Show that the displacement , where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.
The given displacement is a solution to the wave equation.
The expression for the wave speed is .
The displacement is given by where c, d are constants.
The given displacement must satisfy the wave equation Take the partial derivatives of D(x, t) with respect to x,
Take the partial derivatives of D(x, t) with respect to t,
Substituting the above values in the wave equation:
Therefore, it satisfies the wave equation.
From the above equation, the wave speed is obtained as
Therefore, the wave speed is .
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