The Properties of Waves

General Wave Motion
A wave is a distortion in a material or medium, where the individual parts of the material only show periodic motion, but the waveform itself moves through the material. All waves have similar characteristics, and since all forms of wave motion follow the same laws and principles, knowing the fundamentals of wave motion is important in understanding sound, light, and other types of waves.

Definition of wave motion
Wave motion is defined as the movement of a distortion of a material or medium, where the individual parts or elements of the material only move back-and-forth, up-and-down, or in a cyclical pattern.
It appears as if something is actually moving along the material, but in reality it is just the distortion moving, where one part influences the next.
This sounds somewhat abstract, but it can be visualized with examples.

Examples of waves
The following examples shows common transverse, compression and circular waveforms.

Transverse waves
Up-and-down motion creates transverse waves

Wave in ballgame
At the ballgame, someone in the stands may start up a "wave" by standing up and then sitting down. The people on one side then stand up and sit down, then the next people, and so on.
Everyone is still in their seats, but the wave traveled through the ballpark from one end to the other.

Rope or string
You can shake a rope, causing a wave motion. The parts of the rope only move up-and-down, but the wave moves from one end of the rope to the other. A guitar string also has this type of motion. Vibrating strings demonstrates waveform

Light waves
Light or electromagnetic waves are caused by a up-and-down motion of electric and magnetic fields, thus making them transverse waves.

Compressed / longitudinal waves
Back-and-forth motion creates compressed or longitudinal waves.

Slinky
You can stretch out a Slinky along the floor and give one end a back-and-forth shove. The compression will move along the Slinky to its other end.

Sound waves
A loudspeaker cone moves back-and-forth to create a sound, which is a compression wave.
AC electricity
Electrons move back-and-forth in a wire, sending a wave of electric power through the wire. The electrons stay in their general region in AC electricity, while the flow through and out the wire in DC electricity.

Circular wave
There are cases where the material moves in a combination of transverse and compression, moving in a circular or elliptical pattern.

Water waves
Drop a stone in a pool and waves move outward. The surface of the water looks like it goes up and down, but actually the water molecules move in a circular or oval motion the form the wave.

Light waves
Although light is classified as a transverse wave, the motion of the electrical and magnetic fields may be circular instead. It is hard to tell.

Characteristics of waves
The characteristics of a waveform are wavelength, amplitude, velocity, andfrequency. All periodic waveforms have these common characteristics.
There are special cases, where only one crest of the wave is seen, like the the wave at a ballgame or the sound caused by an impact or explosion. In those cases, there is still a wavelength, but there is no frequency, since the waveform is not periodic.

Wavelength
Wavelength is defined as the distance from one crest (or maximum of the wave) to the next crest or maximum.

Waveform showing wavelength and amplitude
The wavelength of an ocean wave is typically several meters. The wavelength of the electromagnetic wave used in a microwave oven is in the order of a centimeter.

Amplitude
The height of the wave is called its amplitude. Some areas consider the middle of the wave to its peak as the amplitude, while others consider peak-to-peak as the amplitude.
Amplitude relates to loudness in sound and brightness in light.

Velocity
The velocity of the wave is the measurement of how fast a crest is moving from a fixed point. For example, the velocity of water waves can be measured as their speed in a given direction with respect to the land.
The speed of sound is about 1000 feet/second. The speed of light is 186,000 miles/second.

Frequency
The frequency of waves is the rate the crests or peaks pass a given point. Frequency is the velocity divided by the wavelength designated as cycles (or peaks) per second. Cycles per second is also called Hertz.
Frequency = Velocity / Wavelength
Another way of writing that is:
Velocity = Wavelength x Frequency
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Tip: A way to help remember equations is to look at their units of measurement. If Velocity is in meters/second, Wavelength is in meters and Frequency is in cycles/second, then the units of the equation would be: meters/second = meters x cycles/second
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The frequency is also the reciprocal of the time between crests passing a point or the period of the vibration. With this measurement:
F = 1/T

Summary
Waves are distortions in a material that may be transverse, compression or a combination of those movements. Light, sound and AC electric waves are important waveforms. The characteristics of a waveform are wavelength, amplitude, velocity, and frequency.

http://www.school-for-champions.com/SCIENCE/waves.htm

Longitudinal and Transverse Wave Motion
Mechanical Waves are waves which propagate through a material medium (solid, liquid, or gas) at a wave speed which depends on the elastic and inertial properties of that medium. There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves. The animations below demonstrate both types of wave and illustrate the difference between the motion of the wave and the motion of the particles in the medium through which the wave is travelling.

Longitudinal Waves
In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation below shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

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Transverse Waves
In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The animation below shows a one-dimensional transverse plane wave propagating from left to right. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion.

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Water Waves
Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The movie below shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. I have identified two particles in blue to show that each particle indeed travels in a clockwise circle as the wave passes.



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Rayleigh surface waves
Another example of waves with both longitudinal and transverse motion may be found in solids as Rayleigh surface waves. The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases. Rayleigh waves are different from water waves in one important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counter-clockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. The movie below shows a Rayleigh wave travelling from left to right along the surface of a solid. I have identified two particles in blue to illustrate the counterclockwise-clockwise motion as a function of depth.



http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html

• A Travelling Wave  http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html
by Ron Kurtus (revised 24 June 2006)

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