Chapter 11, Problem 49P

To determine

To Find: The ratio of the amplitude.

Answer to Problem 49P

The ratio of the amplitude of the two waves with same frequency and different powers is $1.73$ .

Explanation of Solution

Given info:

Power of second wave is trice as that of the first wave.

Thus,

  $P_2=3\times P_1$

Formula used:

The expression for intensity is

  $I=\frac{P}{A}$

Here, P is the power and A is the area.

Calculation:

Intensity can be found by taking the ratio of power to area. Here both waves are having same frequency. So, the final relation of intensity with the power is,

Intensity of first wave $I_1$ =Power of first wave $P_1$

Intensity of first wave $I_2$ =Power of first wave $P_2$

Taking ratio of both the intensities

  $\begin{array}{c}\frac{I_2}{I_1}=\frac{P_2}{P_1}\\ =\frac{A_2{}^2}{A_1{}^2}\\ =\frac{3\times P_1}{P_1}\\ \frac{A_2{}^2}{A_1{}^2}=3\\ \frac{A_2}{A_1}=\sqrt{3}=1.73\end{array}$

Conclusion:

Thus, ratio of the amplitude of the two waves with same frequency and different powers is $1.73$ .