# Sound

File:Processing of sound.jpg
A schematic representation of hearing. (Blue: sound waves. Red: eardrum. Yellow: cochlea. Green: auditory receptor cells. Purple: frequency spectrum of hearing response. Orange: nerve impulse.)

Sound is vibration, as perceived by the sense of hearing. Vibrations usually travel to our ears through the air; the ear converts them into nerve impulses sent to our brains, where the impulses become sound.

In more technical language, sound "is an alternation in pressure, particle displacement, or particle velocity propagated in an elastic material" (Olson 1957) or series of mechanical compressions and rarefactions or longitudinal waves that successively propagate through media that are at least a little compressible (solid, liquid or gas but not vacuum). In sound waves parts of matter (molecules or groups of molecules) move in a direction of the spreading of the disturbance (as opposite to transversal waves). The cause of sound waves is called the source of waves, e.g. a violin string vibrating upon being bowed or plucked.

A sound wave is usually represented graphically by a wavy, horizontal line; the upper part of the wave (the crest) indicates a compression and the lower part (the trough) indicates a rarefaction.

## Attributes of sound

The characteristics of sound are frequency, wavelength, amplitude and velocity.

### Frequency and wavelength

The frequency is the number of air pressure oscillations per second at a fixed point occupied by a sound wave. One single oscillatory cycle per second corresponds to 1 Hz. The wavelength is the distance between two successive crests and is the distance that a wave travels in the time of one oscillatory cycle.

Suppose sound is emitted as a sine wave travelling outward spherically from a point source. The pressure (above ambient, see gauge pressure) of the sound wave can be written as

$P(r,t)=P_{0}\sin \left(2\pi f\left(t-{\frac {r}{c}}\right)\right)$ where P(r,t) is the pressure at distance r at time t, P0 is the amplitude of the pressure variation (0 to peak), f is the frequency of oscillation, and c is the speed of sound.

The wavelength of a sound wave of frequency f and travelling at speed c is given by c/f. Given a speed of 343 m/s, a 20 kHz sound wave has a wavelength of about 17 mm. For comparison, an A440 has a nominal wavelength of about 78 cm, and a 20 Hz sound wave has a wavelength of 17 m.

### Amplitude

The amplitude is the magnitude of sound pressure change within the wave, or basically, the maximum amount of pressure at any point in the sound wave. A sound wave is caused literally by increases in pressure at certain points (of a material) causing a "domino effect" outward, the high pressure points are the crests mentioned above, and behind them are low pressure points which tail them, those are the troughs mentioned above. Amplitude is the maximal displacement of particles of matter that is obtained in compressions, where the particles of matter move towards each other and pressure increases the most and in rarefactions, where the pressure lessens the most. See also particle displacement and particle velocity. While the pressure can be measured in pascals, the amplitude is more often referred to as sound pressure level and measured in decibels, or dBSPL, sometimes written as dBspl or dB(SPL). When the measurement is adjusted based on how the human ear perceives loudness based on frequency, it is called dBA or A-weighting. See decibels for a more thorough discussion.

### Velocity

Sound's propagation speed depends on the type, temperature and pressure of the medium through which it propagates. Under normal conditions, however, because air is nearly a perfect gas, the speed of sound does not depend on air pressure. In dry air at 20 °C (68 °F) the speed of sound is approximately 343 m/s (approximately 1 meter every 2.9 milliseconds). The speed of sound relates frequency to wavelength. Thus, a tone of 343 Hz (F4 minus 31 cents) traveling in air has a wavelength of 1 meter.

## Types of sounds

Noises are irregular and disordered vibrations including all possible frequencies. Their wave diagram does not repeat in time. Noise is an aperiodic series of waves.

Sounds that are sine waves with fixed frequency and amplitude are perceived as pure tones. While sound waves are usually visualised as sine waves, sound waves can have arbitrary shapes and frequency content, limited only by the apparatus that generates them and the medium through which they travel. In fact, most sound waves consist of multiple overtones or harmonics and any sound can be thought of as being composed of sine waves (see additive synthesis). Waveforms commonly used to approximate harmonic sounds in nature include sawtooth waves, square waves and triangle waves.

While a sound may still be referred to as being of a single frequency (for example, a piano striking the A above middle C is said to be playing a note at 440 Hz), the sound perceived by a listener will be colored by all of the sound wave's frequency components and their relative amplitudes, as well as how the sound changes over time (see timbre.) For convenience in this article, however, it is best to think of sound waves as sine waves.

## Perception of sound

The frequency range of sound audible to humans is approximately between 20 and 20,000 Hz. This range varies by individual and generally shrinks with age. It is also an uneven curve - sounds near 3,500 Hz are often perceived as louder than a sound with the same amplitude at a much lower or higher frequency. Above and below this range are ultrasound and infrasound, respectively. The amplitude range of sound for humans has a lower limit of 0dBSPL, called the threshold of hearing. Sound is technically at its upper limit at 194.09 dB. Above this level it should be called a shock wave. Sounds begin to do damage to ears at 85 dBSPL and sounds above approximately 130 dBSPL (called the threshold of pain) cause pain. Again, this range varies by individual and changes with age.

The perception of sound is the sense of hearing. In humans and many animals this is accomplished by the ears, but loud sounds and low frequency sounds can be perceived by other parts of the body through the sense of touch. Sounds are used in several ways, most notably for communication through speech or, for example, music. Sound perception can also be used for acquiring information about the surrounding environment in properties such as spatial characteristics and presence of other animals or objects. For example, bats use one sort of echolocation, ships and submarines use sonar, and humans can determine spatial information by the way in which they perceive sounds.