A sinusoidal wave,
given by the displacement wave equation

where x and y are in
meters and t is in seconds, is moving on a string of linear density**
**m
= 1.2 g/m. At
what average rate is energy transferred by the wave?

Example 1

The energy transfer is = W

Answer

The average rate of energy transfer is equivalent to the average power transmitted. The average power transmitted is given by

From the given displacement wave we can identify

y_{m} = 0.05 m,
w=
300 rad/s, and k = 2p
rad/m.

We can calculate the speed of the wave:

Therefore, the average power transmitted is