A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $30 \mathrm{~m} / \mathrm{s}$. If both trains emit sounds with frequency 300 Hz, (Speed of sound : $330 \mathrm{~m} / \mathrm{s}$) approximate difference of frequencies heard by the person will be :

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Waves & Sound

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of

30 m / s

. If both trains emit sounds with frequency 300 Hz, (Speed of sound :

330 m / s

) approximate difference of frequencies heard by the person will be :

Answer: (B)

For a stationary listener and a moving source the heard frequency is

f^{'} = f \frac{v}{v \mp v _{s}}

. The approaching train gives

f_{1} = 300 \times \frac{330}{330 - 30} = 330

Hz, and the receding train gives

f_{2} = 300 \times \frac{330}{330 + 30} = 275

Hz. The difference of the two heard frequencies is

55

Hz.

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Single correct option