Suggested languages for you:

Q.16

Expert-verified
Found in: Page 451

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# 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

## 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 .