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| {{about|the measurement of audible sound|the music album|Sound Pressure Level}}
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| {{Sound measurements}}
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| '''Sound pressure''' or '''acoustic pressure''' is the local [[pressure]] deviation from the ambient (average, or equilibrium) [[atmospheric pressure]], caused by a [[sound wave]]. In air, sound pressure can be measured using a [[microphone]], and in water with a [[hydrophone]]. The SI unit for sound pressure ''p'' is the [[pascal (unit)|pascal]] (symbol: Pa).
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| [[File:Sound pressure diagram.svg|thumb|250px|Sound pressure diagram: 1. silence, 2. audible sound, 3. atmospheric pressure, 4. instantaneous sound pressure]]
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| '''Sound pressure level''' (SPL) or '''sound level''' is a [[logarithmic scale|logarithmic measure]] of the effective sound pressure of a sound relative to a reference value. It is measured in [[decibel]]s (dB) above a standard reference level. The standard reference sound pressure in air or other gases is 20 [[micropascal|µPa]], which is usually considered the [[threshold of human hearing]] (at 1 [[Hertz|kHz]]). | |
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| == Instantaneous sound pressure ==
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| The '''instantaneous sound pressure''' is the deviation from the local ambient pressure <math>p_{0}</math> caused by a sound wave at a given location and given instant in time.
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| The '''effective sound pressure''' is the [[root mean square]] of the instantaneous sound pressure over a given interval of time (or space).
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| Total pressure <math>p_{\rm total}</math> is given by:
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| :<math>
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| p_{\rm total} = p_{0} + p_{\rm osc} \,
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| </math>
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| where:
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| :<math>p_{0}</math> = local ambient atmospheric (air) pressure,
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| :<math>p_{\rm osc}</math> = sound pressure deviation.
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| ===Intensity===
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| In a sound wave, the complementary variable to sound pressure is the acoustic [[particle velocity]].
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| Together they determine the acoustic intensity of the wave. The local instantaneous [[sound intensity]] is the product of the sound pressure and the acoustic particle velocity.
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| :<math>
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| \vec{I} = p \vec{v}
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| </math>
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| ===Acoustic impedance===
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| For small amplitudes, sound pressure and volume velocity are linearly related and their ratio is the [[acoustic impedance]]. The acoustic impedance depends on both the characteristics of the wave and the [[transmission medium]].
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| The acoustic impedance is given by<ref>{{cite web|last=Wolfe|first=J.|title=What is acoustic impedance and why is it important?|url=http://www.phys.unsw.edu.au/jw/z.html|publisher=University of New South Wales, Dept. of Physics, Music Acoustics|accessdate=1 January 2014}}</ref>
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| :<math>
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| Z = \frac{p}{U}
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| </math>
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| where
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| : ''Z'' is [[acoustic impedance]] or sound impedance
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| : ''p'' is sound pressure
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| : ''U'' is [[volume velocity]]
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| ===Particle displacement===
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| Sound pressure ''p'' is connected to '''[[particle displacement]]''' (or particle amplitude) ξ by
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| :<math>
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| \xi = \frac{v}{2 \pi f} = \frac{v}{\omega} = \frac{p}{Z \omega} = \frac{p}{ 2 \pi f Z} \,
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| </math>.
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| Sound pressure ''p'' is
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| :<math>
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| p = \rho c 2 \pi f \xi = \rho c \omega \xi = Z \omega \xi = { 2 \pi f \xi Z} = \frac{a Z}{\omega} = Z v = c \sqrt{\rho E} = \sqrt{\frac{P_{ac} Z}{A}} \,
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| </math>,
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| normally in units of N/m² = Pa.
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| where:
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| {| class="wikitable"
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| ! Symbol !! [[SI Unit]] !! Meaning
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| ! ''p''
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| | [[pascal (unit)|pascal]]s || sound pressure
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| |-
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| ! ''f''
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| | [[hertz]] || [[frequency]]
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| |-
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| ! ''ρ''
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| | [[kilogram|kg]]/[[Metre|m]]³ || [[density|density of medium]]
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| |-
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| ! ''c''
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| | [[Metre|m]]/[[second|s]] || [[speed of sound]]
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| |-
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| ! ''v''
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| | [[Meters per second|m/s]] || [[particle velocity]]
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| |-
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| ! ''ω'' = 2'' π f ''
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| | [[radian]]s/[[second|s]] || [[angular frequency]]
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| |-
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| ! ''ξ''
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| | [[meter]]s || [[particle displacement]]
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| |-
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| ! ''Z'' = ''c ρ''
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| | [[Newton (unit)|N]]·[[second|s]]/[[Metre|m]]³ || [[acoustic impedance]]
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| |-
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| ! ''a''
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| | [[Metre|m]]/[[second|s]]² || [[particle acceleration]]
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| |-
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| ! ''I''
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| | [[Watt|W]]/[[Metre|m]]² || [[sound intensity]]
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| |-
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| ! ''E''
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| | [[Watt|W]]·[[second|s]]/[[Metre|m]]³ || [[sound energy density]]
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| |-
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| ! ''P''<sub>ac</sub>
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| | [[watt]]s || [[sound power]] or [[acoustic power]]
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| |-
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| ! ''A''
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| | [[Metre|m]]² || [[Area]]
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| |}
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| ===Distance law===
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| 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 [[inverse-square law|1/''r''<sup>2</sub>]], like sound intensity):.<ref>{{cite book|last=Longhurst|first=R.S.|title=Geometrical and Physical Optics|year=1967|publisher=Longmans|location=Norwich}}</ref>
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| The '''distance law''' for the sound pressure ''p'' in 3D is inversely proportional to the distance ''r'' of a punctual sound source{{citation needed|date=October 2012}}.
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| :<math>
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| p \propto \dfrac{1}{r} \,
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| </math>
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| If sound pressure <math>p_1\,</math>, is measured at a distance <math>r_1\,</math>, one can calculate the sound pressure <math>p_2\,</math> at another position <math>r_2\,</math>,
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| :<math>
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| \frac{p_2} {p_1} = \frac{r_1}{r_2} \,
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| </math>
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| :<math>
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| p_2 = p_{1} \cdot \dfrac{r_1}{r_2} \,
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| </math>
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| The sound pressure may vary in direction from the source, as well, so measurements at different angles may be necessary, depending on the situation{{citation needed|date=October 2012}}. An obvious example of a source that varies in level in different directions is a [[bullhorn]].
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| ==Sound pressure level==
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| '''Sound pressure level''' (SPL) or sound level <math>L_p</math> is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in [[decibel]]s (dB) above a standard reference level.
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| :<math>
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| L_p=10 \log_{10}\left(\frac{{p_{\mathrm{{rms}}}}^2}{{p_{\mathrm{ref}}}^2}\right) =20 \log_{10}\left(\frac{p_{\mathrm{rms}}}{p_{\mathrm{ref}}}\right)\mbox{ dB} ,
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| </math>
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| where <math>p_{\mathrm{ref}}</math> is the reference sound pressure and <math>p_{\mathrm{rms}}</math> is the rms sound pressure being measured.<ref>Bies, David A., and Hansen, Colin. (2003). ''Engineering Noise Control''.</ref><ref group=note>Sometimes reference sound pressure is denoted ''p''<sub>0</sub>, not to be confused with the (much higher) ambient pressure.</ref>
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| Sometimes variants are used such as dB (SPL), dBSPL, or dB<sub>SPL</sub>. These variants are not recognized as units in the [[SI]].<ref>[http://physics.nist.gov/cuu/pdf/sp811.pdf Thompson and Taylor 2008, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811]</ref> 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.
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| The commonly used reference sound pressure in air is <math>p_{\mathrm{ref}}</math> = 20 [[micropascal|µPa]] (rms) or 0.0002 dynes/cm<sup>2</sup>,<ref>Ross Roeser, Michael Valente, ''Audiology: Diagnosis'' (Thieme 2007), p. 240.</ref> 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 an SPL of 94 dB. In other media, such as [[underwater acoustics|underwater]], a reference level of 1 µPa is used.<ref name=Morfey>{{cite book|last=Morfey|first=Christopher L.|title=Dictionary of Acoustics|year=2001|publisher=Academic Press|location=San Diego|isbn=978-0125069403}}</ref> These references are defined in [[American National Standards Institute|ANSI]] S1.1-1994.<ref>{{cite web |url=http://www.memtechacoustical.com/noise-terms-glossary |title=Noise Terms Glossary |accessdate=2012-10-14}}</ref>
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| The lower limit of audibility is defined as SPL of 0 [[decibel|dB]], but the upper limit is not as clearly defined. While 1 [[atmosphere (unit)|atm]] (194 dB Peak or 191 dB SPL) is the largest pressure variation an undistorted sound wave can have in [[Earth's atmosphere]], larger sound waves can be present in other [[atmosphere]]s or other media such as under water, or through the Earth.
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| [[File:Lindos1.svg|thumb|right|300px|[[Equal-loudness contour]]]]
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| Ears detect changes in sound pressure. Human hearing does not have a flat [[spectral sensitivity]] ([[frequency response]]) relative to frequency versus [[amplitude]]. Humans do not perceive low- and high-frequency sounds as well as they perceive sounds near 2,000 Hz, as shown in the [[equal-loudness contour]]. 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.{{Citation needed|date=September 2010}}
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| In order to distinguish the different sound measures a suffix is used: A-weighted sound pressure level is written either as dB<sub>A</sub> or L<sub>A</sub>. B-weighted sound pressure level is written either as dB<sub>B</sub> or L<sub>B</sub>, and C-weighted sound pressure level is written either as dB<sub>C</sub> or L<sub>C</sub>. Unweighted sound pressure level is called "linear sound pressure level" and is often written as dB<sub>L</sub> or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL.
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| ===Distance===
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| 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 [[metre]] (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 chamber]] allows for sound to be comparable to measurements made in a free field environment.
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| When sound level <math>L_{p1}</math> is measured at a distance <math>r_1</math>, the sound level <math>L_{p2}</math> at the distance <math>r_2</math> is
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| :<math>
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| L_{p2} = L_{p1} + 20 \cdot \log_{10} \left( \frac{r_1}{r_2} \right)
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| </math>
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| ===Multiple sources===
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| The formula for the sum of the sound pressure levels of ''n'' incoherent radiating sources is
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| :<math>
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| L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(\frac{{p_1}^2 + {p_2}^2 + \cdots + {p_n}^2}{{p_{\mathrm{ref}}}^2}\right)
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| = 10\,\cdot\,{\rm log}_{10} \left(\left({\frac{p_1}{p_{\mathrm{ref}}}}\right)^2 + \left({\frac{p_2}{p_{\mathrm{ref}}}}\right)^2 + \cdots + \left({\frac{p_n}{p_{\mathrm{ref}}}}\right)^2\right)
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| </math>
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| From the formula of the sound pressure level we find
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| :<math>
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| \left({\frac{p_i}{p_{\mathrm{ref}}}}\right)^2 = 10^{\frac{L_i}{10}},\qquad i=1,2,\cdots,n
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| </math>
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| This inserted in the formula for the sound pressure level to calculate the sum level shows
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| :<math>
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| L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(10^{\frac{L_1}{10}} + 10^{\frac{L_2}{10}} + \cdots + 10^{\frac{L_n}{10}} \right)\,{\rm dB}
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| </math>
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| ===Examples of sound pressure and sound pressure levels===
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| <!-- This section is linked from [[Sound]] -->
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| Sound pressure in air:
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| {{Refimprove| table |date=March 2009}}
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| {| class="wikitable"
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| ! Source of sound !! Sound pressure !! Sound pressure level
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| |-
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| ! Sound in air !! [[pascal (unit)|pascal]]* !! [[Decibel|dB]] ref 20 μPa
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| |-
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| |[[shock wave|Shockwave]] (distorted sound waves > 1 [[Atmosphere (unit)|atm]]; waveform valleys are clipped at zero pressure)|| align="right" | >101,325 Pa (peak)|| align="right" | >194 dB(peak)
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| |-
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| |Theoretical limit for undistorted sound at 1 [[atmosphere (unit)|atmosphere]] environmental [[pressure]] || align="right" | 101,325 Pa (peak) || align="right" | ~194.094 dB (peak)
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| |-
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| |[[Stun grenades]]|| align="right" | 6,000–20,000 Pa (peak) || align="right" | 170–180 dB (peak)
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| |-
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| |Simple open-ended [[thermoacoustics|thermoacoustic]] device<ref>Hatazawa, M., Sugita, H., Ogawa, T. & Seo, Y. (Jan. 2004), ‘Performance of a thermoacoustic sound wave generator driven with waste heat of automobile gasoline engine,’ ''Transactions of the Japan Society of Mechanical Engineers (Part B)'' Vol. 16, No. 1, 292–299. [http://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=200407211336MT&q=Performance+of+a+thermoacoustic+sound+wave+generator+driven+with+waste+heat+of+automobile+gasoline+engine&uid=790404233]</ref> || align="right" | 12,619 Pa || align="right" | 176 dB
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| |-
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| |[[.30-06 Springfield|.30-06 rifle]] being fired 1 [[meter|m]] to shooter's side || align="right" | 7,265 Pa (peak) || align="right" | 171 dB (peak)
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| |-
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| |[[M1 Garand]] rifle being fired at 1 m || align="right" | 5,023 Pa (peak) || align="right" | 168 dB (peak)
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| |-
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| |Rocket launch equipment acoustic tests || align="right" | ~4000 Pa || align="right" | ~165 dB
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| |-
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| |[[Jet engine]] at 30 m || align="right" | 632 Pa || align="right" | 150 dB
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| |-
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| |[[Threshold of pain]] || align="right" | 63.2 Pa || align="right" | 130 dB
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| |-
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| |[[Vuvuzela]] horn at 1 m || align="right" | 20 Pa || align="right" | 120 dB(A)<ref>{{Cite journal|format=PDF|title=Vuvuzela – good for your team, bad for your ears|url=http://www.scielo.org.za/pdf/samj/v100n2/v100n2a15.pdf|journal=South African Medical Journal |volume=100|issue=4|date=February 2010|pages=99–100|first1=De Wet|last1=Swanepoel|first2=James W|last2=Hall III |first3=Dirk|last3=Koekemoer|pmid=20459912}}</ref>
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| |-
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| |Risk of instantaneous [[noise-induced hearing loss]] || align="right" | 20 Pa || align="right" | approx. 120 dB
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| |-
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| |[[Jet engine]] at 100 m || align="right" | 6.32 – 200 Pa || align="right" | 110 – 140 dB
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| |-
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| |Non-electric [[chainsaw]] at 1 m || align="right" | 6.3 Pa ||align="right" | 110 dB<ref name="sengpielaudio">{{cite web|publisher="sengpielaudio"|title=Decibel Table - SPL - Loudness Comparison Chart|url=http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm|accessdate=5 Mar 2012}}</ref>
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| |-
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| |[[Jack hammer]] at 1 m || align="right" | 2 Pa || align="right" | approx. 100 dB
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| |-
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| |Traffic on a busy roadway at 10 m || align="right" | 2×10<sup>−1</sup> – 6.32×10<sup>−1</sup> Pa || align="right" | 80 – 90 dB
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| |-
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| |[[Hearing damage]] (over long-term exposure, need not be continuous) || align="right" | 0.356 Pa || align="right" | 85 dB<ref name=Hamby/>
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| |-
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| |[[automobile|Passenger car]] at 10 m || align="right" | 2×10<sup>−2</sup> – 2×10<sup>−1</sup> Pa || align="right" | 60 – 80 dB
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| |-
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| |[[United States Environmental Protection Agency|EPA]]-identified maximum to protect against hearing loss and other disruptive effects from noise, such as sleep disturbance, stress, learning detriment, etc. || align="right" | || align="right" | 70 dB<ref>{{citation |url=http://www.epa.gov/aboutepa/history/topics/noise/01.html|title=EPA Identifies Noise Levels Affecting Health and Welfare |date=1974-04-02 |accessdate=2010-11-01}}</ref>
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| |-
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| |Handheld electric [[Mixer (cooking)|mixer]] || align="right" | || align="right" | 65 dB
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| |-
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| |TV (set at home level) at 1 m || align="right" | 2×10<sup>−2</sup> Pa || align="right" | approx. 60 dB
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| |-
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| |[[Washing machine]], [[dishwasher]] || align="right" | || align="right" | 42-53 dB<ref>{{cite web|url=http://www.boschappliances.com.au/Files/Bosch/Au/au_en/ProductAnnouncement/Images/Bosch_Active_Water.pdf|date=|title=Active Water|page=17|publisher=Bosch|accessdate=4 March 2012}}</ref>
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| |-
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| |Normal conversation at 1 m || align="right" | 2×10<sup>−3</sup> – 2×10<sup>−2</sup> Pa || align="right" | 40 – 60 dB
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| |-
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| |Very calm room || align="right" | 2×10<sup>−4</sup> – 6.32×10<sup>−4</sup> Pa || align="right" | 20 – 30 dB
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| |-
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| |Light leaf rustling, calm breathing || align="right" | 6.32×10<sup>−5</sup> Pa || align="right" | 10 dB
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| |-
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| |[[Auditory threshold]] at 1 kHz || align="right" | 2×10<sup>−5</sup> Pa || align="right" | 0 dB<ref name=Hamby>{{Cite web|url=http://www.makeitlouder.com/Decibel%20Level%20Chart.txt |title=Ultimate Sound Pressure Level Decibel Table |archiveurl=http://www.webcitation.org/5rXlLRYsP |archivedate=2010-07-27 |author=William Hamby}}</ref>
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| |}
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| <nowiki>*</nowiki>All Values are RMS unless otherwise stated.
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| ==See also==
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| *[[Acoustics]]
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| *[[Phon]] (unit)
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| *[[Loudness]]
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| *[[Sone]] (unit)
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| *[[Sound level meter]]
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| *[[Stevens' power law]]
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| *[[Weber–Fechner law]], especially [[Weber–Fechner law#The case of sound|The case of sound]]
| |
| | |
| ==Notes==
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| <references group=note/>
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| | |
| ==References==
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| {{Reflist}}
| |
| | |
| * Beranek, Leo L, "Acoustics" (1993) Acoustical Society of America. ISBN 0-88318-494-X
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| * Daniel R. Raichel, "The Science and Applications of Acoustics" (2006), Springer New York, ISBN 1441920803
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| | |
| ==External links==
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| *[http://www.sengpielaudio.com/SoundPressureAndSoundPower.pdf Sound pressure and Sound power – Effect and Cause]
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| *[http://www.sengpielaudio.com/calculator-soundlevel.htm Conversion of sound pressure to sound pressure level and vice versa]
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| *[http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm Table of Sound Levels - Corresponding Sound Pressure and Sound Intensity]
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| *[http://www.sengpielaudio.com/calculator-ak-ohm.htm Ohm's law as acoustic equivalent - calculations]
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| *[http://www.rane.com/par-s.html#SPL Definition of sound pressure level]
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| *[http://www-ccrma.stanford.edu/~jos/mdft/DB_SPL.html A table of SPL values]
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| *[http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]
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| *[http://www.usmotors.com/products/ProFacts/sound_power_and_sound_pressure.htm Sound pressure and sound power - two commonly confused characteristics of sound]
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| *[http://www.sengpielaudio.com/calculator-levelchange.htm How many decibels is twice as loud? Sound level change and the respective factor of sound pressure or sound intensity]
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| *[http://www.gcaudio.com/resources/howtos/loudness.html Decibel (loudness) comparison chart]
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| {{DEFAULTSORT:Sound Pressure}}
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| [[Category:Sound measurements]]
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