Ncert Exercises & Solutions

A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. The train begins to move with a speed of $10 {ms}^{- 1}$ towards the platform. What is the frequency of the sound for an observer standing on the platform? (sound velocity in air = 330 ${ms}^{- 1}$ )

Hint: Use the concept of Doppler's effect.

As the source (train) is moving towards the observer (platform), hence the apparent frequency observed is more than the natural frequency.

Frequency of whistle,

ν

= 400 Hz

Speed of train,

v_{t} = 10 m / s

The velocity of sound in air, v=330 m/s

Step 1: Find the apparent frequency of the source.

Apparent frequency when the source is moving,

ν_{app} = (\frac{v}{v - v_{t}}) ν

= (\frac{330}{320 - 10}) 400

ν_{app} = \frac{330}{320} \times 400 = 412.5 Hz

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