Question

When a car is approaching the observer, the frequency of horn is $100\, Hz$. After passing the observer, it is $50 \, Hz$. If the observer moves with the car, the frequency will be $\frac{x}{3}$ $Hz$ where $x =$ ______

Answer 1

$ f _1=100= f _0\left(\frac{ C }{ C - V _{ s }}\right) $
$ C =$ speed of sound
$ V _{ s }=$ speed of source
$ f _2=50= f _0\left(\frac{ C }{ C + V _{ s }}\right)$
$ \frac{ f _1}{ f _2}=2=\frac{ C + V _{ s }}{ C - V _{ s }} $
$ 2 C -2 V _{ s }= C + V _{ s } $
$3 V _{ s }= C $
$ V _{ S }=\frac{ C }{3}$
$ 100= f _0 \frac{ C }{\frac{2 C }{3}}=\frac{3}{2} f _0$
$ f _0=\frac{200}{3}$