Question

A sound wave in air has a frequency of 30 Hz and a displacement amplitude of $6.0\times {10}^{-3}mm$. For this sound wave the pressure amplitude (in Pa) is $467\times {10}^{-x}$. Find x.

• A. 0.460 Pa
• B. 1 Pa
• C. 10Pa
• D. 50 Pa

Answer 1

The correct option is A 0.460 Pa

The relation between pressure amplitude $\Delta p_m$
Δpm and displacement amplitude and AA (maximum value of displacement ) is given by ,

$\Delta p_m=\left(vd\omega \right)A$,

or $\Delta p_m=(vd\times 2\pi f)A$

where v=v= speed of sound in air ,

d=d= density of medium (air) ,

$f=$ frequency ,

we have , $v=332m/s,d=1.225kg/m^3,f=30Hz,A=6.0\times {10}^{-3}mm=6.0\times {10}^{-6}m$ ,

therefore , $\Delta p_m=332\times 1.225\times 2\times 3.14\times 30\times 6.0\times {10}^{-6}=0.460Pa$

v