Waves

Question : 21

Total: 27

A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10ms–1. What are the frequency, wavelength, and speed of sound for an observer standing on the station platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of 10ms–1? The speed of sound in still air can be taken as 340ms–1.

Solution:

Here, v=340ms–1 ; υ=400‌Hz
(a) Speed of the wind, vw=10ms–1
As the direction of blow of wind (yard to station) is the same as the direction of sound, therefore, for the observer standing on the platform;
velocity of sound,
v′=v+vw=340+10=350ms–1
As there is no relative motion between source of the sound and the observer, the frequency of sound will remain unchanged.
Thus, frequency of sound = 400 Hz
Wavelength of sound,
λ′=

v′

350

400

=0.875m
(b) Speed of the observer, v0=10ms–1 (towards yard). When the observer moves towards the source of sound, the apparent frequency,
υ′=

v+v0

υ=

340+10

340

×400 =411.8Hz
The wavelength of sound waves is not affected due to the motion of the observer and hence the wavelength of the sound waves will remain unchanged.
Speed of sound relative to the observer
=340+10=350ms–1
Therefore, situations (a) and (b) are not equivalent.

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