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Mechanical waves require an environment to travel through - called a medium. The medium's density, elasticity and temperature determine velocity. Matter with the most elasticity, least density and highest temperature would create the fastest wave.<ref name=“Chptr. 8”>

</ref>

Transverse waves travel perpendicular to the disturbance.<ref name=“Aid”>

</ref> For example, if the end of a slinky is moved up and down, a transverse wave will be created, because although the disturbance is vertical, the wave will travel horizontally across the slinky. Transverse waves have crests (each parabola's tip in the slinky if the parabola is above where the slinky would usually be) and troughs (each parabola's low point in the slinky if the parabola is below where the slinky would usually be). A full transverse wave consist of one crest and one trough.

Longitudinal waves travel parallel to the disturbance - for example, sound waves.<ref name=“Aid” /> Compressions and rarefactions are to longitudinal waves as crests and troughs are to transverse waves, thus a full longitudinal wave consist of one Compression and one rarefaction. Compressions are areas of high pressure, and rarefactions are areas of low.

Surface waves are transverse waves and longitudinal waves mixed into one medium.<ref name=“Chptr. 8” />

Electromagnetic waves are waves that do not require a medium.

Matter waves are produced by electrons.

When two or more waves collide, the result determines the type of collision. If the amplitudes of each wave are in the same direction (i.e. two crest or two troughs) - a larger amplitude will result, called constructive interference. If the amplitudes are in opposite directions, then a smaller amplitude will result, called destructive interference.<ref name=“Chptr. 8” />

The amplitude of a wave is the height of the displacement.<ref name=“Aid” />

The velocity of a wave is how quickly the wave travels.

The frequency of a wave is how many waves pass in one second, and conversely, the period of a wave is how many seconds it takes for one wave to show up. The period is the inverse of the frequency and vice versa.

The wavelength (represented by the Greek symbol lambda - λ) is the length of one wave in meters.

The wave equation is:<ref name=“Aid” /><ref>

</ref>

<big>Velocity</big>
<big>λ</big>	<big>Frequency</big>

and all variations. This includes the formulas:

• <math>Velocity = \lambda \times Frequency</math>
• <math>Frequency = \frac{Velocity}{\lambda}</math>
• <math>\lambda= \frac{Velocity}{Frequency}</math>

• Relativistic Sinusoidal Wave Function

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