Question

Due to a point isotropic sonic source, loudness at a point is $L=60dB$. If density of air $p=\left(15/11\right)kg/m^3$ and velocity of sound in air is $v=330m/s$, the pressure oscillation amplitude at the point of observation is $[I_0$= 10${}^{-12}$ W/m${}^2]$

• A. $0.3N/m^2$
• B. $0.03N/m^2$
• C. 3 $\times {10}^{-3}N/m^2$
• D. 3 $\times {10}^{-4}N/m^2$

Answer 1

The correct option is B $0.03N/m^2$

Given: $L=60dB$

Density of air $p=\frac{15}{11}kg/m^3$

Velocity of sound in air $v=330m/s$

Loudness of the sound $L=10lo{g}_{10}\frac{I}{I_o}$

$60=10{\log }_{10}\frac{I}{{10}^{-12}}$

${10}^6=\frac{I}{{10}^{-12}}⟹I={10}^{-6}$

Let $P_o$ be the pressure amplitude.

Now $I=\frac{P_o^2}{2pv}⟹P_o^2=2pvI$

Thus $P_o^2=2\times \frac{15}{11}\times \left(330\right)\left({10}^{-6}\right)$

$⟹P_o=0.03N/m^2$