Question

A train, standing in a station yard, blows a whistle of frequency $400Hz$ in still air. The wind starts blowing in the direction from the yard to the station with a speed$10m{{s}^{-1}}$ . Which of the following statements is correct? $\left( \text{Speed of sound is still air 340m}{{\text{s}}^{-1}} \right)$
A.The frequency of sound heard by an observer standing on the platform is $400Hz$
B.The speed of sound for the observer standing on the platform is $330m{{s}^{-1}}$
C.The frequency of the sound as heard by the observer standing on the platform will increase
D.The frequency of sound as heard by the observer standing on the platform will decrease

Answer 1

The frequency of the sound changes only when there is a relative motion between the source and the observer; the wind speed may increase or decrease the speed of the sound depending upon the direction of the wind travel relative to the direction of the motion of the train.

Complete answer:
We know that the frequency of the sound changes only when there is a relative motion between the source and the observer. Since in the above given problem both the train and the observer are at rest so there is no relative motion between the train and the observer.
But the wind is blowing with a speed of $10m{{s}^{-1}}$ in the direction from the yard to the station which can only change the speed of sound received by the observer but it can’t change the frequency of the sound blown by the train. The only thing that can change the frequency of the sound is the relative motion between the source and the observer.
Since there is no relative motion between the source and the observer as both of them are at rest, there is no change in the frequency of sound heard by the observer that is the observer will hear with the same frequency that the train blows the vessel.
Hence the observer will hear the vessel with the same frequency that is $400Hz$

Hence option (A) is the correct answer.

Note:
Here in this case the wind is blowing towards the yard which increases the speed of the sound that is the speed of the sound with which the observer will heard the vessel is $speed\text{ }of\text{ }air\text{ }+wind\text{ }speed$ that is $340+10=350m{{s}^{-1}}$