Question

A man standing on a train hears the train whistle. A moment later he hears an answering whistle from an approaching train. Why does the whistle he hears from the approaching train change pitch?
A) The frequency of the waves of the approaching train’s whistle is decreasing
B) The frequency of the waves of the approaching train’s whistle is increasing
C) The loudness of the waves of the approaching train is decreasing
D) The loudness of the waves of the approaching train is increasing
E) The echoes of the two trains’ whistles are combining

Answer 1

Hint:Here we have to apply the concept of Doppler’s effect.
The Doppler’s effect is a variation in the frequency of the wave in response to the observer travelling closer to the wave source.
The Doppler effect can be defined as the effect created by a moving wave source in which there is an apparent upward shift in the frequency of the observer and the source approaching, and an apparent downward shift in the frequency when the observer and the source are receding.

Complete step by step solution:
By the effect of Doppler, if the train on which the man stands is stationary, so the pace of approaching the train whistle, which the man hears, would be:
$f' = f\left( {\dfrac{v}
{{v - {v_s}}}} \right)$

It is obvious that man’s apparent frequency $f'$ is greater than the actual frequency $f$. If the train on which the man is standing is heading toward the incoming train, the level of incoming the train’s whistle heard by the man would be:
$f' = f\left( {\dfrac{{v + {v_ \circ }}}
{{v - {v_s}}}} \right)$

It is obvious that the man’s apparent frequency $f'$ is greater than the actual frequency $f$. In all conditions, the level of waves of the incoming train whistle is rising.

Hence, option B is correct.

Thus, the frequency of the waves of the approaching train’s whistle is increasing.

Additional information:The Doppler effect is detected when the spacing between the sound source and the listener is changing. If the source and the observer meet, the distance reduces, and if the source and the observer recede, the distance increases.

Note:Here we have to observe both the apparent and the real frequency, and then we can determine how the pitch is changing.