Waves Part 1

Given, velocity of car X, $v_{x}=36\,\text{kmh}^{-1}=36 \times \frac{5}{18}\,\text{ms}^{-1}=10\,\text{ms}^{-1}$ Velocity of car $Y,\,v_{y}=72\,\text{kmh}^{-1}$ $=72 \times \frac{5}{18}\,\text{ms}^{-1}=20\,\text{ms}^{-1}$ Frequency of sound heard by passenger in car Y emitted by passenger in car X, f′ =1320 Hz Velocity of sound, $v_{s}$ = 340 m/s. By Doppler’s effect, $f'=\frac{f(v_{s} \pm v_{O})}{(v_{s} \mp v_{s})}$ Velocity of observer is equal to velocity of car, $v_{o}=20\,\text{ms}^{-1}$ Velocity of source is equal to velocity of car X, $v_{s}=10\,\text{ms}^{-1}$ Substituting the values in above expression, we get $1320=\frac{f(340+20)}{(340-10)}$ $\Rightarrow 1320=\frac{360 f}{330}$ $\Rightarrow f=1320 \times \frac{11}{12}=1210\,\text{Hz}$ Thus, the actual frequency is 1210 Hz.