Question

A train is travelling at $120\text{kmph}$ and blows a whistle of frequency $1000\text{Hz}$. The frequencies of the sound heard by a stationary observer, if the train is approaching him and moving away from him are:

[(Velocity of sound in air $=330\text{m/s}$ and assume medium is stationary]

• A. $91\text{Hz}-111\text{Hz}$
• B. $908\text{Hz}-1112\text{Hz}$
• C. $82\text{Hz}-110\text{Hz}$
• D. $820\text{Hz}-1080\text{Hz}$

Answer 1

The correct option is B $908\text{Hz}-1112\text{Hz}$

Let $f_0$ be the frequency of sound heard by the observer, when both source of sound and observer are at rest.

Let $v$ be the velocity of sound in the stationary medium, $v_s$ be the velocity of the source of sound and $v_o$ be the velocity of the observer.

Given: $v_o=0\text{m/s}$
$v=330\text{m/s}$
$f_0=1000\text{Hz}$
$v_s=120\text{km/h}\text{or}\frac{100}{3}\text{m/s}$

When the train is moving towards the stationary observer,

$f_1=f_0\left(\frac{v}{v-v_s}\right)$

Substituting the given data,

$f_1=1000\left(\frac{330}{330-\frac{100}{3}}\right)\approx 1112\text{Hz}$

When the train is moving away from the stationary observer,

$f_2=f_0\left(\frac{v}{v+v_s}\right)$

Substituting the given data,

$f_2=1000\left(\frac{330}{330+\frac{100}{3}}\right)\approx 908\text{Hz}$

The frequencies of sound heard by the stationary observer will be $908\text{Hz}\text{and}1112\text{Hz}$​​​