A railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer beside the railway track. Which of the following graphs best represents the variation of frequency of sound $n$ heard by the observer with the time $t$ ?

[Assume, medium is stationary. Source and observer are collinear]

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Solution

The correct option is B
According to Doppler's effect, when the source is moving towards the observer, then actual frequency is less than the observed frequency.
$(n)_{A} < (n)_{O}$

and when the source is moving away from the observer, then actual frequency is greater than the observed frequency.
$(n)_{A} > (n)_{O}$

Case I: Engine moving towards the observer

$(n)_{A} < (n)_{O}$ .
Also, frequency is constant as the engine moves with constant speed.

Case II: Engine moving away from the observer

$(n)_{A} > (n)_{O}$
Also, frequency is constant as the engine moves with a constant speed.

So, initially the observed frequency is higher and constant and after that, frequency is lesser and again constant.
Graph (b) matches this description.

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