Question

An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 89 km/hr. The speed of sound n the air is 343 m/s.

A) What is the frequency heard by a person standing beside the road in front of the car?

B) What is the frequency heard by a person standing beside the road behind the car?

Answer 1

Given

frequency of the singer is f = 600 Hz , moving with a speed vs = 89 km/hr = 89*5/18 m/s = 24.72 m/s

the speed of sound in air is v = 343 m/s , speed of the person is vo =0 m/s

from doppler effect  

A)

the frequency heard by the a person standing beside the road in front of the car is

f' = f (v+vs)/(v-v0)

f' = 600 (343+24.72)/(343) Hz

f' = 643.242 Hz

B)

the frequency heard by a person standing beside the road behind the car is

f' = f (v-vs)/(v-v0)

f' = 600 (343-24.72)/(343) Hz

f' = 556.758 Hz