Q 11-14-084JEE MainJEE Main 2021 (24 Feb, Shift 2)Medium
Two cars are approaching each other at an equal speed of 7.2 km hr$^{-1}$. When they see each other, both blow horns having a frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m s$^{-1}$.]
Numerical value type. Enter your answer.
Answer: 8
Speed of each car: $u = 7.2$ km/h $= 2$ m/s. Each driver hears the other car's horn (moving source, moving observer, approaching):
$$f' = 676\times\frac{340 + 2}{340 - 2} = 676\times\frac{342}{338} = 684\ \text{Hz}$$
It beats with the driver's own horn (676 Hz): beat frequency $= 684 - 676 = 8$ Hz.
Solution by Sreeraj P, M.Sc Physics