Wave Properties and MOSAIC
A Physics MOSAIC
MIT Haystack Observatory RET
Revised 2011
Background Image from Wikipedia, Roger McLassus, Creative Commons
Reflection
• When a wave encounters a boundary, it will be at
least partially reflected off this boundary.
• In sound waves, this reflection results in an echo.
This is used in
– Echolocation
– Sonar
– Ultrasound imaging
Public Domain
Image from SKMay
Public Domain
Reflection off Fixed, Free Boundaries
Animation courtesy of Dr. Dan Russell, Kettering University
When a wave reflects off a fixed boundary, it becomes inverted.
When a wave reflects off a free boundary, it remains upright.
Refraction
• When a wave encounters a boundary where it is partially
transmitted, the wave speed and wavelength of the wave
will change due to the change in medium, and, as a
result, the direction of the wave will change.
Image from yggmcgill, Wikipedia, Creative Commons
Refraction Wave Fronts
Animation from Oleg Alexandrov, Wikipedia, Public Domain
Wave-Only Properties
• Both reflection and refraction could be understood from the perspective
of both particles and waves, as particles can both reflect and bend when
passing from one medium to another.
• Interference, however, cannot be understood from the perspective of
particles. Two particles cannot occupy the same place at the same time.
• Diffraction, too, can only be understood as a wave property.
Image from Wikipedia, Public Domain
Waves vs. Particles
• de Broglie concluded in 1924 that “any
moving particle or object had an
associated wave” (de Broglie hypothesis).
• This has become accepted as the
principle of wave-particle duality. All
particles have wave properties, but the
wavelength depends on the particle’s
momentum.
h
• Specifically,  
p
• The scale at which one observes wave
behavior is comparable to the
wavelength of the particle, and, since h is
a small number ( 6.626 x 10-34), only very
small particles have noticeable wave
properties.
Image from Public Domain
Sharing a Medium
• What happens when two waves pass through the
same physical space?
?
Superposition Principle
• When two (or more) waves pass through the same medium at
the same time, the resultant displacement of the medium is the
superposition of the displacements from each wave.
• The velocity of each wave is unaffected (in direction or speed).
!
Constructive and Destructive
Interference
• Constructive Interference: Occurs when two
waves pass through the same physical space and
result in a greater displacement than the original
waves.
• Destructive Interference: Occurs when two
waves pass through the same physical space and
result in a lesser displacement than the original
waves.
Interference of Waves
From Wikipedia, Oleg Alexandrov, Public Domain
Beats
When two waves of similar frequencies pass through the same
medium, the resulting wave is perceived with beats, or periodic
alternations of intensity. The frequency of the beats (intensity
variation) is equal to the difference in the frequency of the two
sources being combined.
f beat  f1  f 2
There are many great applets
demonstrating this phenomenon online.
Some are linked to below.
mta.ca
thinkquest.org (with sound)
walter-fendt.de
Image from Wikipedia, user Army1987, all rights released
Interference of Particles (Electrons)
Image from NASA
Diffraction
• Waves diffract, or spread out, when they encounter a barrier
that is comparable in size to their wavelength.
• Waves may even seem to bend around corners if their
wavelength is long enough.
• Diffraction is why the edges of shadows are never sharp, and
why you can hear around corners.
Standing Waves
When waves travel in a closed
medium, interference of the
forward and reflected wave can
cause standing waves.
Standing waves have nodes
(points that have destructive
interference and do not move)
and antinodes (points that
alternate between constructive
and destructive interference and
have maximum displacement).
The result is a pattern that
appears stationary.
By Catherine Schmidt-Jones, Standing Waves and Musical Instruments,
http://cnx.org/content/m12413/1.11/
Doppler Effect
• The Doppler Effect is the
change in frequency
between an emitted and
detected wave due to the
relative motion of the
source and observer.
• When the source and
observer approach one
another, the frequency
increases. (blue shift)
• When the source and
observer move apart, the
frequency decreases. (red
shift)
Images from NASA
Doppler Effects
US Army Photo by Master Sgt. Lek Mateo, Public Domain
Image from NOAA, from weather.gov
www.haystack.mit.edu
Doppler Broadening
• The rotational transition in ozone emits a photon at exactly
11.07524545 GHz.
• Instead of a single frequency, we detect a range of
frequencies, due to the broadening of the signal.
• As ozone molecules move towards or away from us, the
frequency we detect is slightly higher or lower.
• The greater the density of particles or the greater the speed
of the particles, the more broadening occurs.
© Swinburne University of Technology, used with permission
Which Ozone Do We See?
• Only 1% of the ozone in the atmosphere is located in the
mesosphere.
• 99% of the ozone is in the lower atmosphere. The ozone
there is more dense, so the signal frequency is spread out
due to pressure broadening.
• Scientists sometimes distinguish between thermal
broadening (as in all parts of the atmosphere, where the
temperature is above 0 K) and pressure broadening (as in
the lower atmosphere, where the gas is denser).
• Pressure broadening in the lower atmosphere results in a
very broad and “washed-out” signal at 11.07 GHz.
• Thermal broadening in the mesosphere causes some
broadening around 11.07 GHz, but not too much, since the
mesosphere is not that dense (and not that hot).
MOSAIC Setup
MOSAIC Spectrum