Obtain Eq. 9.20 directly from the wave equation, by separation of variables.

Equation 9.20

Step 1</p>

In this problem, we have to find the wave equation for the given variable.

Step 2</p>

The wave equation says look for solution of the form where

Now by dividing we get where left side is and right side is and hence both must be constant. The constant .

Since k is real or positive.