Question

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 $n^{\prime }$ of the sound as heard by the observer is plotted as a function of time $t$ (figure.). Identify the expected curve.

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Whistling train is the source of sound, $v_s=V$.
Before crossing a stationary observer on station, frequency heard is
$n^{\prime }=\frac{vn}{\left(v-v_s\right)}=\frac{vn}{v-V}=$ constant and $n^{\prime }>n$.
Here, $v$ is velocity of sound in air and $n$ is actual frequency of whistle.
After crossing the stationary observer, frequency heard is
$n^{\prime }=\frac{vn}{\left(v+v_s\right)}=\frac{vn}{v+V}=$ constant and $n^{\prime }<n$
Therefore, the expected curve is (c).