A car is moving with a speed of 72 km `"hour"^(-1)` towards a roadside source that emits sound at a frequency of 850 Hz. The car driver listens to the sound while approaching the source and again while moving away from the source after crossing it. If the velocity of sound is 340 `ms^(-1)` the difference of the two frequencies, the driver hears is

Options

A. 50 Hz
B. 85 Hz
C. 100 Hz
D. 150 Hz

Answer

C

Explanation

Here, velocity of the car,
`v_("cat") = 72 km "hour"^(-1) = 72 xx 5/18 ms^(-1) = 20 ms^(-1)`
Velocity of sound, `v= 340 ms^(-1)`
frequency of source, `v= 850 Hz`
while approaching the source
`u.. = u((v+v_("car"))/v)`
while moving away from the source,
`u.. = u((v-v_("car"))/v)`
Difference in frequencies, `Deltau = u.-v..`
`=(2uv_("car"))/v`
`=(2 xx 850 xx 20)/340 = 100 Hz`