Chapter 12, Problem 19P

To determine

To Calculate: The ratio of intensities of two sound waves.

Answer to Problem 19P

The ratio of the intensities of two sound waves is 4.

Explanation of Solution

Given:

Both the sound waves having equal displacement and amplitudes.

Formula used:

The intensity is given as,

  $I=2\rho v{\pi }^2{f}^2{A}^2$

Here, $A$ is the amplitude of the wave,

  $\rho$ is the density of the medium,

  $f$ is the frequency of the sound wave,

  $v$ is the speed of the wave.

Calculation:

In the given formula, all quantities are constant except for the frequency.

Therefore, the ratio of intensities of two sound waves is equal to the ratio of square of their frequencies,

  $\frac{I_{2f}}{I_f}=\frac{{\left(2f\right)}^2}{{\left(f\right)}^2}=4$

Conclusion:

The ratio of intensities is 4.