CK-12-Physics - Intermediate

11.4. Doppler Effect http://www.ck12.org

the actual wavelength of the sound in the air is the same. The difference is that as we move toward the source, we
move past more waves per second. So the wavelength is unchanged, but the effective wave speed is different.

In this case, the car is the receiver of the sound rather than the source, so we will call the car’s speedvrfor velocity
of the receiver. If the car is heading toward the source, then the waves are effectively moving faster.

v′=v+vr → f′=

v′

λ

=

v+vr

λ

The effect is similar. Moving toward the source means that there is a higher frequency, so a higher pitch or note.

As before, the opposite is true if the car is moving away from the source. Because the car is moving away, the waves
have to catch up to the car, so their effective speed is slower. We can represent this by putting in a negative number
forvrin the equation above.

• Positivevris the receiver moving toward the source for faster effective wave speed


• Negativevris the receiver moving away from the source for slower effective wave speed

Source and Observer in Motion

Now let us consider if we are in a car that is chasing after an ambulance. In this case, the source of sound is moving
away with velocityvs, making a longer wavelength. The receiver is moving toward the sound with velocityvr,
making an effectively higher wave speed.

f′=

v′

λ′

=

v+vr

λ+vsT

=

v+vr

vT+vsT

=

(

1

T

)(

v+vr

v+vs

)

=f

(

v+vr

v+vs

)

Here both the velocity of the source and the velocity of the receiver are defined as before.

http://demonstrations.wolfram.com/IntroductionToTheDopplerEffect/

Check Your Understanding

a. The siren of an ambulance produces a sound of frequency 700 Hz. If the ambulance approaches a person standing
by the road with a velocity of 31.0 m/s, what is the frequency heard by the person? Take the velocity of sound to be
v=343 m/s.

Answer: The ambulance is the source of the sound moving towards a stationary receiver. The source moving toward
is an effectively shorter wavelength, so negativevs.

f′=f

v

v+vs

= (700 Hz)

(

343 m/s

343 m/s+(−31 m/s)

)

=770 Hz

b. The ambulance passes the person standing. The siren of an ambulance produces a sound of 700 Hz as it moves
away from a stationary receiver with a velocity of 31 m/s. What is the frequency perceived by the observer?

Answer:The source is moving away for an effectively longer wavelength, sovsis positive.

f′=f

v

v+vs

= (700 Hz)

(

343 m/s

343 m/s+ 31 .0 m/s

)

=642 Hz