Wave

A wave is a disturbance that propagates. The most common waves we encounter are sound, a mechanical wave that propagates through air, liquid or solids, and is of a frequency detected by the [auditory system]?; electromagnetic radiation, observed as light, [radio waves]?, x-rays?, etc. In the last case, what propagates is a disturbance of the electromagnetic field. And, of course, sea waves, which are perturbations that propagate through water. Also of importance are [seismic waves]? (in earthquakes), etc.

When the perturbation of the particular medium is expressed in a mathematical way, we obtain some form of the wave equation.

All periodic waves are characterized by several numbers:

The period? (T) and frequency (f) are related by:

f = 1/T ,

where the period is the time taken for one cycle of the wave to repeat itself, and the frequency is the number of cycles per unit time, usually measured in hertz.

The amplitude? of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the [electric field]? (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave) or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.

When waves are expressed mathematically, the angular frequency (ω, radians/second) is often used; it is related to the frequency f by:

f = ω / 2π .

Waves that are moving are called travelling waves, and have a disturbance that varies both with time t and distance z. This can be expressed mathematically as:

y = A(z,t) cos( ωt - kz + φ) ,

where A(z,t) is the amplitude envelope of the wave, k is the wave number and φ is the phase. The velocity v of this wave is given by:

v = ω / k = λf ,

where λ is the wavelength of the wave.

[Transverse waves]? have vibrations perpendicular to the direction of travel, for example electromagnetic waves and waves on a string. [Longtitudinal waves]? have vibrations along the direction of the wave, for example sound waves.

Transverse waves can be polarised.

Properties of wave motions

All waves have common behaviour under a number of standard situations. All waves can experience the following:

• Reflection
• Refraction
• Diffraction
• Interference
• Dispersion

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A discussion of the different types of waves would also be appropriate (i.e. in earthquakes there are S, P, and L waves, generalizing to a definition based on a moving pattern or some such).

Of course, for the above expression(s) to be scrupuluously valid one should add the caveat that exactly the same conditions must apply across all sections of the wave. Hence you could not use it for waves in water coming up a shelving beach...

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/Talk