Question

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 $(v_{\text{sound}}=350{\mathrm{ms}}^{-1})$
(A) 612 Hz
(B) 625 Hz
(C) 636 Hz
(D) None of these

Answer 1

Hint
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.

Complete step by step answer
Let the original frequency of the source $f_0=600\mathrm{Hz}$
Velocity of train ${\mathrm{V}}_{\text{train }}=72\times {\displaystyle \frac{5}{18}}=20\mathrm{m}/\mathrm{s}$
Using Doppler effect when a source is moving towards stationary observer,
Apparent frequency heard $\mathrm{f}={\mathrm{f}}_0\left[{\displaystyle \frac{{\mathrm{V}}_{\text{sound }}}{{\mathrm{V}}_{\text{sound }}-{\mathrm{V}}_{\text{train }}}}\right]$
 $\therefore \mathrm{f}=600\left[{\displaystyle \frac{350}{350-20}}\right]$
 $\Rightarrow \text{f}=636\text{Hz}$

Therefore, option $\mathrm{C}$ is the correct answer.

Note
We need to have knowledge about wave velocity, distance traversed by a periodic, or cyclic, motion per unit time in any direction. The velocity of a wave is equal to the product of its wavelength and frequency (number of vibrations per second) and is independent of its intensity. velocity depends on the frequency, and, for a fixed wavelength, velocity will increase if the frequency will be more, it’s because, so, if frequency will increase, velocity will increase. For one thing, while nothing has ever been observed travelling faster than light, that does not mean it is not theoretically possible to break this speed limit in very special circumstances. There are galaxies in the Universe moving away from one another at a velocity greater than the speed of light.