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# The train is approaching the station with $72 \mathrm{km} \mathrm{h}^{-1} .$ When $1 \mathrm{km}$ away it blows a whistle of frequency $600 \mathrm{Hz}$ . The frequency heard by the person is $\left(v_{\text {sound}}=350 \mathrm{ms}^{-1}\right)$ (A) 612 Hz(B) 625 Hz(C) 636 Hz(D) None of these

Last updated date: 10th Sep 2024
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It is required to be known that the speed of the sound depends on the density of the medium through which it is travelling. The higher the density of the medium, the faster the propagation of sound. Since the density of solids is higher than that of liquids and gases, sound travels faster in solids. Speed travels faster in the summer season. During the summer season, the temperature of the air increases. At higher temperature, the molecules of air have more kinetic energy. Hence, they vibrate faster leading to increase in speed of sound. Based on this concept we have to solve this question.

Let the original frequency of the source $f_{0}=600 \mathrm{Hz}$
Velocity of train $\mathrm{V}_{\text {train }}=72 \times \dfrac{5}{18}=20 \mathrm{m} / \mathrm{s}$
Apparent frequency heard $\mathrm{f}=\mathrm{f}_{0}\left[\dfrac{\mathrm{V}_{\text {sound }}}{\mathrm{V}_{\text {sound }}-\mathrm{V}_{\text {train }}}\right]$
$\therefore \mathrm{f}=600\left[\dfrac{350}{350-20}\right]$
$\Rightarrow \text{f}=636\text{Hz}$
Therefore, option $\mathrm{C}$ is the correct answer.