Question

Show that the function f(x, t) = x 2 + 4axt−4a 2 t 2 satisfies the wave equation if one assumes a certain relationship between the constant a and the wave speed u. What is this relationship?

Answer #1

The wave equation is

Given

Differentiating it with respect to x, we get

Differentiating it again with respect to x, we get

Differentiating the function with respect to time, we get

Differentiating it again with respect to time, we get

Substituting equation (2) and (3) into equation (1) we get

The relationship between constant a and the wave speed u is

or

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