Waves

Let car B be the observer (moving towards S). The frequency observed is $f_1$ = $f_0 \left( \frac{c+v}{c} \right)$ When sound gets reflected, the frequency observed by source S is $f_2$ = $f_1 \left( \frac{c}{c-v} \right)$ where V is the speed of car and C is the speed of sound. Therefore, $f_2$ = $f_0 \left( \frac{c+v}{c-v} \right)$ Now, $df_x$ = $f_0 \left[ \frac{(c-v)dv - (c+v)(-dv)}{(c-v)^2} \right]$ = $\frac{2 f_0 c dv}{(c-v)^2}$ That is, $\frac{2 f_0 c dv}{(c-v)^2}$ = $\left( \frac{1.2}{100} \right) f_0$ ⇒ $dv$ = $\frac{1.2}{100} \times \frac{(c-v)^2}{2c}$ Since v << c, we get c − v ~ c. Therefore, dv = $\frac{1.2}{100} \times \frac{c}{2}$ = 1.98 m/s = 1.98 × $\frac{18}{5}$ km/h = 7 km/h