Q 11-14-108JEE MainJEE Main 2020 (4 Sep, Shift 2)Medium
The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from $420\ \text{Hz}$ to $490\ \text{Hz}$ when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is $330\ \text{m s}^{-1}$:
Answer: (A) $91\ \text{km h}^{-1}$
The wall receives (and reflects) the frequency of a moving source; the driver is a moving observer for the echo:
$$f' = f\,\frac{v + v_b}{v - v_b} \Rightarrow \frac{490}{420} = \frac76 = \frac{330 + v_b}{330 - v_b}$$
$13v_b = 330 \Rightarrow v_b \approx 25.4\ \text{m s}^{-1} \approx 91\ \text{km h}^{-1}$.
Solution by Sreeraj P, M.Sc Physics