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 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.