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Q.15

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 451

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Short Answer

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 .

See the step by step solution

Step by Step Solution

Given :

The displacement is given by where c, d are constants.

Calculating the partial derivatives to show that the given displacement satisfy the wave equation:

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.

Calculating the speed of the wave:

From the above equation, the wave speed is obtained as

Therefore, the wave speed is .

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