Wave speed and d'Alembert's formula

j5rp · Aug 20, 2013

Does d'Alembert's formula hold if the wave speed is not constant?
For example, if the speed c in the link is not a constant, but instead a function of the coordinate x. Is the formula still valid?

HallsofIvy · Aug 21, 2013

No, it is not. d'Alembert's formula is based on the fact that the wave equation is a "hyperbolic" equation with two "characteristic lines". If c is variable that may not be true. (If it is true, we can use the same idea but with not have functions of x- ct and x+ ct.)

Wave speed and d'Alembert's formula

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Wave speed and d'Alembert's formula

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