Question

Due to a point isotropic sonic source, loudness at a point is $L=60dB$ If density of air is $\rho =\left(15/11\right)kg/m^3$ and velocity of sound in air is $v=33m/s$ , 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 $0.03N/m^2$

$60dB=10dBlog\frac{I}{I_0}$
$\Rightarrow$ $I=({10}^6\times {10}^{-12})W/m^2={10}^{-6}W/m^2$
$[I_0={10}^{-12}W/m^2]$
$I=\frac{(\Delta P_m{)}^2}{2\rho v}$
where $\rho =\frac{15}{11}kg/m^3,v=330m/s$
$\therefore (\Delta P_m{)}^2=2\rho vI=2\times \frac{15}{11}\times 330\times {10}^{-6}$
$\Rightarrow \Delta P_m=0.03N/m^2$