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` would be given by
`I_(A)=(P)/(4pixx1^(2))`
and `I_(B)=(P)/(4pixx2^(2))`
since, intensity `prop` (Amplitude)xx(Frequency)^(2) (here,amplitude means displacement amplitude)
the frequency is same at both the points.
`((Amp)_(A))/((Amp)_(B))=sqrt((I_(A))/(I_(B)))`
`=sqrt((2^(2))/(1^(2)))=2.1`