Question

Find the amplitude of vibration of the particles of air through which a sound wave of intensity $2.0\times {10}^{-6}W{m}^{-2}$ and frequency 1.0 kHz is passing. Density of air =$1.2kg{m}^{-3}$and speed of sound in air =$330m{s}^{-1}$

• A. $1.6\times {10}^{-9}m$
• B. $3\times {10}^{-8}m$
• C. $1.6\times {10}^{-11}m$
• D. None of these

Answer 1

The correct option is C

$1.6\times {10}^{-11}m$

The relation between the intensity of sound and the displacement amplitude is

$I=2{\pi }^2{s}_0^{2}v{p}_0{f}^2$

or, $s_0^2=\frac{I}{2{\pi }^2{f}^2{p}_{0}v}$

$=\frac{2.0\times {10}^{-6}W{m}^{-2}}{2{\pi }^2\times (1.0\times {10}^6{s}^{-1})\times \left(1.2kg{m}^{-3}\right)\times \left(330m{s}^{-1}\right)}$

$=2.56\times {10}^{-22}{m}^2$

or, $s_0=1.6\times {10}^{-11}m$