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Dear Chris,I hope this e-mail is finding you well.
I read with interest your TLE column this month on harmonics.
I find it to be a fascinating topic.
Note that not all sources of non-linearity are due to imbalances in up and down strokes.
In water for example, non-linearity can come from change of velocity with pressure.
The higher the pressure, the higher the velocity; so when you send a sine function through water (with enough energy to affect velocity) peaks travel faster than troughs.
Thus the sine function gradually transforms into a see-saw function.
The Fourier transform of a see-saw function is a series of spikes (harmonics) with an amplitude following 1/n.
(Note that water also suffers from imbalance of up and down strokes: it is easier to push water than to pull it (a hard pull creates a vacuum in a phenomenon known as cavitation).)
Best regards,
Guillaume [Cambois]
