Question

Two sound waves have amplitudes in the ratio 2:5. Ratio of the intensities of the sound waves is:

• A. 2:5
• B. 5:2
• C. 4:25
• D. 25:4

Answer 1

The correct option is C 4:25

Given:
Ratio of amplitudes:
$\frac{A_1}{A_2}=\frac{2}{5}$

Let corresponding intensities be $I_1$ & $I_2$.

Intensity of the sound wave is proportional to the square of its amplitude. Hence, ratio of intensities is:
$\frac{I_1}{I_2}=\frac{A_1^2}{A_2^2}$
$\frac{I_1}{I_2}={\left(\frac{2}{5}\right)}^2=\frac{4}{25}$