NCERT Class 11 Physics Solutions: Chapter 15 – Waves-Part 11

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Question 15.20:

A train, standing at the outer signal of a railway station blows a whistle of frequency in still air. What is the train approaches the platform with a speed of , recedes from the platform with a speed of What is the speed of sound in each case? The speed of sound in still air can be taken as

Answer:

Explanation:

Frequency of the whistle

Speed of the train,

Speed of sound,

The apparent frequency of thewhistle as the train approaches the platform is given by the relation:

Explanation:

The apparent frequency of the whistle as the train recedes from the platform is given by the relation:

Explanation:

the relative motion is showing in figure.

Figure Shown the Relative Motion

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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, i.e.,

Question 15.21

A train, standing in a station-yard, blows a whistle of frequency in still air. The wind starts blowing in the direction from the yard to the station with at a speed of . What are the frequency, wavelength, and speed of sound for an observer standing on the station’s 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? The speed of sound in still air can be taken as

Answer:

For the stationary observer:

For the running observer: Not exactly identical

For the stationary observer:

Frequency of the sound produced by the whistle,

Speed of sound

As there is no relative motion between the source and the observer, the frequency of the sound heard by the observer will be the same as that produced by the source, i.e.,

The wind is blowing toward the observer. Hence, the effective speed of the sound increases by , i.e.,

Effective speed of the sound,

The wavelength of the sound heard by the observer is given by the relation:

For the running observer:

The observer is moving toward the source. As a result of the relative motions of the source and the observer, there is a change in frequency

This is given by the relation:

Since the air is still, the effective speed of sound

The source is at rest. Hence, the wavelength of the sound will not change, i.e., remains

Hence, the given two situations are not exactly identical.