Source and observer start moving simulatneously along x and y-axis respectively. The speed of source is twice the speed of observer `V_0`. If the ratio of observer frequency to the frequency of the source is `0.75`, find the velocity of sound.

Options

A. `(11)/(sqrt(5))V_0`
B. `(17)/(sqrt5)V_0`
C. `(16)/(sqrt5)V_0`
D. `(19)/(sqrt5)V_0`

Answer

C

Explanation

`OS=2OP`
`cosalpha=(2)/(sqrt5)`,`cosbeta=(1)/(sqrt5)`
`f'=f[(V-V_0cosbeta)/(V+V_Scosalpha)]=f[(V-(V_0)/(sqrt5))/(V+(2V_0)xx((2)/(sqrt5)))]`
`f[(V-(V_0)/(sqrt5))/(V+(4V_0)/(sqrt5))]`
Let `(V_0)/(sqrt5)=x`. Given `(f')/(f)=(3)/(4)=(V-x)/(V+4x)`
or `1-(3)/(4)=(5x)/(V+4x)` or `V=16x=(16)/(sqrt5)V_0`