Question

Question: (II) Two sound waves have equal displacement amplitudes, but one has 2.2 times the frequency of the other. What is the ratio of their intensities?

Short answer

The ratio of intensities of sound waves is \(4.84\).

Step-by-step solution

Understanding the relation between the intensity and frequency of sound

In this problem, for estimating the ratio of intensities utilize the relation between frequency and intensity.

Given data

The frequency of one sound wave is \({f_1} = 2.2{f_2}\).

Here, \({f_2}\) is the frequency of other sound wave.

Evaluating the ratio of intensity of sound waves

The ratio of intensities of sound waves is calculated below:

\(\frac{{{I_1}}}{{{I_2}}} = {\left( {\frac{{{f_1}}}{{{f_2}}}} \right)^2}\)

Substitute the values in the above equation.

\(\begin{array}{c}\frac{{{I_1}}}{{{I_2}}} = {\left( {\frac{{2.2{f_2}}}{{{f_2}}}} \right)^2}\\\frac{{{I_1}}}{{{I_2}}} = 4.84\end{array}\)

Hence, the ratio of intensities of sound waves is \(4.84\).