Membrane modes

More complicated vibrating systems such as membranes and plates also have vibrating modes and resonance frequencies. Another example is given by a rectangular membrane with fixed edges. The first normal modes of the membrane are shown in the animation below. The red line shows the displacement nodal lines. These animations suggest that the modes of a rectangular membrane with fixed edges can be seen as two-dimensional string modes since standing waves in one direction appear to be independent of standing waves in the other direction.


Here we show the first six vibration modes of an ideal circular membrane with fixed edges. It can be seen as a model for the vibration of the head of a drum.


Unlike the string the natural frequencies of the circular membrane are not simply related to each other, which is why most drums do not have a definite pitch.

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