Question

A train blows a whistle of frequency $640Hz$ in air. Find the difference in apparent frequencies of the whistle for a stationary observer, when the train moves towards and away from the observer with the speed of $72km/hr$
[Speed of sound in air $=340m/s$]

Answer 1

Given : $V_S=72km/hr=20m/s$, $n=640Hz$, $V=340m/s$
To find : $nA-n{A}^{\prime }=$ ?
Formula : (a) When the train moves towards the stationary observer then
$n_A=n\left(\frac{V}{V-V_S}\right)$
(b) When the train moves away from the stationary observer then
$n_{A^{\prime }}=n\left(\frac{V}{V+V_S}\right)$
Calculation from formula (a)
$n_A=640\left[\frac{340}{340-20}\right]$
$n_A=680Hz$
From formula (b)
$n_{A^{\prime }}=640\left[\frac{340}{340+20}\right]$
$n_{A^{\prime }}=604.4Hz$
Difference in apparent frequency $=680-604.4=75.6Hz$.