A source of sound and a detector are placed at the same place on ground At `t=0`, the source `S` is projected towards reflector with velocity `v_0` in vertical upward directon and reflector starts moving down with constant velocity `v_0` At `t-0`, the vertical separation between the reflector and source is `H((gtv_0^2)/(2g))`. The speed of sound in air is `v(gtgtv_0)`, Take `f_0` as the frequency of sound waves emitted by source. Based on above information answer the following questions.
Q. Wavelength of sound waves as received by detector before reflection at `t=(v_0)/(2g)` is

Options

A. `(v)/(f_0)`
B. `((v+v_0)/(2))/(f_0)`
C. `(((v-v_0)/(2))^2)/(vf_0)`
D. none of these

Answer

C

Explanation

As the source is initially projected with velocity `v_0` upwards, the velocity of the source after a time `(v_0)/(2g)` is
`v=v_0-(v_0)/(2g)xxg=(v_0)/(2)`
And the source is moving away from observer, so frequency heard
`=[(v)/(v+(v_0)/(2))]f_0`
So wavelength of sound
`=(v+(v_0)/(2))/(f_0)`