1. Tardigrade
  2. Question
  3. Physics
  4. 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.

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Q. 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.

Waves

Solution:

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