Question

What is the displacement amplitude of a sound wave having frequency of $100\text{Hz}$ and pressure amplitude $10\text{Pa}$?
[speed of sound in air $=340\text{m/s}$ and density of air $=1.29{\text{kg/m}}^3$]

• A. $2.5\times {10}^{-5}\text{m}$
• B. $3.6\times {10}^{-5}\text{m}$
• C. $4.5\times {10}^{-5}\text{m}$
• D. $1.5\times {10}^{-5}\text{m}$

Answer 1

The correct option is B $3.6\times {10}^{-5}\text{m}$

We know the relation between maximum value of pressure in the medium and displacement of the particles in the medium is given by,

$P_o=B{A}_{o}k......\left(1\right)$

Also, speed of sound,

$v=\sqrt{\frac{B}{\rho }}$

$\Rightarrow B=v^2\rho ......\left(2\right)$

Wave number,

$k=\frac{2\pi }{\lambda }=\frac{2\pi f}{v}.....\left(3\right)$

On putting $\left(2\right)$ and $\left(3\right)$ in $\left(1\right)$,

$P_o=v^2\rho \times A_o\times \frac{2\pi f}{v}=2\pi v\rho A_{o}f$

$\Rightarrow A_o=\frac{P_o}{2\pi v\rho f}$

$A_o=\frac{10}{2\times 3.14\times 340\times 1.29\times 100}$

$\Rightarrow A_o=3.6\times {10}^{-5}\text{m}$