Sound pressure

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Sound pressure

Sound pressure is the local pressure

Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
deviation from the ambient (average, or equilibrium) pressure caused by a sound

Sound

Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....
wave

Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
. Sound pressure can be measured using a microphone

Microphone

A microphone, sometimes referred to as a mike or?more recently?mic, is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal....
in air and a hydrophone

Hydrophone

A 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 is the pascal

Pascal (unit)

The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
(symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure p₀ caused by a sound

Sound

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Encyclopedia

Sound pressure is the local pressure

Pressure

Sound

Wave

Microphone

Hydrophone

Pascal (unit)

Sound

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistics 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). In a sound wave, the complementary variable to sound pressure is the acoustic particle velocity

Particle velocity

Particle velocity is the velocity v of a particle in a Transmission 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....
. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance

Acoustic impedance

The acoustic impedance Z is a frequency f dependent parameter 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 medium

Transmission medium

A transmission medium is a material substance which can wave propagation energy waves. For example, the transmission medium for sound received by the ears is usually air, but solids and liquids may also act as transmission media for sound....
. The local instantaneous sound intensity

Sound intensity

The sound intensity, I, 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....
is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity.

The sound pressure deviation (instantaneous acoustic pressure) p is

where

F = force,

A = area.

The entire pressure p_total is

where

p₀ = local ambient pressure,

p = sound pressure deviation.

Sound pressure level

Sound pressure level (SPL) or sound

Sound

Level

Level may refer to:*A floor of a building*A level of a mine, see shaft mining. A level with access to the surface is an adit*Level , a stage of the game...
L_p is a logarithmic measure

Logarithmic scale

A logarithmic scale is a scale that uses the logarithm of a physical quantity instead of the quantity itself.Presentation of data on a logarithmic scale can be helpful when the data covers a large range of values – the logarithm reduces this to a more manageable range....
of the rms

Root mean square

Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
of a sound relative to a reference value. It is measured in decibel

Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
s (dB).

where is the reference sound pressure and is the rms sound pressure being measured.

Sometimes variants are used such as dB (SPL), dBSPL, or dB_SPL. These variants are not permitted by SI

Si, si, or SI may refer to :...
.

The unit dB (SPL) is often abbreviated to just "dB", which gives some the erroneous notion 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

Mosquito

Mosquitoes are common flying insects in the family Culicidae that are found around the world. There are about 3,500 species. They have a pair of scaled wings, a pair of halteres, a slender body, and six long legs....
flying 3 m away). When dealing with hearing

Hearing (sense)

Hearing is one of the traditional five senses. It is the ability to perceive sound by detecting vibrations via an organ such as the ear. The inability to hear is called deafness....
, the perceived loudness of a sound correlates roughly logarithmically to its sound pressure. See also Weber-Fechner law. Most measurements of audio equipment will be made relative to this level, meaning 1 pascal will equal 94 dB of sound pressure.

In other media, such as underwater

Underwater acoustics

Underwater 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....
, a reference level of 1 µPa is more often used.

These references are defined in ANSI

American National Standards Institute

The American National Standards Institute or ANSI 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....
S1.1-1994.

The human ear

Ear

The ear is the sense organ that detects sounds. The vertebrate ear shows a common biology from fish to humans, with variations in structure according to order and species....
is a sound pressure sensitive detector. It does not have a flat spectral response, so the sound pressure is often frequency weighted

Weighting filter

A weighting filter is used to emphasise or suppress some aspects of a phenomenon compared to others, for measurement or other purposes....
such that the measured level will match the perceived level. When weighted in this way the measurement is referred to as a sound level. The International Electrotechnical Commission

International Electrotechnical Commission

The International Electrotechnical Commission is a Non-profit organization, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies ? collectively known as "electrotechnology"....
(IEC) has defined several weighting schemes. A-weighting

A-weighting

A Weighting curve is a graph that is used to 'weight' measured values of a variable according to their importance in relation to some outcome. The most commonly know example is in sound level measurement where a specific set of weighting curves known as A, B, C and D weighting are often used....
attempts to match the response of the human ear to pure tones, while C-weighting is used to measure peak sound levels. If the (unweighted) SPL is desired, many instruments allow a "flat" or unweighted measurement to be made. See also Weighting filter
Weighting filter

A weighting filter is used to emphasise or suppress some aspects of a phenomenon compared to others, for measurement or other purposes....
.

When measuring the sound created by an object, it is important to measure the distance from the object as well, since the SPL decreases in distance from a point source

Point source

A point source is a localised relatively-small source of something.Point source may also refer to:*Point source , a localised source of pollution...
with 1/r (and not with 1/r²

Inverse-square law

In physics, an inverse-square law is any physical law stating that some physical quantity or strength is Inverse ly proportionality to the square of the distance from the source of that physical quantity....
, like sound intensity

Sound intensity

The sound intensity, I, 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....
). It often varies in direction from the source, as well, so many measurements 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 p in N/m² or Pa is

where

Z is acoustic impedance

Acoustic impedance

The acoustic impedance Z is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments....
, sound impedance, or characteristic impedance

Characteristic impedance

The characteristic impedance or surge impedance of a uniform transmission line, usually written , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections....
, in Pa·s/m

v is particle velocity

Particle velocity

J is acoustic intensity or sound intensity

Sound intensity

The sound intensity, I, 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....
, in W/m²

Sound pressure p is connected to particle displacement
Particle displacement

Particle displacement or particle amplitude is a measurement of distance of the movement of a particle in a medium as it transmits a wave....
(or particle amplitude) ?, in m, by .

Sound pressure p is ,

normally in units of N/m² = Pa.

where:

Symbol	SI Unit	Meaning
p	pascal Pascal (unit) The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter.... s	sound pressure
f	hertz Hertz The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....	frequency Frequency Frequency 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....
?	kg Kilogram The kilogram or kilogrammeThe spelling kilogram is used by the International Committee for Weights and Measures and the U.S.... /m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... ³	density of air Density of air The density of air, ? , 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....
c	m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... /s Second The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....	speed of sound Speed of sound Sound is a vibration that travels through an elasticity medium as a wave. The speed of sound describes how much distance such a wave travels in a certain amount of time....
v	m/s	particle velocity Particle velocity Particle velocity is the velocity v of a particle in a Transmission 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 Second The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....	angular frequency Angular frequency In physics , angular frequency ? is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity....
?	meters	particle displacement Particle displacement Particle displacement or particle amplitude is a measurement of distance of the movement of a particle in a medium as it transmits a wave....
Z = c • ?	N Newton The newton is the International System of Units SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics.... ·s Second The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time.... /m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... ³	acoustic impedance Acoustic impedance The acoustic impedance Z is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments....
a	m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... /s Second The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time.... ²	particle acceleration 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 per second squared....
J	W WATT WATT is a radio station broadcasting a News radio-Talk radio-Sports radio format. Licensed to Cadillac, Michigan, it first began broadcasting in 1945.... /m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... ²	sound intensity Sound intensity The sound intensity, I, 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....
E	W WATT WATT is a radio station broadcasting a News radio-Talk radio-Sports radio format. Licensed to Cadillac, Michigan, it first began broadcasting in 1945.... ·s Second The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time.... /m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... ³	sound energy density 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. The letter "lower case w" sign is easily mixed with the sign , therefore we choose the letter E....
P_ac	watt WATT WATT is a radio station broadcasting a News radio-Talk radio-Sports radio format. Licensed to Cadillac, Michigan, it first began broadcasting in 1945.... s	sound power Sound power Sound power or acoustic power Pac is a measure of sound energy E per time t unit.It is measured in watts, or sound intensity I times area A:... or acoustic power
A	m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes.... ²	Area Area Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....

The distance law for the sound pressure p is inverse-proportional to the distance r of a punctual sound source. (proportional)

The assumption of 1/r² with the square is here wrong. That is only correct for sound intensity

Sound intensity

The sound intensity, I, 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....
.

Note: The often used term "intensity of sound pressure" is not correct. Use "magnitude
Magnitude (mathematics)

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
", "strength", "amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
", or "level
Level

Level may refer to:*A floor of a building*A level of a mine, see shaft mining. A level with access to the surface is an adit*Level , a stage of the game...
" instead. "Sound intensity
Sound intensity

The sound intensity, I, 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....
" is sound power
Sound power

Sound power or acoustic power Pac is a measure of sound energy E per time t unit.It is measured in watts, or sound intensity I times area A:...
per unit area, while "pressure" is a measure of force per unit area. Intensity is not equivalent to pressure.

Hence

Examples of sound pressure and sound pressure levels

Sound pressure in air:

Source of sound	Sound pressure	Sound pressure level
	pascal Pascal (unit) The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....	dB Decibel The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level.... re 20 µPa
Krakatoa Krakatoa Krakatoa , also spelled Krakatao, is a Island#Oceanic islands in the Sunda Strait between the islands of Java and Sumatra in Indonesia. The name is used for the island group, the main island , and the volcano as a whole.... explosion at 100 miles (160 km) in air	20,000 Pa	180 dB
Simple open-ended thermoacoustic device	12,000 Pa	176 dB
M1 Garand M1 Garand The M1 Garand was the first semi-automatic rifle to be generally issued to the infantry of any nation. In 1936, it officially replaced the bolt-action M1903 Springfield as the standard service rifle of the United States Armed Forces and was subsequently replaced by the selective-fire M14 rifle in 1957.... being fired at 1 m	5,000 Pa	168 dB
Jet engine Jet engine A jet engine is a reaction engine that discharges a fast moving jet of fluid to generate thrust in accordance with Isaac Newton Newton's laws of motion.... at 30 m Metre The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....	630 Pa	150 dB
Rifle Rifle A rifle is a firearm designed to be fired from the shoulder, with a barrel that has a helical groove or pattern of grooves cut into the barrel walls.... being fired at 1 m	200 Pa	140 dB
Threshold of pain Threshold of pain In hearing, the threshold of pain is the sound pressure or sound pressure level beyond which sound becomes unbearable for a human listener. This threshold varies only slightly with frequency....	100 Pa	130 dB
Hearing damage (due to short-term exposure)	20 Pa	approx. 120 dB
Jet Jet engine A jet engine is a reaction engine that discharges a fast moving jet of fluid to generate thrust in accordance with Isaac Newton Newton's laws of motion.... at 100 m	6 – 200 Pa	110 – 140 dB
Jack hammer Jack Hammer Jack Hammer may be:* Jack Hammer * Fictional characters: "Jack" Hammer, Rescue Heroes#Main Jack Hammer, aka Weasel See also:* Jackhammer, pneumatic drill construction tool... at 1 m	2 Pa	approx. 100 dB
Hearing damage (due to long-term exposure)	6×10^-1 Pa	approx. 85 dB
Major road at 10 m	2×10^-1 – 6×10^-1 Pa	80 – 90 dB
Passenger car Automobile An automobile or motor car is a wheeled motor vehicle for transportation passengers, which also carries its own car engine or motor. Most definitions of the term specify that automobiles are designed to run primarily on roads, to have seating for one to eight people, to typically have four wheels, and to be constructed principally f... at 10 m	2×10^-2 – 2×10^-1 Pa	60 – 80 dB
TV (set at home level) at 1 m	2×10^-2 Pa	approx. 60 dB
Normal talking at 1 m	2×10^-3 – 2×10^-2 Pa	40 – 60 dB
Very calm room	2×10^-4 – 6×10^-4 Pa	20 – 30 dB
Leaves rustling, calm breathing	6×10^-5 Pa	10 dB
Auditory threshold at 1 kHz	2×10^-5 Pa	0 dB

Sound pressure in water:

Source of sound	Sound pressure	Sound pressure level
	pascal Pascal (unit) The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....	dB Decibel The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level.... re 1 µPa
Pistol shrimp		218 dB
Sperm Whale Sperm Whale The Sperm Whale is the largest of all toothed whales and largest living toothed animal. The whale was named after the milky-white waxy substance, spermaceti, found in its head and originally mistaken for sperm or semen....		163-180 dB
Fin Whale Fin Whale The Fin Whale , also called the Finback Whale, Razorback, or Common Rorqual, is a marine mammal belonging to the suborder of baleen whales....		160-186 dB
Humpback Whale Humpback Whale The humpback whale is a Baleen whale whale. One of the larger rorqual species, adults range in length from 12–16 metres and weigh approximately 36,000 kilograms ....		144-174 dB
Bowhead Whale Bowhead Whale The Bowhead Whale , also known as Greenland Right Whale or Arctic Whale, is a baleen whale of the right whale family Balaenidae. A stocky dark-colored whale without a dorsal fin, it can grow to 20 meters in length....		128-189 dB
Blue Whale Blue Whale The Blue Whale is a marine mammal belonging to the suborder of baleen whales . At up to 32.9 metres in length and 172 metric tonnes or more in weight, it is the largest whale and the largest living animal and is believed to be the largest organism ever to have existed....		155-188 dB
Southern Right Whale Southern Right Whale The Southern Right Whale is a baleen whale, one of three species classified as right whales belonging to the genus Eubalaena. Around 12,000 Southern Right Whales are spread throughout the southern part of the Southern Hemisphere....		172-187 dB
Gray Whale Gray Whale The Gray Whale is a whale that travels between feeding and breeding grounds yearly. It reaches a length of about 16 meters , a weight of 36 tons and an age of 50–60 years....		142-185 dB
Auditory threshold of a diver at 1 kHz	2.2 × 10^-3 Pa	67 dB

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

Sound pressure

Sound pressure level

Examples of sound pressure and sound pressure levels

See also

External links