Simple Nature - Light and Matter

a frequency that is lower than normal.
The Doppler effect will also occur if the observer is moving but
the source is stationary. For instance, an observer moving toward a
stationary source will perceive one crest of the wave, and will then be
surrounded by the next crest sooner than she otherwise would have,
because she has moved toward it and hastened her encounter with
it. Roughly speaking, the Doppler effect depends only the relative
motion of the source and the observer, not on their absolute state
of motion (which is not a well-defined notion in physics) or on their
velocity relative to the medium.
Restricting ourselves to the case of a moving source, and to waves
emitted either directly along or directly against the direction of mo-
tion, we can easily calculate the wavelength, or equivalently the
frequency, of the Doppler-shifted waves. Letube the velocity of the
source. The wavelength of the forward-emitted waves is shortened
by an amountuTequal to the distance traveled by the source over
the course of one period. Using the definitionf= 1/Tand the equa-
tionv=fλ, we find for the wavelengthλ′of the Doppler-shifted
wave the equation

λ′=

(

1 −

u

v

)

λ.

A similar equation can be used for the backward-emitted waves, but
with a plus sign rather than a minus sign.

Doppler-shifted sound from a race car example 6

.If a race car moves at a velocity of 50 m/s, and the velocity of

sound is 340 m/s, by what percentage are the wavelength and

frequency of its sound waves shifted for an observer lying along

its line of motion?

.For an observer whom the car is approaching, we find

1 −

u

v

= 0.85,

so the shift in wavelength is 15%. Since the frequency is inversely

proportional to the wavelength for a fixed value of the speed of

sound, the frequency is shifted upward by

1/0.85 = 1.18,

i.e., a change of 18%. (For velocities that are small compared

to the wave velocities, the Doppler shifts of the wavelength and

frequency are about the same.)

Doppler shift of the light emitted by a race car example 7

.What is the percent shift in the wavelength of the light waves

emitted by a race car’s headlights?

.Looking up the speed of light in the back of the book,v= 3.0×

108 m/s, we find

1 −

u

v

= 0.99999983,

Section 6.1 Free waves 369