A point sound source is situated in a medium of dulk modulus `1.6 xx 10^(5) N//m^(2)`. An observer standing at a distance `10 m `from the source writes down the equeation for the wave as `y = A sin (15 pi x - 6000 pi t)`. Here `y` and `x` are in meter and `t` is in second. The maximum pressure ampulitude received to the observer's ear is `(24 pi)` pa, then find.
(a) the density of the medium,
(b) the displacement ampulitude `A` of the wave recived by the observer and
(c ) the power of the sound source.

Answer

A, B, C

Explanation

Comparing with the equation of a travelling wave
`y=asin(Kx-omegat)`
`k=15pi` and `omega=6000pi`
`:.` velocity of the sound, `v=(omega)/(k)`
`=(6000pi)/(15pi)=400ms^(-1)` as `v=sqrt((B)/(p))`
Hence, `p=(B)/(v^(2))=(1.6xx10^(5))/((400)R^(2))=1kg//m^(3)`
(b) Pressure amplitude, `p_(0)=BAK`
Hence, `A=(P_(0))/(BK)=(24pi)/(1.6xx10^(5)xx15pi)`
`=10^(-5)m=10mum`
(c) Intersity received by the person,
`I=(W)/(4piR^(2))=(W)/(4pi(10)^(2))`
Also, `I=(p_(0)^(2))/(2pv)implies(W)/(4pi(10)^(2))=((24pi)^(2))/(2xx1xx400)`
`W=288pi^(3)W`