Ncert Exercises & Solutions

A train whistling at constant frequency is moving towards a station at a constant speed v. The train goes past a stationary observer on the station. The frequency n' of the sound as heard by the observer is plotted as a function of time t (figure). Identify the expected curve.

1.

2.

3.

4.

(3) Hint: Use the concept of Doppler's effect.

Step 1: Find the frequency when the train is approaching the station.

Let the original frequency of the source is

n_{0}

.

Let the speed of the sound wave in the medium is v.

As observer is stationary.

Apparent frequency when the train is approaching,

n_{a} = (\frac{v}{v - v_{s}}) n_{o}

= (\frac{v}{v - v_{s}}) n_{o} = n_{a} > n_{o}

It is a constant value.

Step 2: Find the frequency when the train is receding from the station.

When the train is going away from the observer,

Apparent frequency,

n_{a} = (\frac{v}{v + v_{s}}) n_{o} = n_{a} < n_{o}

It is also a constant value.

Hence, the expected curve is (3).