A Classical Approach of Newtonian Mechanics

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