Q 11-14-087JEE MainJEE Main 2021 (20 Jul, Shift 1)Medium
The frequency of a car horn encountered a change from 400 Hz to 500 Hz. When the car approaches a vertical wall. If the speed of sound is $330\ \text{m s}^{-1}$. Then the speed of car is ______ km h$^{-1}$.
Numerical value type. Enter your answer.
Answer: 132
The driver hears the echo: the wall receives the sound from a moving source and the driver is a moving observer:
$$f' = f\frac{v + u}{v - u} \Rightarrow \frac{500}{400} = \frac{330 + u}{330 - u}$$
$4(330 + u) = 5(330 - u) \Rightarrow 9u = 330 \Rightarrow u = \dfrac{110}{3}$ m/s $= 132$ km/h.
Solution by Sreeraj P, M.Sc Physics