Chapter 11, Problem 48P

To determine

To Find: The ratio of the amplitude.

Answer to Problem 48P

The ratio of the amplitude of the two waves with different energies is $1.41$ .

Explanation of Solution

Given info:

Energy of second wave is twice as that of the first wave.

Thus,

  $E_2=2\times E_1$

Formula used:

The expression for intensity is

  $I=\frac{E}{V}$

Here, E is the energy and V is the volume.

Calculation:

Intensity can be found by taking the energy per unit volume. Here both waves are passing through the same portion of the Earth, so the volume of both portion must be same. So, the final relation of intensity with the energy is,

Intensity offirst wave $I_1$ =Energy of first wave $E_1$

Intensity offirst wave $I_2$ =Energy of first wave $E_2$

Taking ratio of both the intensities,

  $\begin{array}{l}\frac{I_2}{I_1}=\frac{E_2}{E_1}\text{ =}\frac{2\times E_1}{E_1}\\ =\frac{A_2{}^2}{A_1{}^2}\\ \frac{A_2{}^2}{A_1{}^2}=2\\ \frac{A_2}{A_1}=\sqrt{2}=1.41\end{array}$

Conclusion:

Thus, the ratio of the amplitude of the two waves with different energies is $1.41$ .