A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be ........ Hz.

As source and detector move away from each other as shown below

$\underset{\mathrm{Source}}{\leftarrow } \underset{\mathrm{Detector}}{\to }$

${\mathrm{v}}_{\mathrm{s}}=$velocity of source with respect to ground = 20 m/s

${\mathrm{v}}_{\mathrm{d}}=$velocity of detector with respect to ground = 20 m/s

According to Doppler’s effect,

$\begin{array}{l}{\mathrm{f}}_{\text{apparent }}=\frac{\mathrm{f}\left({\mathrm{v}}_{\text{sound }}-{\mathrm{v}}_{\mathrm{d}}\right)}{\left({\mathrm{v}}_{\text{sound }}+{\mathrm{v}}_{\mathrm{s}}\right)}\\ \Rightarrow 1800=\frac{\mathrm{f}(340-20)}{(340+20)}\\ \Rightarrow 1800=\mathrm{f}\left(\frac{320}{360}\right)\\ \mathrm{f}=\frac{1800\times 36}{32}\\ =\frac{1800\times 9}{8}\\ =\frac{16200}{8}\\ \Rightarrow \mathrm{f}=2025\mathrm{Hz}\end{array}$