Question

A bomb blast gives a sound of intensity $0.8{\text{W/m}}^2$ and frequency $1.5\text{kHz}$. If the density of air is $1.25{\text{kg/m}}^3$ and speed of sound in air is $330\text{m/s}$, then the amplitude of the sound wave is approximately

• A. $4.4\mu \text{m}$
• B. $5.5\mu \text{m}$
• C. $6.6\mu \text{m}$
• D. $7.7\mu \text{m}$

Answer 1

The correct option is C $6.6\mu \text{m}$

We know that the intensity of sound is given by,
$I=\frac{1}{2}\rho {\omega }^2{A}_o^{2}v$,
where, $\rho$ is the density of medium, $\omega$ is the angular frequency of sound, $A_o$ is the displacement amplitude of particles of medium and $v$ is the speed of sound.
$\Rightarrow I=2{\pi }^2{f}^2\rho A_o^{2}v$
$[\omega =2\pi f]$
$\Rightarrow A_o=\sqrt{\frac{I}{2{\pi }^2{f}^2\rho v}}$
$\Rightarrow A_o=\sqrt{\frac{0.8}{2\times {3.14}^2\times (1.5\times {10}^3{)}^2\times 1.25\times 330}}$
$\Rightarrow A_o=6.6\times {10}^{-6}\text{m}=6.6\mu \text{m}$