PHY222 PHYSICAL OPTICS AND
DOPPLER EFFECT
by
Mr. Y. Kalolo
Lecture 2 DOPPLER EFFECT
Table Of Contents
1. The Electromagnetic Spectrum
2. The Doppler Effect
Section 1:
The Electromagnetic Spectrum
THE ELECTROMAGNETIC SPECTRUM
THE ELECTROMAGNETIC SPECTRUM
An electromagnetic (EM) wave, like any periodic wave, has a
frequency f and a wavelength λ that are related to the
speed v of the wave by v = f λ
For EM waves travelling through a vacuum, or to a good
approximation, through air, the speed is v = c, so c = f λ
EM waves exist with an enormous range of frequencies,
from values less than 104 Hz to greater than 1024 Hz
Since all these waves travel through a vacuum at the same
speed of c = 3.00 x 108 m/s, equation c = f λ can be used
to find the correspondingly wide range of wavelengths.
The ordered series of electromagnetic wave frequencies or
wavelengths is called the electromagnetic spectrum.
THE ELECTROMAGNETIC SPECTRUM
© Cutnell J.D. & Johnson K.W. (2010) Introduction to Physics, 8 th Ed. John Wiley & Sons Pvt Ltd
REGIONS OF THE EM SPECTRUM
Historically, regions of the spectrum have been given names such as
radio waves and infrared waves. Although the boundary between
adjacent regions is shown as a sharp line in the drawing, the boundary is
not so well defined in practice, and the regions often overlap.
Beginning on the left in the spectrum, we find radio waves. Lower-
frequency radio waves are generally produced by electrical oscillator
circuits, while higher-frequency radio waves (called microwaves) are
usually generated using electron tubes called klystrons.
Infrared radiation (heat waves), originates with the vibration and
rotation of molecules within a material.
Visible light is emitted by hot objects, such as the sun, a burning log, or
the filament of an incandescent light bulb, when the temperature is high
enough to excite the electrons within an atom.
Ultraviolet frequencies can be produced from the discharge of an
electric arc.
X-rays are produced by the sudden deceleration of high-speed
electrons.
And, finally, gamma rays are radiation from nuclear decay.
VISIBLE LIGHT
Our eyes are only sensitive to visible light.
Only waves with frequencies between about 4.0 x 1014 Hz
and 7.9 x 1014 Hz are perceived by the human eye as visible
light (visible light is the most narrow in the spectrum)
Usually visible light is discussed in terms of wavelengths (in
vacuum) rather than frequencies.
The wavelengths of visible light are extremely small and,
therefore, are normally expressed in nanometers (nm);
1 nm = 10-9 m.
An obsolete (non-SI) unit occasionally used for wavelengths
is the angstrom (Å);
1 Å = 10-10 m.
Example 1: The Wavelength of Visible Light
Find the range in wavelengths (in vacuum) for visible light in the
frequency range between 4.0 x 1014 Hz (red light) and 7.9 x 1014 Hz
(violet light). Express the answers in nanometers.
VISIBLE LIGHT
The eye/brain recognizes light of different wavelengths as
different colors. A wavelength of 750 nm (in vacuum) is
approximately the longest wavelength of red light, whereas
380 nm (in vacuum) is approximately the shortest
wavelength of violet light. Between these limits are found
the other familiar colors.
The association between color and wavelength in the visible
part of the electromagnetic spectrum is well known.
The wavelength also plays a central role in governing the
behavior and use of electromagnetic waves in all regions of
the spectrum. For instance, the next Conceptual Example
considers the influence of the wavelength on diffraction.
Conceptual Example 2: The Diffraction of AM and FM Radio Waves
As discussed in previous section, diffraction is the ability of
a wave to bend around an obstacle or around the edges of an
opening. Based on that discussion, which type of radio wave
would you expect to bend more readily around an obstacle
such as a building, (a) an AM radio wave or (b) an FM radio wave?
Section 10:
The Doppler Effect
THE DOPPLER EFFECT
Have you ever heard an approaching fire truck and noticed
the change in the sound of the siren as the truck passes?
While the fire truck approaches, the pitch of the siren
is relatively high, but as it passes and moves away,
the pitch suddenly drops.
• Something similar, but less familiar, occurs when an
observer moves towards or away from a stationary source
of sound.
• Such phenomena are collectively referred to as the Doppler
Effect.
THE DOPPLER EFFECT
The Doppler effect is the apparent change in the frequency
of a wave motion when there is relative motion between the
source and the observer.
Named after Christian Johann Doppler (1803-1853)
Doppler effect occurs in both sound waves (siren or train
horn) and light waves
Amount of the shift and its sign depends on
– relative speed of the source & observer
– direction (towards or away)
Moving Source
• Consider the sound emitted by a siren
of a stationary fire truck
• Each solid blue arc represents a
condensation of the sound wave
• In Figure (a). sound pattern is
symmetrical, listener standing in
front of or behind the truck detect
the same number of condensations
per second, and consequently, hear
same frequency.
• Once truck begins to move ahead of
truck the condensations are now closer
together, resulting in decrease in
wavelength of the sound (Figure b.)
• This “bunching-up” is because truck
“gains ground” on a previously emitted
condensation before emitting the next
one.
Moving Source 2..
• Since the condensations are closer
together, the observer standing in front
of the truck senses more of them
arriving per second than she does when
the truck is stationary.
• The increased rate of arrival
corresponds to a greater sound
frequency, which the observer hears as a
higher pitch.
• Behind the moving truck, the
condensations are farther apart than
they are when the truck is stationary.
• This increase in the wavelength occurs
because the truck pulls away from
condensations emitted toward the rear.
• Consequently, fewer condensations per
second arrive at the ear of an observer
behind the truck, corresponding to a
smaller sound frequency or lower pitch.
Moving Source 3..
• If the stationary siren in Figure a.
emits a condensation at the time t =0
s, it will
emit the next one at time T, where T is
the period of the wave.
• The distance between these two
condensations is the wavelength (λ) of
the sound produced by the stationary
source
Moving Source 4..
Moving Source 5..
• But for the stationary siren, we have and
Source moving
toward stationary
observer:
….Eqn 1.
Moving Source - Away
• The same reasoning that led to Equation 1 can be used to
obtain an expression for the observed frequency fo:
Source moving
away from
stationary
….Eqn 2.
observer
Example 1: The Sound of a Passing Train
A high-speed train is traveling at a speed of 44.7 m/s (100 mi/h) when
the engineer sounds the 415 Hz warning horn. The speed of sound is 343
m/s. What are the frequency and wavelength of the sound, as perceived
by a person standing at a crossing, when the train is (a) approaching and
(b) leaving the crossing?
Moving Observer
Moving Observer 2..
Observer moving
toward stationary
….Eqn 3. source:
Moving Observer - Away
Observer moving
away from
stationary source:
….Eqn 4.
Moving Source vs Moving Observer
• It should be noted that the physical mechanism producing
the Doppler effect is different when the source moves and
the observer is stationary than when the observer moves
and the source is stationary:
Example 2: An Accelerating Speedboat and the Doppler Effect
A speedboat, starting from rest, moves along a straight line away from a
dock. The boat has a constant acceleration of +3.00 m/s2 (see figure below).
Attached to the dock is a siren that is producing a 755 Hz tone. If the air
temperature is 20 °C, what is the frequency of the sound heard by a person
on the boat when the boat’s displacement from the dock is +45.0 m?
An Accelerating Speedboat
Moving Source vs Moving Observer
summary
Moving Source
change in f
Moving Observer
change in relative velocity f
Moving Source and Observer
change in and relative velocity f
General Case
Source and
observer both
moving:
….Eqn 5.
• In the numerator, the plus sign applies when the observer moves toward the
source, and the minus sign applies when the observer moves away from
source.
• In the denominator, the minus sign is used when the source moves toward
the observer, and the plus sign is used when the source moves away from
the observer.
Equations –
Moving Source and Moving Observer
vs vo vs vo
S O S O
vs vo vs vo
S O S O
source vs observer vo observed
frequency
fo
stationary stationary = fs
stationary receding < fs
stationary approachin > fs
g
receding stationary < fs
approaching stationary > fs
receding receding < fs
approaching approachin > fs
g
approaching receding ?
receding approachin ?
g CP 595
THE DOPPLER EFFECT IN LIGHT
Works same as it does for sound
Light moving away from the observer
o Decrease in measured frequency
o Wavelength gets longer: REDSHIFT
Light moving towards the observer
o Increase in measured frequency
o Wavelength gets shorter: BLUESHIFT
Red Shift
A r e d s h i f t i s an y d e c r e as e i n f r e q u e n c y , w i t h a
corresponding increase in wavelength, of an electromagnetic
wave;
In visible light, this shifts the color from the blue end of the
spectrum to the red end.
The Doppler Red shift results from the relative motion of
the light emitting object and the observer. If the source of
light is moving away from you then the wavelength of the
light is stretched out, i.e., the light is shifted towards the
red.
Blue Shift
A bl u e s h i f t i s an y i n c re as e i n f re q u e n c y , w i th a
co rresp o nding decrease in w avelength, o f an
electromagnetic wave;
In visible light, this shifts the color from the red end of
the spectrum to the blue end.
The Doppler Blue shift results from the relative motion of
the light emitting object and the observer. If the source of
light is moving toward you then the wavelength of the light
is compressed, i.e., the light is shifted towards the blue.
Light experiences the Doppler Effect too!
Objects that
are moving
quickly away
from us have
their
wavelength
shifted
toward the
RED end of
the
Objects that are moving
spectrum
quickly toward us have their
wavelength shifted toward
the BLUE end of the
spectrum
USES OF THE DOPPLER SHIFT:
In Astronomy
Radio astronomers can find the motion of a source (stars,
galaxies, gases, etc.) by observing whether the emission or
absorption lines in its spectrum are shifted in wavelength
relative to their wavelengths at rest
Light From Distant Cosmic Objects is Doppler
Shifted
The same spectral lines
seen in a distant galaxy
Sun’s optical cluster - shifted to a
spectral lines longer wavelength / lower
frequency by the Doppler
Effect
Radar and the Doppler Effect in Meteorology
Radar waves are scattered off of a target in the atmosphere
such as rain drops, which act as tracers for the wind’s velocity.
So…if the wind is moving towards the radar, the returning radio
waves will be shifted to higher frequencies, and if moving away
from the radar, the radio waves will be shifted to lower
frequencies.
higher
lower
NEXRAD = NEXt Generation Weather RADar
(based on Doppler-shifted radar) is used to
identify storms that are likely to spawn
Doppler Radar for Hurricane Katrina
tornadoes
The Doppler Effect in Meteorology
Radar (Radio Detection and Ranging)
transmits microwaves to detect
precipitation particles in the atmosphere
(such as rain, snow, and hail).
After a radar sends out a signal, it "
listens" for returning signals. A returning
signal, called an echo, occurs when the
transmitted signal strikes and reflects
off objects (raindrops, ice, snow, trees,
buildings, mountains, birds, or even
insects) within its path. A Doppler Radar Tower
Part of the reflected signal is received
back at the radar. The amount and type
of precipitation that is falling can be
determined.
The Doppler Effect in Bats
Bats navigate by emitting high frequency sound
waves
(ultrasonic) and then detecting the reflected
waves…
An example: Imagine the bat and the moth flying
towards each other. The moth will “receive”
a frequency that is higher than the bat’s
emitted frequency.
When the sound reflects off the moth,
the moth now acts as a “new source” and the bat
is the receiver a 2nd doppler shift!!
The frequency of this “new source” for the 2nd doppler shift will be the
frequency received or heard by the moth from the 1st doppler shift.
The frequency received by the bat will be even higher than the frequency the
moth “heard.”
The bat’s brain then “calculates” the speed and direction of the moth’s
motion from the difference in the emitted and received frequencies… lunch!
The Doppler Effect in Dolphins
• Dolphins hunt underwater by
emitting ultrasonic sounds and
detecting the reflections.
Radar Guns
• All waves (not just sound) can be doppler shifted. A police
radar gun bounces a high frequency radio wave off of a
moving car. The system then calculates the speed of the
car by comparing the frequency of the emitted “radar”
waves with the frequency of the reflected waves.
• … just like the bat, there are 2 doppler shifts.
Reading Assignment
Define the following with appropriate diagrams:
Sonic boom
Shock waves
References
Cutnell J.D. & Johnson K.W. (2010) Introduction to Physics,
8th Ed. John Wiley & Sons Pvt Ltd
END OF “DOPPLER EFFECT”
END OF PHY222 CLASS SLIDES
