5-5 Vibrational Mode of a Stretched Membrane

How can a stretched membrane produce sound?

Only membranes with unison thickness that are stretched over a circular ring with equal tension throughout can produce sound. (This is why we tune drum heads going from one rod to the rod opposite it instead of in a circular direction. This is the only way to ensure that the drum head's membrane has equal tension throughout.)

When a membrane is disturbed (such as a drumstick hitting a drum head) the waves propagates in two directions instead of just one. Instead of having nodal points, a membrane will actually have nodal lines. Furthermore, instead of having harmonics, the membranes will produce overtones.

How can you find the frequency of the overtones in a stretched membrane?

The frequency of the overtones of a stretched membrane is found with the formula:

    f1 = (0.383/R) X (the square root of T/d)
    R in the radius in meters, T in the tension in Newtons, and d is the real density in kilograms per square meter
    (f1 is the frequency of the lowest vibrational node)

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