In the figure shown, an observer `O_1` floats (static) on water surface with ears in air while another observer `O_2` is moving upwards with constant velocity `V_1=(V)/(5)` in water. The source moves down with constant velocity `V_S=(V)/(5)` and emits sound of freqeuncy `f`. The velocity of sound in air is `V` and that in water is `4V`. For the situation shown in figure.

Options

A. The wavelength of the sound received by `O_1` is `(4V)/(5f)`
B. The wavelength of the sound received by `O_1` is `(V)/(f)`
C. The frequency of the sound received by `O_2` is `(21f)/(16)`
D. The wavelength of the sound received by `O_2` is `(16V)/(5f)`

Answer

A, C, D

Explanation

For observer `O_1`,
`lamda_4=(V-V_S)/(f)=((V-V)/(5))/(f)=(4V)/(5f)`
For `O_2`, there is change of medium Hence, at the surface of water, keeping frequency unchanged.
`(V)/(lamda_a)=(4V)/(lamda_W)`
`implieslamda_W=4lamda_a=(16V)/(5f)`
Velocity of wave relative
`f''=("to observer")/(lamda_W)=(4V+(V)/(5))/(lamda_W)`
`=(21V)/(5)(5f)/(16V)=(21f)/(16)`