A point `A` is located at a distance `r = 1.5 m` from a point source of sound of frequency `600 H_(Z)`. The power of the source is `0.8 W`. Speed of sound in air is `340 m//s` and density of air is `1.29 kg//m^(3)`. Find at the point `A`, (a) the pressure oscillation amplitude`(Deltap)_(m)` (b) the displacement oscillation amplitude `A`.

Answer

A, B, C, D

Explanation

(a) At a distance `r` from a point source of power `P`, the intensity of the sound is
`I = (P)/(4 pi r^(2)) = (0.8)/((4 pi) (1.5)^(2))`
or `I = 2.83 xx 10^(-2) W//m^(2)` ..(i)
Further, the intensity of sound in terms of `(Delta p)_(m)`, `rho` and `nu` is given by
`I = ((Delta p)^(2)m)/ (2 rho nu)` ...(ii)
From Eqs. (i) and (ii),
`(Deltap)_(m) = sqrt(2 xx 2.83 xx 10^(-2) xx 1.29 xx340)`
`= 4.98 N//m^(2)`
(b) Pressure oscillations amplitude `(Deltap)_(m)` and
displacement oscillation amplitude `A` are
related by the equation
`(Delta p)_(m) = BAK`
subsituting `B = pnu^(2)`, `k = (omega)/(nu)`
and `omega = 2 pi f`
We, ger, `(Delta p)_(m) = 2 pi Arho nu f`
`:. A = ((Deltap)_(m))/(2 pi rho nu f) = (4.98)/(2 pi)(1.29)(340)(600)`
`= 3.0 xx 10^(-6) m`