phy1020.DVI

Chapter 12

The Doppler Effect

You have probably noticed that the frequency of sound emitted by a moving source depends on its speed; for
example, when you’re standing by the side of a road near fast-moving traffic, the engine sounds decrease in
frequency as the car passes you. (This is especially noticeable at the Indianapolis 500, for example.) This
effect is called theDoppler effect, after Christian Doppler, an Austrian physicist who first described the effect
in the 19th century.
This change in frequency is observed whether the source or the observer is moving. If the source and
observer are getting closer together, the frequency ishigherthan if both were stationary; if they are getting
farther apart, the frequency islower.
A little thought reveals why this is. If thesourceof the sound is moving toward a stationary observer,
then the source will have moved in between emitting wave fronts, causing effective wavelength to be shorter,
resulting in a higher frequency heard by the observer. On the other hand, if theobserverof the sound is
moving toward a stationary source, then the observer runs into the wavefronts faster than if he were stationary,
so he hears a higher frequency.
The frequency shift my be described by the following equation, which covers either the source or the
observer moving (or both):

f^0 Df



vsnd ̇vobs

vsndvsource



: (12.1)

Herefis the frequency emitted by the source, andf^0 is the frequency heard by the observer. Three speeds
go into this equation, and they are all measured with respect to the air:vsndis the speed of sound (nominally
343 m/s);vobsis the speed of the observer, andvsourceis the speed of the source of the sound. All of these
speeds are taken to be positive; the directions are taken into account with the ̇andsigns. The rule for
using these signs is:

“Top sign toward, bottom sign away.”

In other words, if the source and observer are moving toward each other, we use the top signs:Cin the
numerator andin the denominator. If they are moving away from each other, we use the bottom signs:
in the numerator andCin the denominator. To be fully explicit:

• If the observer is movingtowardthe source, useCin the numerator.


• If the observer is movingawayfrom the source, usein the numerator.


• If the source is movingtowardthe observer, usein the denominator.


• If the source is movingawayfrom the observer, useCin the denominator.