Wave and MOSAIC Basics
A Physics MOSAIC
MIT Haystack Observatory RET
Revised 2011
MOSAIC Background
• MOSAIC stands for Mesospheric Ozone System
for Atmospheric Investigations in the Classroom.
• It is a method by which the level of ozone in the
mesosphere (the layer above the troposphere
and the stratosphere) can be measured.
• Ozone, when in the stratosphere, is very
important as it helps to protect us from
ultraviolet radiation which can cause skin cancer.
Layers of Atmosphere
Image from PhysicalGeography.net
Ozone
• Ozone is a molecule of three oxygen atoms (O3).
• In the mesosphere, ozone is formed at night by
the combination of a normal oxygen molecule
(O2) and an Oxygen atom (O) in the presence of a
catalyst molecule M (such as Nitrogen).
– O + O2 + M
O3 + M
• Ozone is broken down during the day by
absorbing UV light (or another oxygen or
hydrogen molecule)
– O3 + UV
O + O2
How is the Ozone detected?
• As the ozone molecule rotates it emits some
of its energy as radio waves of a certain
frequency: 11.0724545 GHz (Gigahertz).
• These radio waves can be detected by a
satellite dish similar to the one used for
satellite TV reception.
MOSAIC Ozone detection system
Image by Christopher Clements
What is a Wave?
• A wave is a disturbance that travels through space in time, usually
involving the transfer of energy without the loss of mass through
oscillations.
• Examples of waves include sound, light, water waves, “the wave”
(as seen below), waves on strings, and earthquakes.
From Vironevaeh on Flickr, Creative Commons
Simple Harmonic Motion
• Each particle in the medium that a wave passes
through oscillates around a fixed position like a
cork on an ocean wave or a child on a swing.
• This type of motion is called simple harmonic
motion, and has the following properties
– Caused by linear restoring force
– Energy conserved, but oscillates between PE and KE
– Total energy proportional to (amplitude of
oscillation)2.
Two Types of Waves
• Transverse Waves
• Longitudinal Waves
Images from NASA; stargazers.gsfc.nasa.gov
Two Types of Waves
• As you have seen with the slinky, there are two
possible directions of oscillation that can produce
a wave.
– Transverse wave: the oscillations are perpendicular to
the direction of wave propagation.
– Longitudinal waves: the oscillations are parallel to the
direction of wave propagation.
• Examples
– Transverse: EM radiation, waves on strings, “the
wave”
– Longitudinal: Sound, p-waves
Transverse Waves:
Crests, Troughs, Wavelength
• From your observations of the slinky you could draw a
transverse wave like this.
• The highest point of the wave is called a crest, and the
lowest point is called a trough. The distance between
two crests (or two troughs) is the wavelength (l) of the
wave.
Image from NASA
Longitudinal Waves:
Compressions, Rarefactions, Wavelength
• From your observations of the slinky, you could draw a
longitudinal wave like the one below.
• The positions of maximum density are called compressions, and
the positions of least density are called rarefactions. The
distance between compressions (or rarefactions) is the
wavelength (l) of the wave.
Compressions
wavelength
Image from NASA
Rarefactions
Amplitude
• The height of the wave from the center to the top (or
bottom) is called the amplitude (A). It is measured in
meters (m).
A
A
A
Image from NASA
Frequency and Period
• The number of full waves per second is called the frequency
(f, or n). The frequency of a wave is fixed by the frequency of
the source of the wave. It is measured in Hertz (Hz = s-1).
• The time for one full wave is called the period (T). It is
measured in seconds (s).
• Frequency and period are inverses of each other. T = 1/f, and
f = 1/T.
Displacement (m)
What is the period
of this wave?
What is the
frequency of this
wave?
1
2
Time (s)
3
Wave Speed
• The speed of a wave (v) is how fast the wave is propagating
(or moving).
• The speed of a wave depends on the properties of the
medium it is moving through, not on the wave’s properties.
– This should make sense, since if the speed depended on the
properties of the wave, loud sounds would reach you before
quiet ones, or high sounds would reach you before low ones.
• The speed of a wave can be related to the properties of the
wave, by v = fl.
– Because v is a constant (for a single medium), this means f and
l are inversely related.
• The frequency of a wave is fixed by the source of the wave,
and will be constant for a given wave, regardless of the
medium.
Changing Wave Speed
• Stringed instruments are tuned by changing the tension in the
strings, thus changing the speed of the waves along the
string, and therefore, the resonant frequency. (The
wavelength depends on the length of the string and doesn’t
change.)
Image from dumbledad, on Flickr, Creative Commons
Changing Media
• When a wave goes from one medium to another, its
wave speed changes.
• The frequency of the wave remains constant, and equal
to the frequency of the source.
• This results in a change of wavelength.
Image from Wikipedia, Public Domain
MOSAIC Wave Speed
• In the case of the MOSAIC system the frequency
of the radio waves received are 11.0724545 GHz.
• This means that there are 11.0724545 x 109 (or
about 11 billion) crests and troughs reaching the
antenna each second.
• The speed of these waves (and all
electromagnetic waves) in air is 3.0 x 108 m/s
• What is the wavelength of these waves?
Two (More) Types of Waves
• Waves can be further classified by their
requirements for propagation.
– Mechanical waves: require a medium to propagate. In
other words, they cannot travel through a vacuum.
– Electromagnetic waves: do not require a medium to
propagate. In other words, they can travel through a
vacuum.
In Space…
…no one can hear you scream!
Image from NASA
That’s because sound, unlike light, is a mechanical wave,
and cannot travel through the near-vacuum of space.
Mechanical Waves
• These waves all need a medium (substance) to
travel through.
• They can either be transverse (waves on a string
or water or earthquake s waves) or longitudinal
(sound waves traveling through the air or a solid,
or earthquake p waves).
Electromagnetic Waves
• The MOSAIC system uses electromagnetic
waves called radio waves.
• All electromagnetic waves travel at the same
speed in a vacuum (3.0 x 108 m/s), and slower
in other media.
• They are all transverse waves; the oscillations
(in this case, of electric and magnetic fields)
occur perpendicular to the direction of wave
travel.