Question

A point source of power $50\pi \text{W}$ is producing sound waves of frequency $1876\text{Hz}$. What is the pressure amplitude at a distance $\sqrt{330}\text{m}$ from the point source?
[Speed of sound is $330\text{m/s}$ and density of air is $1{\text{kg/m}}^3$]

• A. $5{\text{N/m}}^2$
• B. $6{\text{N/m}}^2$
• C. $7{\text{N/m}}^2$
• D. $8{\text{N/m}}^2$

Answer 1

The correct option is A $5{\text{N/m}}^2$

Intensity at distance $r$,
$\Rightarrow I=\frac{P}{4\pi r^2}$ .......(1)
Also,
$I=\frac{\Delta {P_o}^2}{2\rho v}$ ..........(2)
From (1) and (2),
$\frac{\Delta {P_o}^2}{2\rho v}=\frac{P}{4\pi r^2}$
$\Rightarrow \Delta P_o=\sqrt{\frac{P\rho v}{2\pi r^2}}$
$\Rightarrow \Delta P_o=\sqrt{\frac{50\pi \times 1\times 330}{2\pi \times 330}}$
$\Rightarrow \Delta P_o=5{\text{N/m}}^2$