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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 sтАУ1, (b) recedes from the platform with a speed of 10 m sтАУ1? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 340 m sтАУ1.



Answer -

(i)┬а(a)Frequency of the whistle, ╬╜ = 400 Hz

Speed of the train,┬аvT= 10m/s

Speed of sound,┬аv┬а= 340 m/s

The apparent frequency┬аof the whistle as the trainapproaches the platform is given by the relation:

(b) The apparent frequency┬аof the whistle as the trainrecedes from the platform is given by the relation:

(ii)┬аThe apparent change in the frequency of sound is caused bythe relative motions of the source and the observer. These relative motionsproduce no effect on the speed of sound. Therefore, the speed of sound in airin both the cases remains the same, i.e., 340 m/s.

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