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`.

Explanation

We have `(P)/( 4pi r^(2))=` intensity `=((Deltap)_(m)^(2))/( 2 rho v)`
or `(Delta p)_(m)=sqrt((rho v P)/(2 pi r^(2)))`
`=sqrt((1.293kg//m^(3)xx340 m//sxx0.80w)/(2pi xx1.5 xx1.5m^(2)))=sqrt((1.293xx340xx.8)/(2pixx1.5xx15))((kg kg m^(2)s^(-3)ms^(-1))/(m^(5)))^(1/2)`
`=4.9877(kg m ^(-1) s ^(-2))=5 Pa`.
`((Deltap)_(m))/(p)=5 xx 10^(-5) `
`(b)` We have `Deltap=-rho v^(2)(delta xi)/( deltax)`
`(Deltap)_(m)=rho v^(2)k xi_(m)= rho v 2pi v xi_(m)`
`xi_(m) a= ((Deltap)_m)/( 2pi rho v v )=(5)/( 2pixx1.293x340xx600)=3 mu m`
`(xi_(m))/( lambda)=(3xx10^(-6))/( 340xx600)=(1800)/( 340)xx 10^(-6)=5 xx 10^(-6)`