L = 2. M=2, n=2, m=1 mode of square membrane

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(Code that made above animation: heat_and_wave_on_square_3d.py)

Frequencies of rectangular membrane as a function of H/L

The "spectrum" of the solutions, i.e. the set of (square-roots of) the eigenvalues, is to a large extent what gives each object it's characteristic sound.

mystery object 1

mystery object 2

mystery object 3

(Code that made above plot: rectangular_membrane_frequencies.py) rectangular_membrane_frequencies.py

Let us examine the spectrum of the square membrane.

virtual piano