The principle of superposition says that waves add linearly. Let's see what happens when
we add a large number of waves that have different amplitudes, and wavelengths, but constrain
the wavelengths so that each wavelength is an integer times some primary wavelength. So
for instance, start with a wavelength of 1m, then add one with 2, 3, 4, 5,... all with
different amplitudes. Add them up and you get a final wave that is the linear sum of all
of them.
The following will let you build a wave that is the sum of a bunch of other waves with different
amplitudes, with each wave having a wavelength that is an integer multiple of the first wave,
called the "fundamental". At the top is an up arrow and down arrow that lets you change the
total number of waves (initialized to 1). Increase the number and the program adds a new wave
to the list on the right, but initially with amplitude zero. Drag the blue line up to increase
the amplitude and see how the final wave behaves as you keep adding waves and modifying amplitudes.
Hint: try the following coefficients:
square wave: only keep odd number waves (every other wave, e.g. wave n=1, 3, 5...) and set the amplitude to $1/n$
sawtooth wave: keep every wave, set amplitude to $1/n$
triangle wave: odd number waves, amplitude $1/n^2$ with every other amplitude being negative (starting
with a positive amplitude for the first one)
Number of waves:
Drew BadenLast update Jan 21, 2025
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