JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Waves & Sound

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 m / s

. Then the speed of car is ____

km / h

Answer: 132

Solution

The wall first acts as a stationary observer and receives

f_{1} = f_{0} \frac{v}{v - v _{c}}

from the approaching horn. It reflects that sound unchanged, and the driver, now moving towards this stationary source, hears

f_{2} = f_{1} \frac{v + v _{c}}{v} = f_{0} \frac{v + v _{c}}{v - v _{c}}

With

f_{0} = 400

Hz,

f_{2} = 500

Hz and

v = 330

m/s,

\frac{5}{4} = \frac{330 + v _{c}}{330 - v _{c}} ⟹ 1650 - 5 v_{c} = 1320 + 4 v_{c}

v_{c} = \frac{330}{9} = 36.67

m/s. Converting, the speed of the car is

36.67 \times \frac{18}{5} = 132

km/h.

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Integer answer