Question

A car is travelling on a straight road running along a field. A person standing at a distance of 'd' from the road. If the speed of car is 30 $m{s}^{-1}$ and the actual frequency of its horn is 297 Hz. If the frequency heard by the observer when the car is closest to him is $\frac{75x}{2}$ Hz then x is :
(the velocity of sound in air is 300 $m{s}^{-1}$)

Answer 1

The frequency heard by the observer is ,$f^{\prime }=\frac{vf}{v-u\cos \theta }$ where $v,u$ velocity of sound and car and $f$ be actual frequency of horn.

Here, $\cos \theta =ut/vt=u/v$

$\therefore f^{\prime }=\frac{vf}{v-u\left(u/v\right)}=\frac{v^{2}f}{v^2-u^2}=\frac{(300{)}^2\times 297}{(300{)}^2-(30{)}^2}=300Hz$

thus, $\frac{75x}{2}=300\Rightarrow x=8$