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Introduction to the Physics of Waves by Tim Freegarde

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4

Sinusoidal waveforms

4.1 Sinusoidal solutions

We have already seen in Sections 3.3 and 3.4 that it can be convenient to consider sinusoidal solutions to a wave equation, for their simple transformations under differentiation often allow the differential equations to be reduced to mere algebraic expressions that relate the constant parameters characterizing the wave motion. Sinusoidal waves are certainly not the only wave motions that are possible, but they often prove to be an extremely important and fundamental class of solution. We shall see shortly that they allow us to determine standing-wave motions that determine the operation of many musical instruments, and these musical examples and analogies will help us at various points throughout ...

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