The intensities of two sound waves, one in air and the second one in water are equal (i) What is the ratio of the pressure amplitude of the wave in water to that of the wave in air? If the pressure amplitudes are equal instead, what is the ratio of the intensities of hte waves? Density of air is `1.293 kg//m^2`. Velocity of sound in air and water are `330ms^(-1) and 1450ms^(-1)` respectively.

Explanation

Intensity `=I=2pi^2 n^2 A^2 pv .........(i)`
Pressure amplitude `P=2pi p vnA ........(ii)`
From the above two equations, `I=P^2/(2pv)`
Let the intensity and pressure amplitude in air and water be `I_(a), P_(a) and P_(w)` respectively.
`I_(w)/I_(a)=P_(w)^2/P_(a)^2. p_(a)/p_(w).v_(a)/v_(w)`
`P_(w)/P_(a)=sqrt((I_(W)p_(w)v_(w))/(I_(a)P_(a)v_(a)))=sqrt(1 xx (1000)/(1.293) xx (1450)/(330))=58.3`
(ii) `P_(w)=P_(a)`
`I_(w)/(I_(a))=P_(w)^2/P_(a)^2 .(p_(a) v_(a))/(p_(w) v_(w))=1 xx (1.293)/(1000) xx (330)/(1450) =2.94 xx 10^(-4)`