Wave and MOSAIC Basics

A Physics MOSAICMIT 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.

Image from NASA

Compressions

Rarefactions

wavelength

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).

Image from NASA

A A

A

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.

What is the period of this wave?

What is the frequency of this wave?

1 2 3Time (s)

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t (m

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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 = f.– 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.

…no one can hear you scream!

That’s because sound, unlike light, is a mechanical wave, and cannot travel through the near-vacuum of space.

In Space…

Image from NASA

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.