the maximum pressure variation that the human ear can tolerate in loud sound is about `30 N //m^(2) ` . The corresponding maximum displacement for a sound wave ina air having a frequency of ` 10^(3) Hz`is
take velocity of sound in air as 300 m/s and density of air ` 1.5 kg // m ^(3)`

Options

A. `(10^(-4))/(3pi)`m
B. `(piX10^(-2))/(3)`m
C. `(2X10^(-4))/(pi)`m
D. `(2piX10^(-2))/(3)`m

Answer

A

Explanation

`Deltarho_(max)=BAKimpliesA=(Deltarho_(max))/(BK)`
`V=sqrt((B)/(rho))=(omega)/(K)impliesK=2pifsqrt((rho)/(B))`
`A=(Deltarho_(max))/(2pifsqrt(Brho))=(Deltarho_(max))/(2pifrhoV)`