An observer `A` is moving directly towards a stationary sound source while another observer `B` is moving away from the source with the same velocity. Which of the following statements are correct?

Options

A. Average of freqeuncies recorded by `A` and `B` is equal to natural frequency of the source
B. Wavelength of wave received by `A` is less than that of waves received by `B`.
C. Wavelength of waves received by two observers will be same.
D. Both the observers will observe the wave travelling with same speed.

Answer

A, C

Explanation

Let velocity of each observer be `u` as shown in the figure.
`_Ararr^u` `_Brarr^u`
Then freqeuency received by `A` will be
`n_1=n_0((v+u)/(v))`
where `n_0` is natural frequency of the source and `v` is sound propagation velocity. The frequency received by `B` will be
`n_2=n_0((v-u)/(v))`
Since `((n_1+n_2))/(2)=n_0`, therefore, option (a) is correct.