A source `S` of sound wave of fixed frequency `N` and an observer `O` are located in air initially at the space points `A` and `B`, a fixed distance apart. State in which of the following cases, the observer will NOT see any Doppler effect and will receive the same frequency `N` as produced by the source.

Options

A. Both the source `S` and observer `O` remain stationary but a wind blows with a constant speed in an arbitrary direction.
B. The observer remains stationary but the source `S` moves parallel to and in the same direction and with the same speed as the wind.
C. The source remains stationary but the observer and the wind have the same speed away from the source.
D. The source and the observer move directly against the wind but both with the same speed.

Answer

A, D

Explanation

In both case (a) and (d) the source and observer are relatively at rest, thus neither of htem is approaching or separating from each other. Effectively, it is the medium that moves in each of these cases. The received (apparent) frequency differs from the emitted frequency if and only if the time required for the wave to travel from the source to observer is different fror different wavefronts. With a uniform steady motion of the medium, past the observer and source, the transit time from source to observer is the same for all wavefronts. Hence it follows that apparent freqeuncy is equal to the true emitted frequency. Thus there is no Doppler effect. In cases (b) and (c ), Doppler effect will be observed as the source and observer have a relative speed and so they will approach or recede from each other.