Q 11-14-098JEE MainJEE Main 2020 (5 Sep, Shift 2)Medium
A driver in a car, approaching a vertical wall, notices that the frequency of his car horn has changed from $440$ Hz to $480$ Hz when it gets reflected from the wall. If the speed of sound in air is $345\ \text{m s}^{-1}$, then the speed of the car is:
Answer: (A) $54$ km/hr
The wall receives sound from a moving source and the driver (moving observer) receives the reflected sound, so
$$f' = f\,\frac{v+u}{v-u}$$
$$\frac{480}{440} = \frac{12}{11} = \frac{345+u}{345-u}$$
$$12(345-u) = 11(345+u) \Rightarrow 23u = 345 \Rightarrow u = 15\ \text{m/s} = 54\ \text{km/hr}$$
Solution by Sreeraj P, M.Sc Physics