A source of sound operates at 2.0 kHz, 20 W emitting sound uniformly in all direction. The speed of sound in air is `340 m s^(-1)` at a distance of air is `1.2kgm ^(-3)` (a) What is the intensity at a distance of 6.0 m from the source ? (b) What will be the pressure amplitude at this point ? (c ) What will be the displacement amplitude at this point ?

Explanation

(a) `I = (P)/(4 pi r^(2)) = (20)/(4 pi(6)^(2)) = 0.044 W//m^(2)`
` I = (p_(0)^(2))/(2 rho v)`
Pressure amplitude
`p_(0) = sqrt(2 rho v I) = sqrt(2 xx 1.2 xx 340 xx 0.044)`
`=6 N//m^(2)`
( c) `p_(0) = BKs_(0)`
`v = sqrt((B)/(rho)) rArr B = rho v^(2)`
`k = (2pi)/(lambda) = (2pi)/(v//f) = (2pi f)/(v)`
`p_(0) = rho v^(2) .(2pi f)/(v) s_(0)`
Displacement amplitude
`s_(0) = (p_(0))/(2pi f rho v) = (6)/(2pi xx 2000 xx 1.2 xx 340) = 1.2 xx 10^(-6) m`
OR
`I = 2pi^(2) s_(0)^(2) f^(2) rho v`
`s_(0) = sqrt((I)/(2pi^(2) f^(2) rho v)) = sqrt((0.044)/(2pi^(2) xx (2000)^(2) xx 1.2 xx 340))`
`= 1.2 xx 10^(-6) m`