Sound pressure or
acoustic pressure is the local
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
deviation from the ambient (average, or equilibrium)
atmospheric pressureAtmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...
caused by a sound wave. Sound pressure can be measured using a
microphoneA microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...
in air and a
hydrophoneA hydrophone is a microphone designed to be used underwater for recording or listening to underwater sound. Most hydrophones are based on a piezoelectric transducer that generates electricity when subjected to a pressure change...
in water. The SI unit for sound pressure
p is the
pascalThe pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
(symbol: Pa).
Sound pressure level (SPL) or
sound level is a
logarithmic measureA logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...
of the effective sound pressure of a sound relative to a reference value. It is measured in
decibelThe decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s (dB) above a standard reference level. The commonly used "zero" reference sound pressure in air is 20 µPa
RMSIn mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
, which is usually considered the threshold of human hearing (at 1
kHzThe hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
).
Instantaneous sound pressure
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 squareIn mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
of the instantaneous sound pressure over a given interval of time (or space).
Total pressure
is given by:
where:
= local ambient atmospheric (air) pressure,
= sound pressure deviation.
Intensity
In a sound wave, the complementary variable to sound pressure is the acoustic
particle velocityParticle velocity is the velocity v of a particle in a medium as it transmits a wave. In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string....
.
Together they determine the acoustic intensity of the wave. The local instantaneous
sound intensitySound intensity or acoustic intensity is defined as the sound power Pac per unit area A. The usual context is the noise measurement of sound intensity in the air at a listener's location.-Acoustic intensity:...
is the product of the sound pressure and the acoustic particle velocity.
Acoustic impedance
For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the
acoustic impedanceThe acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...
. The acoustic impedance depends on both the characteristics of the wave and the
transmission mediumA transmission medium is a material substance that can propagate energy waves...
.
The acoustic impedance is given by
where
- Z is acoustic impedance
The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...
or sound impedance
- p is sound pressure
- U is particle velocity
Particle velocity is the velocity v of a particle in a medium as it transmits a wave. In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string....
Particle displacement
Sound pressure
p is connected to
particle displacementParticle displacement or particle amplitude is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a wave....
(or particle amplitude) ξ by
.
Sound pressure
p is
,
normally in units of N/m² = Pa.
where:
| Symbol | SI Unit | Meaning |
| p |
pascal The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
s |
sound pressure |
| f |
hertz The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
|
frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
|
| ρ |
kg The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...
/mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
³ |
density of air The density of air, ρ , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity...
|
| c |
mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
/sThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
|
speed of soundThe speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
|
| v |
m/s |
particle velocity Particle velocity is the velocity v of a particle in a medium as it transmits a wave. In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string....
|
 = 2 ·  · f |
radians/s The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
|
angular frequencyIn physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...
|
| ξ |
meters |
particle displacement Particle displacement or particle amplitude is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a wave....
|
| Z = c • ρ |
N·s The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
/mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
³ |
acoustic impedance The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...
|
| a |
mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
/sThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
² |
particle acceleration In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre/second². In acoustics or physics, acceleration is defined as the rate of change of velocity. It is thus a vector...
|
| I |
W The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
/mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
² |
sound intensity Sound intensity or acoustic intensity is defined as the sound power Pac per unit area A. The usual context is the noise measurement of sound intensity in the air at a listener's location.-Acoustic intensity:...
|
| E |
W The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
·sThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
/mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
³ |
sound energy density The sound energy density or sound density is an adequate measure to describe the sound field at a given point as a sound energy value...
|
| Pac |
watt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
s |
sound power or acoustic power |
| A |
mThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
² |
AreaArea is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
|
Distance law
When measuring the sound created by an object, it is important to measure the distance from the object as well, since the sound pressure decreases with distance from a point source with a 1/
r relationship (and not
1/r2In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....
, like sound intensity).
The
distance law for the sound pressure
p in 3D is inverse-proportional to the distance
r of a punctual sound source.
If sound pressure
, is measured at a distance
, one can calculate the sound pressure
at another position
,
The sound pressure may vary in direction from the source, as well, so measurements at different angles may be necessary, depending on the situation. An obvious example of a source that varies in level in different directions is a bullhorn.
Sound pressure level
Sound pressure level (SPL) or sound level
is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in
decibelThe decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s (dB) above a standard reference level.
where
is the reference sound pressure and
is the rms sound pressure being measured.
[Sometimes reference sound pressure is denoted p0, not to be confused with the (much higher) ambient pressure.]
Sometimes variants are used such as dB (SPL), dBSPL, or dB
SPL. These variants are not recognized as units in the
SISi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
. The unit dB (SPL) is sometimes abbreviated to just "dB", which can give the erroneous impression that a dB is an absolute unit by itself.
The commonly used reference sound pressure in air is
= 20 µPa (rms), which is usually considered the threshold of human hearing (roughly the sound of a mosquito flying 3 m away). Most sound level measurements will be made relative to this level, meaning 1 pascal will equal SPL of 94 dB. In other media, such as
underwaterUnderwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water and its boundaries. The water may be in the ocean, a lake or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and...
, a reference level of 1 µPa is more often used. These references are defined in
ANSIThe American National Standards Institute is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organization also coordinates U.S. standards with international...
S1.1-1994.
The distance of the measuring microphone from a sound source is often omitted when SPL measurements are quoted, making the data useless. In the case of ambient environmental measurements of "background" noise, distance need not be quoted as no single source is present, but when measuring the noise level of a specific piece of equipment the distance should always be stated. A distance of one
metreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
(1 m) from the source is a frequently-used standard distance. Because of the effects of reflected noise within a closed room, the use of an
anechoic chamberAn anechoic chamber is a room designed to stop reflections of either sound or electromagnetic waves.They are also insulated from exterior sources of noise...
allows for sound to be comparable to measurements made in a free field environment.
The lower limit of audibility is therefore defined as SPL of 0
dBThe decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
, but the upper limit is not as clearly defined. While 1
atmThe standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...
(SPL of 194 dB) is the largest pressure variation an undistorted sound wave can have in
Earth's atmosphereThe atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...
. Larger sound waves can be present in other
atmosphereAn atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
s or other media such as under water, or within the Earth in the form of
shock wavesShock Waves, , is a 1977 horror movie written and directed by Ken Wiederhorn...
.
Ears detect changes in sound pressure. Human hearing does not have a flat
spectral sensitivitySpectral sensitivity is the relative efficiency of detection, of light or other signal, as a function of the frequency or wavelength of the signal....
(
frequency responseFrequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
) relative to frequency versus amplitude. Humans do not perceive low- and high-frequency sounds as well as sounds near 2,000 Hz, as shown in the
equal-loudness contourAn equal-loudness contour is a measure of sound pressure , over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours...
. Because the frequency response of human hearing changes with amplitude, three weightings have been established for measuring sound pressure: A, B and C. A-weighting applies to sound pressures levels up to 55 dB, B-weighting applies to sound pressures levels between 55 and 85 dB, and C-weighting is for measuring sound pressure levels above 85 dB.
In order to distinguish the different sound measures a suffix is used: A-weighted sound pressure level is written either as dB
A or L
A. B-weighted sound pressure level is written either as dB
B or L
B, and C-weighted sound pressure level is written either as dB
C or L
C. Unweighted sound pressure level is called "linear sound pressure level" and is often written as dB
L or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL.
Multiple sources
The formula for the sum of the sound pressure levels of
n incoherent radiating sources is
From the formula of the sound pressure level we find
This inserted in the formula for the sound pressure level to calculate the sum level shows
Examples of sound pressure and sound pressure levels
Sound pressure in air:
| Source of sound | Sound pressure | Sound pressure level |
| Sound in air | pascal The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
RMS | dBThe decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
re 20 μPa |
ShockwaveA shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
(distorted sound waves > 1 atmThe standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...
; waveform valleys are clipped at zero pressure) |
>101,325 Pa |
>194 dB |
| Theoretical limit for undistorted sound at 1 atmosphere The standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of pressure. For practical purposes it has been replaced by the bar which is 105 Pa...
environmental pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
|
101,325 Pa |
~194.094 dB |
| Stun grenades |
6,000–20,000 Pa |
170–180 dB |
| Rocket launch equipment acoustic tests |
~4000 Pa |
~165 dB |
| Simple open-ended thermoacoustic Thermoacoustics is about the interaction between thermodynamic and acoustic phenomena. Thermoacoustics is a relatively new field of science and engineering. Few devices based on this principle have been made thus far...
device |
12,619 Pa |
176 dB |
.30-06 rifleThe .30-06 Springfield cartridge or 7.62×63mm in metric notation, was introduced to the United States Army in 1906 and standardized, and was in use until the 1960s and early 1970s. It replaced the .30-03, 6 mm Lee Navy, and .30 US Army...
being fired 1 m to shooter's side |
7,265 Pa |
171 dB (peak) |
M1 GarandThe M1 Garand , was the first semi-automatic rifle to be generally issued to the infantry of any nation. Called "the greatest battle implement ever devised" by General George S...
rifle being fired at 1 m |
5,023 Pa |
168 dB |
| Jet engine A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...
at 30 m |
632 Pa |
150 dB |
| Threshold of pain The threshold of pain is the point at which pain begins to be felt. It is an entirely subjective phenomenon. The intensity at which a stimulus begins to evoke pain is the threshold intensity. So, if a hotplate on a person's skin begins to hurt at 42°C , then that is the pain threshold temperature...
|
63.2 Pa |
130 dB |
| Vuvuzela The vuvuzela , also known as lepatata Mambu , colloquially known in South Africa as "Moerstripper", is a plastic horn, about long, which produces a loud monotone note, typically around B3 . Some models are made in two parts to facilitate storage, and this design also allows pitch variation...
horn at 1 m |
20 Pa |
120 dB(A) |
| Hearing damage (possible) |
20 Pa |
approx. 120 dB |
| Jet engine A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...
at 100 m |
6.32 – 200 Pa |
110 – 140 dB |
| Jack hammer at 1 m |
2 Pa |
approx. 100 dB |
| Traffic on a busy roadway at 10 m |
2×10−1 – 6.32×10−1 Pa |
80 – 90 dB |
| Hearing damage (over long-term exposure, need not be continuous) |
0.356 Pa |
85 dB |
Passenger carAn automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...
at 10 m |
2×10−2 – 2×10−1 Pa |
60 – 80 dB |
EPAThe U.S. Environmental Protection Agency is an agency of the federal government of the United States charged with protecting human health and the environment, by writing and enforcing regulations based on laws passed by Congress...
-identified maximum to protect against hearing loss and other disruptive effects from noise, such as sleep disturbance, stress, learning detriment, etc. |
|
70 dB |
| TV (set at home level) at 1 m |
2×10−2 Pa |
approx. 60 dB |
| Handheld electric mixer A mixer is a kitchen appliance intended for mixing, folding, beating, and whipping food ingredients. Mixers come in two major variations, hand mixers and stand mixers....
|
|
65 dB |
Washing machineA washing machine is a machine designed to wash laundry, such as clothing, towels and sheets...
, dish washer |
|
50-53 dB |
| Normal conversation at 1 m |
2×10−3 – 2×10−2 Pa |
40 – 60 dB |
| Very calm room |
2×10−4 – 6.32×10−4 Pa |
20 – 30 dB |
| Light leaf rustling, calm breathing |
6.32×10−5 Pa |
10 dB |
| Auditory threshold at 1 kHz |
2×10−5 Pa |
0 dB |
See also
- Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
- Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
- Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
, especially the Acoustics section
- Phon
The phon was proposed in DIN 45631 and ISO 532 B as a unit of perceived loudness level LN for pure tones by S. S. Stevens.-Definition:The purpose of the phon scale is to compensate for the effect of frequency on the perceived loudness of tones...
(unit)
- Loudness
Loudness is the quality of a sound that is primarily a psychological correlate of physical strength . More formally, it is defined as "that attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud."Loudness, a subjective measure, is often...
- Sone
The sone was proposed as a unit of perceived loudness by Stanley Smith Stevens in 1936. In acoustics, loudness is the subjective perception of sound intensity...
(unit)
- Sound level meter
Sound level meters measure sound pressure level and are commonly used in noise pollution studies for the quantification of almost any noise, but especially for industrial, environmental and aircraft noise. However, the reading given by a sound level meter does not correlate well to...
- Sound power level
- Stevens' power law
Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the...
- Weber–Fechner law
The Weber–Fechner law is a confusing term, because it combines two different laws. Some authors use the term to mean Weber's law, and others Fechner's law. Fechner himself added confusion to the literature by calling his own law Weber's law...
, especially The case of sound
External links