A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 m s^–1, (b) recedes from the platform with a speed of 10 m s^–1? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 340 m s^–1.

Question

A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 m s^–1, (b) recedes from the platform with a speed of 10 m s^–1? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 340 m s^–1.

Philoid · Accepted Answer

(i) (a) Given,

Frequency of the whistle, f = 400 Hz

Speed of the train, v_T= 10 m/s

Speed of sound, v = 340 m/s

The apparent frequency (f') of the whistle as the train approaches the platform is given by

f’ = [v/(v-v_T)]f

⇒ f’ = [340/(340-10)]×400

⇒ f’ = 412.12 Hz

(b) The apparent frequency (f’') of the whistle as the train recedes from the platform is given by

f’’ = [v/(v+v_T)]f

⇒ f’ = [340/(340+10)]×400

⇒ f’ = 388.57 Hz

(ii) The apparent change in the frequency of sound is caused by the relative motions of the source and the observer. These relative motions produce no effect on the speed of sound. Therefore, the speed of sound in air in both the cases remains the same which is equal to 340 m/s.

NOTE: The Doppler effect is the phenomenon due to which there is a change in frequency or wavelength of a wave received by an observer who is moving relative to the wave source.