Question

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

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

Answer 1

The correct option is A

3:2

Let $L_1$, $A_1$, $L_2$ and $A_2$ be intensities and amplitudes of first and second sound respectively. Since intensity is proportional to square of the amplitude, we can write:
$\frac{I_1}{I_2}$ = $({\frac{A_1}{A_2})}^2$
$\Rightarrow$ $\frac{A_1}{A_2}$ = $\sqrt{\frac{I_1}{I_2}}$
$\Rightarrow$ $\frac{A_1}{A_2}$ = $\sqrt{\frac{9}{4}}$
$\Rightarrow$ $\frac{A_1}{A_2}$ = $\frac{3}{2}$ = $3:2$