers these questions with the classic model of an ideal rectangular membrane fixed at its edges. You set the relative width and height, where you strike, the fundamental frequency and how fast the sound dies away. The tool lists the first 24 vibration modes with their frequencies and how strongly your strike excites each one, plots their patterns and renders a short WAV sample.

It is a synthesis model for learning and sound design. It does not simulate round drums, real drumhead materials, air loading or tension changes, and it does not predict how a specific instrument will sound.

Worked example

The default is a rectangle of Relative width 1 and Relative height 1.4, struck at Strike X 0.35 and Strike Y 0.4, with a Fundamental frequency of 130 Hz. The lowest modes are 1,1 at 130 Hz, 1,2 at 184.468 Hz, 2,1 at 224.659 Hz and 2,2 at 260 Hz. The strike weight of the fundamental is 0.847, and the off-centre strike excites many overtones with mixed signs.

Now a square membrane, width 1 and height 1, struck exactly in the centre (0.5, 0.5) at 110 Hz, 2 seconds long with Decay rate 2. The result: "Rendered 24 membrane modes."

Every mode with an even number in it has weight 0: the centre is a node line of those patterns, so a centre hit cannot excite them. What is left is the fundamental and a few odd modes, which is why a centre hit sounds round and dull. Move the strike to 0.2, 0.3 and the zero weights fill in.

Notice also that the square shape makes pairs such as 1,2 and 2,1 share one frequency. A rectangle splits them apart, which gives a richer, less harmonic sound.

How to read the result

• The mode plots show each pattern; blue and warm colours mark opposite phase, so the boundary between them is a node line that does not move. Click inside the membrane, or edit X and Y, to move the strike.
• Vibration modes lists Horizontal mode, Vertical mode, Frequency (Hz) and Strike weight. A weight near 0 means that mode is barely heard; the sign shows its phase.
• membrane.wav is a mono sample at 22.05 kHz with a short fade at both ends. Nothing plays automatically.
• Exports: vector SVG, CSV and result JSON.

Tips and common mistakes

• Only the ratio of width to height matters. 2 × 1 sounds the same as 1 × 0.5.
• Strikes exactly on the edge (0 or 1) excite nothing, because the edge does not move.
• Lower Decay rate for longer ringing and higher values for a short, damped thump.
• Use a low fundamental, such as 60 to 150 Hz, to hear drum-like results. High values sound more like a bell or a wood block.
• The overtones of a membrane are not whole-number multiples of the fundamental. That is why drums have a less defined pitch than strings.

FAQ

Why only rectangles?

Rectangular membranes have exact, simple mode formulas. Round drums follow Bessel functions and need a different model.

Is the sample a recording?

No. It is synthesized from the listed modes with their strike weights and an exponential decay.

Why do some modes not appear in the sound?

Modes with a strike weight of 0 are silent, and modes outside the audible range are left out of the sample.

Can I change the drumhead material?

Not directly. Material and tension only change the fundamental frequency in this model, so adjust that value.