a police car moving at a constanr velocity with its siren on passes a starionary listener the frequency changes the sound of siren detected by the listener 170Hz and drops to 130Hz. take the speed of sound in air to be 340m.s^-1
1} calculate the speed of the police car
The Doppler effect formula for sound is given by:
f' = f((v + vo)/(v + vs))
Where:
f = frequency of the sound emitted by the source (police car)
f' = frequency of the sound detected by the listener
v = speed of sound in air (340 m/s)
vo = velocity of the observer (listener)
vs = velocity of the source (police car)
Given:
f = 170 Hz
f' = 130 Hz
First, let's calculate the ratio of the frequencies:
f'/f = (v + vo)/(v + vs)
130/170 = (340 + 0)/(340 + vs)
0.7647 = 340/(340 + vs)
0.7647(340 + vs) = 340
259.5298 + 0.7647vs = 340
0.7647vs = 80.4702
vs = 80.4702/0.7647
vs = 105.25 m/s
Therefore, the speed of the police car is 105.25 m/s.