Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

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