Thursday, January 15, 2009

Nonlinear waves

A bit late for this post, but I wanted to get it up here anyway to acknowledge the kindness of the sender.  The original email date was 10/22/2008.

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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]

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