The spread of frequency as observed by the passengers in train B is [2007]

Question

Two trains A and B moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from $f_{1}$ = 800 Hz to $f_{2}$ = 1120 Hz, as shown in the figure. The spread in the frequency (highest frequency − lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s. [2007]

Q. The spread of frequency as observed by the passengers in train B is

Smart Achievers · Accepted Answer

(1)

For the passengers in train B, the source is approaching with velocity $20 m/s$ and the observer is receding with velocity $f_{2}$

$ν' = ν_{1} [\frac{v - v_{0}}{v - v_{s}}] = 800 [\frac{340 - 30}{340 - 20}] = 800 \times \frac{31}{32}$

$ν'' = ν_{2} [\frac{v - v_{0}}{v - v_{s}}] = 1120 \times \frac{31}{32}$

$∴$ $ν'' - ν' = (1120 - 800) \times \frac{31}{32} = 320 \times \frac{31}{32} = 310 Hz$

Solution

1 310 Hz

2 330 Hz

3 350 Hz

4 290 Hz

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