The simplest explanation of a wave is a oscillation which spreads to its adjacent regions. Electromagnetic waves, sound waves, seismic waves, water waves and other types of waves have characteristic properties as well as common properties.
There are two types of waves transverse and longitudinal. Transverse waves are waves in which the vibrations are perpendicular to the direction of movement wave, the most important example of these are the waves in the electromagnetic spectrum (light waves, radio waves…). Longitudinal waves are waves in which the vibrations are parallel to the direction of movement of the wave. Examples include sound waves and seismic p-waves.
The frequency of a vibrating object is the rate at which it oscillates. The higher the frequency the faster the oscillations are occurring. Frequency is therefore shown in the formula ƒ=1/T where ƒ is frequency and T is the time taken for a complete oscillation to its original position.
Waves are characterised by their wavelength, the distance travelled in one complete cycle of wave oscillation. The wavelength of a wave is the distance along the direction of movement from a wave crest to the next wave crest. The SI unit of wavelength is the metre.
The velocity of a wave is at how fast the wave is moving in a certain direction. A wave of frequency ƒ travelling at speed v has a wavelength » given by v=ƒ». This is a fundamental formula in the understanding of how waves work and the relationship must be memorised. Where this formula is obtained from is also very simple, we should understand that velocity=distance/time for a certain distance, therefore in one whole cycle of wave oscillation the velocity would be the distance travelled in the period (wavelength ») divided by the time that it took to complete that period (T), v=»/T and frequency=1/T therefore it can be substituted in to give v=ƒ». This is very important and you may need to re-read the material to make sure you understand this.