Question

Find the displacement amplitude of particles of air of density $1.5{\text{kg/m}}^3$ if the intensity and frequency of sound are $8\times {10}^{-6}{\text{W/m}}^2$ and $5000\text{Hz}$ respectively.
[speed of sound in air $=330\text{m/s}$]

• A. $5.7\text{nm}$
• B. $4.7\text{nm}$
• C. $3.7\text{nm}$
• D. $2.7\text{nm}$

Answer 1

The correct option is A $5.7\text{nm}$

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.
$\Rightarrow I=2{\pi }^2{f}^2\rho A_o^{2}v$
$[\omega =2\pi f]$
$\Rightarrow A_o=\sqrt{\frac{I}{2{\pi }^2{f}^2\rho v}}$
$\Rightarrow A_o=\sqrt{\frac{8\times {10}^{-6}}{2\times {3.14}^2\times {5000}^2\times 1.5\times 330}}$
$\Rightarrow A_o=5.7\times {10}^{-9}\text{m}=5.7\text{nm}$