A source of sound and an observer are moving away from each other with a speed of $20\ \mathrm{ms}^{-1}$.…
A source of sound and an observer are moving away from each other with a speed of $20\ \mathrm{ms}^{-1}$. Find the apparent frequency heard by the observer, if original frequency of the source is $100\ \mathrm{Hz}$. (Take, speed of sound in air = $330\ \mathrm{ms}^{-1}$)
Solution
Sol. Given, $v_0 = v_s = 20\ \mathrm{ms}^{-1}$
Apparent frequency heard by the observer,
$ f' = \left(\frac{v - v_o}{v + v_s}\right) f = \left(\frac{330 - 20}{330 + 20}\right) 100\ \mathrm{Hz}$
$= \left(\frac{310}{350}\right) 100\ \mathrm{Hz} = 88.57\ \mathrm{Hz}$
Answer: $88.57\ \mathrm{Hz}$