A point source of sound is placed in a non-absorbing medium two points A and B are at the distance of 1 m and 2 m, respectively, from the source. The ratio of amplitudes of waves at A to B is

Options

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

Answer

D

Explanation

Let the power of source be P and it is placed at O. then intensity at A and B qould be given by
`I_(A)=(P)/(4pixx1^(2))` and `I_(8)=(P)/(4pixx2^(2)`
since, intensity `prope (Amplitude)^(2)xx (Frequency)^(2)` (here, amplitude means displacement amplitude), the frequency is same at both the points.
`implies((Amp)_(A))/((Amp)_(B))=sqrt(I_(A)/I_(b))=sqrt((2^(2)/(1))^(2))=2:1`