JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Waves & Sound

Two cars are approaching each other at an equal speed of

7.2 km / hr

. When they see each other, both blow horns of 676 Hz . The beat frequency heard by each driver will be ____ Hz . [Velocity of sound in air is

340 m / s

]

Answer: 8

Solution

Each car moves at

7.2 km h^{- 1} = 2 m s^{- 1}

. The horn on a driver's own car is at rest relative to that driver and reaches the ear unshifted at

676

Hz. The other horn is a source approaching at

2 m s^{- 1}

while the listener approaches it at

2 m s^{- 1}

, so

f^{'} = f (\frac{v + v _{o}}{v - v _{s}}) = 676 (\frac{340 + 2}{340 - 2}) = 676 \times \frac{342}{338} = 684 Hz

The two frequencies superpose at the ear, so the beat frequency heard by each driver is

684 - 676 = 8

Hz.

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Numerical answer