Information about Sound Waves

Sound measurements
Sound pressure p
Sound pressure level (SPL)
Particle velocity v
Particle velocity level (SVL)
(Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power Pac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c

Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves). Sound is further characterized by the generic properties of waves, which are frequency, wavelength, period, amplitude, speed, and direction (sometimes speed and direction are combined as a velocity vector, or wavelength and direction are combined as a wave vector).

Humans perceive sound by the sense of hearing. By sound, we commonly mean the vibrations that travel through air and are audible to people. However, scientists and engineers use a wider definition of sound that includes low and high frequency vibrations in the air that cannot be heard by humans, and vibrations that travel through all forms of matter, gases, liquids, solids, and plasmas.

The matter that supports the sound is called the medium. Sound propagates as waves of alternating pressure, causing local regions of compression and rarefaction. Particles in the medium are displaced by the wave and oscillate. The scientific study of the absorption and reflection of sound waves is called acoustics.

Noise is often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal.

Perception of sound

Sound is perceived through the sense of hearing. Humans and many animals use their ears to hear sound, but loud sounds and low-frequency sounds can be perceived as vibrations by other parts of the body via the sense of touch. Sounds are used in several ways, notably for communication through speech and music. They can also be used to acquire information about properties of the surrounding environment such as spatial characteristics and presence of other animals or objects. For example, bats use echolocation, ships and submarines use sonar and most humans acquire some spatial information by the way in which they perceive sounds. Elephants and alligators use very low frequency sounds to communicate, and mice, bats, cetaceans, and some insects use high frequency sounds, both outside the human hearing range.

Humans can generally hear sounds with frequencies between 20 Hz and 20 kHz (the audio range) although this range varies significantly with age, occupational hearing damage, and gender; nearly all people in the developed world can no longer hear 20,000 Hz by the time they are teenagers, and progressively lose the ability to hear both higher frequencies and low level sounds as they get older. Most human speech communication takes place between 200 and 8,000 Hz and the human ear is most sensitive to frequencies around 1000-3,500 Hz. Sound above the hearing range is known as ultrasound, and that below the hearing range as infrasound.

The amplitude of a sound wave is specified in terms of its pressure. The human ear can detect sounds with a very wide range of amplitudes and so a logarithmic decibel amplitude scale is used. The quietest sounds that humans can hear have an amplitude of approximately 20 µPa (micropascals) or a sound pressure level (SPL) of 0 dB re 20 µPa (often incorrectly abbreviated as 0 dB SPL). Prolonged exposure to sound pressure levels exceeding 85 dB can permanently damage the ear, resulting in tinnitus and hearing impairment. Sound levels in excess of 130 dB are more than the human ear can safely withstand and can result in serious pain and permanent damage. At very high amplitudes, sound waves exhibit nonlinear effects, including shock.

Just how sound travels, or propagates, is difficult to imagine for many, as sound is invisible. Sound is an oscillating pressure wave, in which air is compressed, then decompressed, as sound moves away from its origin. Imagine a tube exposed to air whereby sound travels longitudinally through it. The air acts rather like a Slinky spring would if confined to the tube. As sound is generated at one end, a pressure wave will begin to travel through the air in the tube. Watching an earth worm move by pulsating its long body may help the imagination. The cycle length (i.e., the distance between successive 'bunched up parts of the slinky') is a particular sound's wave length, though most real world sounds are a mixture of many wave lengths. Low frequency sounds (eg, low organ or piano notes, bass guitars, etc) have large wave lengths, on the order of 10-50 feet long. High frequency sounds (eg, some parts of the noise associated with transient sounds as in many percussion instruments), have wave lengths as small as 1/2 inch.

Speed of sound

Main article: Speed of sound

The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in gases depends on temperature. In air at sea level, the speed of sound is approximately 769.5 mph (1,238.3 km/h) at 68 °F (20 °C),^[1] in water 3,315.1 mph (5,335.1 km/h) at 20 °C (68 °F),^[2] and in steel 13,332.1 mph (21,446 km/h)^[3] . The speed of sound is also slightly sensitive (a second order effect) to the sound amplitude, which means that there are nonlinear propagation effects, such as the production of harmonics and mixed tones not present in the original sound. (see parametric array).

Sound pressure

Main article: Sound pressure

Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure caused by a sound wave at a given location and given instant in time. The effective sound pressure is the root mean square of the instantaneous sound pressure averaged over a given interval of time. In a sound wave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity.

The loudest sound ever in air reported was the 1883 volcanic eruption of Krakatoa, whereby sound pressure levels reached 180 dB re 20 µPa at a distance of 100 miles (160 km).

Sound pressure level

As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale.

The sound pressure level (SPL) or L_p is defined as

where p is the root-mean-square sound pressure and p₀ is a reference sound pressure. Commonly used reference sound pressures, defined in the standard ANSI S1.1-1994, are 20 µPa in air and 1 µPa in water. Without a specified reference level, a value expressed in decibels cannot represent a sound pressure level.

Since the human ear does not have a flat spectral response, sound pressure levels are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.

Examples of sound pressure and sound pressure levels

See also the Sound pressure article.

Source of sound	RMS sound pressure	sound pressure level
	Pa	dB re 20 µPa
immediate soft tissue damage	50000	approx. 185
rocket launch equipment acoustic tests		approx. 165
threshold of pain	100	134
hearing damage during short-term effect	20	approx. 120
jet engine, 100 m distant	6–200	110–140
jack hammer, 1 m distant / discotheque	2	approx. 100
hearing damage from long-term exposure	0.6	approx. 85
traffic noise on major road, 10 m distant	0.2–0.6	80–90
moving passenger car, 10 m distant	0.02–0.2	60–80
TV set -- typical home level, 1 m distant	0.02	ca. 60
normal talking, 1 m distant	0.002–0.02	40–60
very calm room	0.0002–0.0006	20–30
quiet rustling leaves, calm human breathing	0.00006	10
auditory threshold at 2 kHz -- undamaged human ears	0.00002	0

Equipment for dealing with sound

Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers.

References

Sound measurement

See also

• Acoustics | Auditory imagery | Audio signal processing | Beats | Cycles | Diffraction | Doppler effect | Echo | FindSounds | Music | Note | Phonons | Physics of music | Pitch | Radiation of sound | Resonance | Rijke tube | Reflection | Reverberation | Sonic weaponry | Sound localization | Soundproofing | Rotary Woofer | Steam whistle | Timbre | Voyager Golden Record | Audio bit depth | Sound branding | Sounds and Mind

External links

• HyperPhysics: Sound and Hearing
• Introduction to the Physics of Sound
• Hearing curves and on-line hearing test
• Audio for the 21st Century
• Conversion of sound units and levels
• Sounds Amazing a learning resource for sound and waves
• Sound calculations
• sound - diracdelta.co.uk - definition and links to further pages.