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 (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 ${\mathrm{n}}_{0}$
Let the speed of the sound wave in the medium is v. As observer is stationary.
Apparent frequency when the train is approaching,
${\mathrm{n}}_{\mathrm{a}}=\left(\frac{\mathrm{v}}{\mathrm{v}-{\mathrm{v}}_{\mathrm{s}}}\right){\mathrm{n}}_{\mathrm{o}}$
$=\left(\frac{\mathrm{v}}{\mathrm{v}-{\mathrm{v}}_{\mathrm{s}}}\right){\mathrm{n}}_{\mathrm{o}}={\mathrm{n}}_{\mathrm{a}}>{\mathrm{n}}_{\mathrm{o}}$
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, ${\mathrm{n}}_{\mathrm{a}}=\left(\frac{\mathrm{v}}{\mathrm{v}+{\mathrm{v}}_{\mathrm{s}}}\right){\mathrm{n}}_{\mathrm{o}}={\mathrm{n}}_{\mathrm{a}}<{\mathrm{n}}_{\mathrm{o}}$
It is also a constant value.
Hence, the expected curve is (3).