11.2 THE DOPPLER EFFECT
Notes
III. HOW THE DOPPLER EFFECT WORKS WITH SOUND
A. SOUND FREQUENCY AND PITCH
The frequency of sound waves is proportional to the pitch that we hear. DEMO Tuning Forks
↑f = higher pitch
and
↓f = lower pitch
You know that the pitch of the note from the siren of a
fast-travelling ambulance or police car appears to a stationary
observer to drop suddenly as it passes. This means that the
frequency changes as the object passes. But the frequency
does not really change (ask the person driving the vehicle!)
DEFINE: Doppler Effect : The apparent change in the
frequency of a wave motion when there is relative motion
between the source and the observer
Source: Physics for the IB Diploma Study Guide, Kirk
Occurs with electromagnetic waves as well as with sound and water waves.
The human ear is amazingly sensitive to small changes in pitch. The human ear can hear
frequencies between about 20 Hz and 20 kHz (< 20 Hz is called infrasonic, and > 20 kHz is
called ultrasonic). The equations here hold for sound waves.
Figures (a) and (b) show a truck sounding a siren at rest and moving. In figure (b), the
wavelengths in front of the truck are shorter than the ones behind it. The speed of sound is the
same ahead of and behind the truck, and v = fλ. Therefore, f and λ are inversely proportional.
So,
↑λ
means
↓f
which means
↓ pitch (behind)
and
↓λ
means
↑f
which means
↑ pitch (in front).
Source: Physics, 8th Ed, Cutnell & Johnson
1
Generally, remember:
so
Source: Physics for the IB Diploma, 5th Ed, Tsokos
B. STATIONARY OBSERVER AND A MOVING SOURCE
us
and
In this case:
Let v = speed of wave
v
Let us = speed of source
In 1 s, first wave moves v towards
observer
us
In 1 s, source emits f waves
In 1 s, source moves us towards
observer
v - us
f wavefronts in this
distance
f waves contained in a distance v - us
separation of waves (wavelength) is
so
source moving towards observer
source moving away from observer
Check that if us = 0, then f’ = f ? YES.
NOTE THAT:
λ ≠ λ’
Graph of f against d looks like this:
Source: Physics for the IB Diploma, 5th Ed, Tsokos
2
C. MOVING OBSERVER AND A STATIONARY SOURCE
Let u0 = speed of observer approaching source = us
Think of as a moving source (relative speeds are what is important; distance closing between
observer and source)
Observer measures higher waves speed = v + u0
So,
becomes
(
)
(
)
NOTE THAT:
(
(
)
)
or
observer moving towards source
observer moving away from source
λ = λ’
WATCH AP LESSON 45 – SOUND WAVES AND THE DOPPLER EFFECT
DO HW #5,8
IV. HOW THE DOPPLER EFFECT WORKS WITH EM WAVES
A. LIGHT FREQUENCY AND COLOR
Source: Physics, 8th Ed, Cutnell & Johnson
REMEMBER: The speed of EM waves is 2.99792458 x 108 m/s = ‘c’.
↓ f = reds and oranges
↑ f = blues and purples
LIGHT, SINCE A WAVE, UNDERGOES A DOPPLER SHIFT ALSO!
3
B. THE RED SHIFT OF THE UNIVERSE
In the Doppler shift for sound the velocities, uo and us are always measured relative to the air.
There is also a Doppler Effect for electromagnetic waves in empty space, such as light waves or
radio waves. In this case there is no medium that we can use to measure velocities and all that
matters is the relative velocity of the source and receiver. Note this was not the case with
sound, because we always incorporated the speed of sound which was determined mainly by
the medium and its temperature.
Provided the speed of the source or observer << c, the Doppler effect for EM waves is given
by the following:
where
v = speed of source or observer
c = speed of light
f = frequency emitted
Remember the EM visible light
spectrum (from about 4 x 1014 Hz
to about 7.9 x 1014 Hz).
Source: Physics, 8th Ed, Cutnell & Johnson
Astronomers use the Doppler effect for light to calculate speeds of distant stars and galaxies.
Astronomers know the chemical makeup of stars and hence their ‘true’ color. By comparing the
line spectrum of light from the star with light from a laboratory source, the Doppler shift of the
star's light can be measured. Then the speed of the star can be calculated!
Stars moving towards Earth show a ‘blue shift’. This is because the wavelengths of light
emitted by the star are shorter than if the star had been at rest (frequency is higher, wavelength
is shorter). So the spectrum is shifted towards shorter wavelengths, i.e. to the blue end of the
spectrum.
Stars moving away from the Earth show a ‘red shift’. The emitted waves have a longer
wavelength than if the star had been at rest, so the spectrum is shifted towards longer
wavelengths, i.e. towards the red end of the spectrum.
Astronomers have discovered that all the distant galaxies are moving away from us and by
measuring their red shifts, they have estimated their speeds. The furthermost galaxies have
been estimated to have speeds approaching the speed of light.
4
V. OTHER USES AND APPLICATIONS OF THE DOPPLER EFFECT
Besides using the Doppler Effect to determine recession speeds of distant celestial bodies, it is also
used in:
-
Determining the speed of rotation of the sun. Photographs are taken of opposite edges of
the sun; each contains absorption lines due to elements such as iron vaporized in the sun, and
also some absorption lines due to oxygen in the earth’s atmosphere. When the two
photographs are put together so that the oxygen lines coincide, the iron lines in the two
photographs are displaced relative to one another. Measurements show a rotational speed of
about 2 kms-1.
-
Radar speed guns. Microwaves are emitted from a transmitter in short bursts. Each burst
reflects off any obstacle in the path of the microwaves. In between sending out bursts, the transmitter is open to detect reflected microwaves. If the reflection is caused by a moving obstacle,
the reflected microwaves are Doppler-shifted. By measuring the Doppler shift the speed at
which the obstacle moves (along the line between it and the transmitter/receiver) can be calculated.
-
Medicine. Measuring the speed of blood flow through arteries.
-
Meteorology. Wind fields in thunderstorms are observed to determine whether there is
rotation in the cloud indicating the presence of a tornado.
Source: http://www.crh.noaa.gov
DO HW #10
5