A stationary point source of sound emits sound uniformly in all directions in a non absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source. The ratio of amplitudes of the waves at P and Q is

Options

A. 4:9
B. 9:4
C. 1:2
D. 2:1

Answer

D

Explanation

For an isotropic point source of power P, intensity I at a distance r from it will be

`I=P/(4pi r^(2))`
Since power (P) remains the same
`:.(I_(1))/(I_(2))=((r_(2))/(r_(1)))^(2)=(9/4)^(2)`
`:'I prop A^(2)`, where A is the amplitude of a wave
`:.(A_(1))/(A_(2))=sqrt((I_(1))/(I_(2)))=9/4`