Waves transmit sound through mediums such as liquids (e.g. water), gases (e.g. air) and solids (e.g. wood, plastic, metal, etc.). They are classified into different types depending on how the direction of the motion of the wave relates to the direction of displacement of the medium.
In transverse waves the direction of displacement or vibration is at right angles to the direction the wave is moving in. An example of a transverse wave would be a light or water wave.
In longitudinal waves the direction of displacement or vibration is parallel to the direction the wave is moving in. An example of a longitudinal wave would be a sound wave.
Wavelength is measured differently for transverse and longitudinal waves. In transverse waves it is the distance between a trough or crest and the following trough or crest, while in longitudinal waves it is measured as the shortest distance between two peak compressions.
The amplitude of a transverse wave is measured from the centre or midpoint of the wave (or its undisturbed position) to the peak of a crest. It is not measured from the trough to the crest.
Amplitude of longitudinal waves is the maximum distance the vibrating particle travels from its undisturbed distance.
Frequency measures the number of waves that are either produced from a source or that pass through a particular point every second. The unit frequency is measured in is Hertz (Hz). The number of Hertz is the number of wave cycles per second.
The velocity of a wave is its speed. Velocity can be worked out by using the equation
Velocity (m/s) = Frequency (Hz) x Wavelength (m)
Velocity is measured in metres per second. The speed of sound through air is roughly 1/3 km/s or 333 m/s. Speed of sound changes depending on the medium the sound wave is passing through. For example in water the speed of sound is about 1500 m/s (although this changes depending on temperature) and in steel its speed is about 5000 m/s.
A standing wave (or stationary wave) is a wave that remains in the same position and does not move. Most sound waves that reach our ears are not standing waves. Normally waves travel outwards, slowly spreading out and losing strength. A standing wave is created when the wave is 'trapped' between two or more surfaces. Musical instruments work by using trapped sound waves to produce different pitches and tones (sounds with a particular pitch). To be a tone a group of sound waves has to be very regular and all exactly the same distance apart.
When the sound waves are produced or bounce back off the end of a container, if it is the perfect length for that certain wavelength then instead of interfering with each other and cancelling each other out, the waves will reinforce each other. If you could watch the reinforced waves it would look like they are standing still - which is why they are called standing waves.
All standing waves have nodes, where there is no wave motion, and antinodes, where the wave is largest. The nodes determine which wavelengths will fit into a certain container/musical instrument.
References:
Basic wave theory - http://www.passmyexams.co.uk/GCSE/physics/basic-waves-theory.html
BBC Bitesize (General properties of waves) -
http://www.bbc.co.uk/schools/gcsebitesize/science/aqa/waves/generalwavesrev3.shtml
Standing waves - http://cnx.org/content/m12413/latest/
Acoustic Anechoic Chamber - http://www.acousticpc.com/re_anechoic_chamber.html