Basics of Sound

The Sound Source

Sound is produced when an object (the sound source) vibrates and causes the air around it to move. This vibration alternately compresses and rarefies the surrounding air, resulting in a series of compressions and rarefactions travelling away from the sound source, like a 3D version of ripples travelling away from a stone dropped in water.
These are longitudinal waves; the air particles move in the same dimension as the direction of wave travel.
The alternative wave type is transverse wave motion, such as is found in vibrating strings. The motion of the string is at 90° to the apparent direction of wave travel.

The rate at which the sound source oscillates is the frequency of the sound it produces; this is quoted in hertz (Hz) or cycles per second (cps).
The amount of compression and rarefaction of the air which results from the source's oscillation is the amplitude of the sound wave. This is related to the loudness of the wave when it is perceived by the ear.
The distance between two adjacent peaks of compression or rarefaction as the wave travels through the air is the wave's wavelength, which is often represented by λ (the Greek letter lambda). The wavelength depends on how fast the sound wave is travelling; a fast wave will result in a larger λ.
This diagram shows a sine wave in simple harmonic motion. Note how the graph shows both positive (compressions) and negative (rarefactions) amplitudes on the vertical axis.

Sound in Air

Air is made up of gas molecules and has an elastic property.
The air molecules themselves oscillate about a fixed point, but the wave appears to move away from the source.
The speed of travel depends on the density and elasticity of the substance through which it passes.
The speed of sound in air is approximately 344 ms^-1 (depending on the temperature).
In steel, the speed of sound is approximately 5100 ms^-1.
c = ƒλ or λ = c ÷ ƒ
c = speed of the wave ƒ = frequency λ = wavelength

Simple & Complex Sounds

Sine waves consist of energy at only one frequency; often called pure tones.
Most real sounds are made up of a combination of vibration patterns which result in a more complex waveform.
If a waveform is repetitive it has a pitch. All repetitive waveforms can be broken down into a series of harmonics by a mathematical process called Fourier Analysis.
Waveforms can also be shown as line spectra. Waveforms are called a time-domain plot, while line spectrum graphs are known as frequency-domain plots.
Some synthesisers can use Fourier Analysis to deconstruct a waveform into its constituent harmonics and then resynthesise the sound.
This java applet allows direct control of the level of individual harmonics to create various timbres.

Frequency Spectra

The line spectrum for a sine wave has only one componment at the frequency of the sine wave. This is known as the fundamental frequency of oscillation.
More complex sound waves (such as a square wave) have additional components above the fundamental frequency. These are known variously as harmonics, overtones or partials.
Harmonics are frequency components of a sound which occur at integer multiples of the fundamental frequency (two times, three times etc.). Most simple vibrating sources are capable of vibrating in a number of harmonic modes at the same time.
The fundamental is the first harmonic. The second harmonic is also known as the first overtone.
If there are overtones which are not related in a simple integer-multiple fashion to the fundamental they are known as inharmonic partials. It is possible for sounds with inharmonic partials to be pitched as long as they have a strong fundamental.

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