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Q.16

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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 D(x, t) = ln(ax + bt) , where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.

The given displacement is a solution to the wave equation.

The wave speed is b/a .

See the step by step solution

Step by Step Solution

Given information:

The displacement is given by where a, b are constants

Calculate the partial derivatives to show that the given displacement satisfy 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,

Substitute the values in the above wave equation:

Therefore, the given displacement satisfies the wave equation.

Calculating the wave speed:

As calculated in the above equation, the wave speed is obtained as .

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