13 WAVE MOTION 13.6 The Doppler effect
1
v 343
2
v
o
343
Worked example 13.4: Truck passing stationary siren
Question: A truck, moving at vo = 80 km/hr, passes a stationary police car whose
siren has a frequency of f = 500 Hz. What is the frequency change heard by the
truck driver as the truck passes the police car? The speed of sound is v = 343 m/s.
Answer: The truck’s speed is
v =
80 × 1000
3600
= 22.22 m/s.
When the truck is moving towards the police car, the siren’s apparent frequency
is
f =
1 +
vo
!
f =
1 +
22.2 2
!
× 500 = 532.3 9 Hz.
When the truck is moving away from the police car, the siren’s apparent frequency
is
f =
1 −
vo
!
f =
1 −
22.2 2
!
× 500 = 467.6 1 Hz.
Hence, the frequency shift is
∆f = f 1 − f 2 = 532.39 − 467.61 = 64.79 Hz.
Worked example 13.5: Ambulance and car
Question: An ambulance is traveling down a straight road at speed vs = 42 m/s.
The ambulance approaches a car which is traveling on the same road, in the same
direction, at speed vo = 33 m/s. The ambulance driver hears his/her siren at a
frequency of f = 500 Hz. At what frequency does the driver of the car hear the
siren? The speed of sound is v = 343 m/s.
Answer: The apparent frequency fJ of a sound wave is given by
fJ^ =
1 − vo/v
f,
1 − vs/v
where vo is the speed of the observer (i.e., the car driver), vs is the speed of the
source (i.e., the ambulance), v is the speed of sound, and f is the wave frequency