Figure shows two line sources of sound, `S_1 and S_2` separated by a distance 4 m.The two sources are in same phase at all times.The source emit same power and their lengths are also same.A detector moves along a circle with center at `S_2` and radius 3m. The wavelength of the sound is 1m.When it is at A the intensity of sound due to source `S_2` only is `I_0`.

The intensity o sound of B due to `S_1 and S_2` is :

Options

A. `70/25I_0`
B. `I_0[8/5+2sqrt(3/5)]`
C. `(8I_0)/5`
D. `I_0[8/5+2sqrt(9/25)]`

Explanation

Applying cosine rule in the triangle `S_1S_2A, cos 60^0=(3^2+4^2-S_1A^2)/(2xx3xx4)rArr S_1A=sqrt13`.For line sources intensity is inversely proportional to the distance from the source.At A, let the intensity due to the source `S_1` be I, then `Isqrt13=I_0 3`.
Similarly at B, let the intensity due to source `S_1` be I', then `I'5=I_0 3`.Path difference =2m=`2lambda`
`therefore` the interference will be constructive `therefore I_(res)=I_0+I'+2sqrt(I_0+I')`