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(A) According to the Doppler effect,when a source of sound moves with a constant velocity $V_S$ towards a stationary observer,the observed frequency $

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(A) According to the Doppler effect,when a source of sound moves with a constant velocity $V_S$ towards a stationary observer,the observed frequency $f^{\prime}$ is given by $f^{\prime} = f_0 \left( \frac{V}{V - V_S} \right)$,where $f_0$ is the source frequency and $V$ is the speed of sound.After the source crosses the observer,it moves away from the observer with the same velocity $V_S$. The observed frequency $f^{\prime\prime}$ is then given by $f^{\prime\prime} = f_0 \left( \frac{V}{V + V_S} \right)$.Since $V - V_S  \frac{V}{V + V_S}$. Therefore,the frequency $f^{\prime}$ before crossing is greater than the frequency $f^{\prime\prime}$ after crossing.Since the velocity is constant,the frequency remains constant before and after the crossing,with a sudden drop at the moment of crossing. This corresponds to the graph where the frequency is higher initially and drops to a lower constant value after the crossing.

$A$ train is moving towards a stationary observer (at $t = 0$) with a constant velocity of $20 \ m/s$ and after some time it crosses the observer. Which of the following curves best represents the frequency $f$ received by the observer as a function of time?

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