Question

If the intensities of two sounds are in ratio 9:4, what is the ratio of their amplitudes?

• A. 3:2
• B. 2:3
• C. 81:16
• D. 16:81

Answer 1

The correct option is A

3:2

Given:
Ratio of intensity of sounds,
$\frac{I_1}{I_2}=\frac{9}{4}$

Let:
$A_1$: Amplitude of first sound
$A_2$: Amplitude of second sound

Since intensity is proportional to square of the amplitude, we can write:
$\frac{I_1}{I_2}={\left(\frac{A_1}{A_2}\right)}^2$
$⟹\frac{A_1}{A_2}=\sqrt{\frac{I_1}{I_2}}$
$\frac{A_1}{A_2}=\sqrt{\frac{9}{4}}=\frac{3}{2}$

Therefore, ratio of their amplitudes is 3:2.