The faintest sound the human ear can detect at a frequency of ` kHz` (for which ear is most sensitive) corresponds to an intensity of about `10^(-12)w//m^(2)`. Assuming the density of air `cong1.5kg//m^(3)` and velocity of sound in air `cong300m//s`, the pressure amplitude and displacement amplitude of the sound will be rspectively ____`N//m^(2)` and ____`m`.

Options

A. `3xx10^(-5)Pa, (1)/(3pi)xx10^(-10)m`
B. `2xx10^(-5)Pa, (2)/(3pi)xx10^(-10)m`
C. `5xx10^(-5)Pa, (1)/(pi)xx10^(-10)m`
D. `5xx10^(-5)Pa, (4)/(3pi)xx10^(-10)m`

Answer

A

Explanation

`I=(P_m^2)/(2rhoV)`
`10^(-12)=(P_m^2)/(2(1.5)(300))`
`P_m=3xx10^(-5)Pa`
`P_m=BAK=(rhoV^2) A (2pi)/(v//f)`
`P_m=(2pirhoVf)A`
`3xx10^-5=(2pi)(1.5)(300)(10^3)A`
`A=1/3pixx10^(-10)m`