Movatterモバイル変換

[0]ホーム
URL:

Jump to content
WikipediaThe Free Encyclopedia
Search

Sound pressure

From Wikipedia, the free encyclopedia
Local pressure deviation caused by a sound wave
Not to be confused withSound energy density.
Sound measurements
Characteristic
Symbols
 Sound pressure p, SPL,LPA
 Particle velocity v, SVL
 Particle displacement δ
 Sound intensity I, SIL
 Sound power P, SWL,LWA
 Sound energy W
 Sound energy density w
 Sound exposure E, SEL
 Acoustic impedance Z
 Audio frequency AF
 Transmission loss TL

Sound pressure oracoustic pressure is the localpressure deviation from the ambient (average or equilibrium)atmospheric pressure, caused by asound wave. In air, sound pressure can be measured using amicrophone, and in water with ahydrophone. TheSI unit of sound pressure is thepascal (Pa).[1]

Mathematical definition

[edit]
Sound pressure diagram:
  1. Silence
  2. Audible sound
  3. Atmospheric pressure
  4. Sound pressure

A sound wave in atransmission medium causes a deviation (sound pressure, adynamic pressure) in the local ambient pressure, astatic pressure.

Sound pressure, denotedp, is defined byptotal=pstat+p,{\displaystyle p_{\text{total}}=p_{\text{stat}}+p,}where

  • ptotal is the total pressure,
  • pstat is the static pressure.

Sound measurements

[edit]

Sound intensity

[edit]
Main article:Sound intensity

In a sound wave, the complementary variable to sound pressure is theparticle velocity. Together, they determine the sound intensity of the wave.

Sound intensity, denotedI and measured inW·m−2 in SI units, is defined byI=pv,{\displaystyle \mathbf {I} =p\mathbf {v} ,}where

  • p is the sound pressure,
  • v is the particle velocity.

Acoustic impedance

[edit]
Main article:Acoustic impedance

Acoustic impedance, denotedZ and measured in Pa·m−3·s in SI units, is defined by[2]Z(s)=p^(s)Q^(s),{\displaystyle Z(s)={\frac {{\hat {p}}(s)}{{\hat {Q}}(s)}},}where

Specific acoustic impedance, denotedz and measured in Pa·m−1·s in SI units, is defined by[2]z(s)=p^(s)v^(s),{\displaystyle z(s)={\frac {{\hat {p}}(s)}{{\hat {v}}(s)}},}where

Particle displacement

[edit]
Main article:Particle displacement

Theparticle displacement of aprogressivesine wave is given byδ(r,t)=δmcos⁡(k⋅r−ωt+φδ,0),{\displaystyle \delta (\mathbf {r} ,t)=\delta _{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}),}where

It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wavex are given byv(r,t)=∂δ∂t(r,t)=ωδmcos⁡(k⋅r−ωt+φδ,0+π2)=vmcos⁡(k⋅r−ωt+φv,0),{\displaystyle v(\mathbf {r} ,t)={\frac {\partial \delta }{\partial t}}(\mathbf {r} ,t)=\omega \delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=v_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{v,0}),}p(r,t)=−ρc2∂δ∂x(r,t)=ρc2kxδmcos⁡(k⋅r−ωt+φδ,0+π2)=pmcos⁡(k⋅r−ωt+φp,0),{\displaystyle p(\mathbf {r} ,t)=-\rho c^{2}{\frac {\partial \delta }{\partial x}}(\mathbf {r} ,t)=\rho c^{2}k_{x}\delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=p_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{p,0}),}where

Taking the Laplace transforms ofv andp with respect to time yieldsv^(r,s)=vmscos⁡φv,0−ωsin⁡φv,0s2+ω2,{\displaystyle {\hat {v}}(\mathbf {r} ,s)=v_{\text{m}}{\frac {s\cos \varphi _{v,0}-\omega \sin \varphi _{v,0}}{s^{2}+\omega ^{2}}},}p^(r,s)=pmscos⁡φp,0−ωsin⁡φp,0s2+ω2.{\displaystyle {\hat {p}}(\mathbf {r} ,s)=p_{\text{m}}{\frac {s\cos \varphi _{p,0}-\omega \sin \varphi _{p,0}}{s^{2}+\omega ^{2}}}.}

Sinceφv,0=φp,0{\displaystyle \varphi _{v,0}=\varphi _{p,0}}, the amplitude of the specific acoustic impedance is given byzm(r,s)=|z(r,s)|=|p^(r,s)v^(r,s)|=pmvm=ρc2kxω.{\displaystyle z_{\text{m}}(\mathbf {r} ,s)=|z(\mathbf {r} ,s)|=\left|{\frac {{\hat {p}}(\mathbf {r} ,s)}{{\hat {v}}(\mathbf {r} ,s)}}\right|={\frac {p_{\text{m}}}{v_{\text{m}}}}={\frac {\rho c^{2}k_{x}}{\omega }}.}

Consequently, the amplitude of the particle displacement is related to that of the acoustic velocity and the sound pressure byδm=vmω,{\displaystyle \delta _{\text{m}}={\frac {v_{\text{m}}}{\omega }},}δm=pmωzm(r,s).{\displaystyle \delta _{\text{m}}={\frac {p_{\text{m}}}{\omega z_{\text{m}}(\mathbf {r} ,s)}}.}

Inverse-proportional law

[edit]
Further information:Inverse-square law

When measuring the sound pressure created by a sound source, it is important to measure the distance from the object as well, since the sound pressure of aspherical sound wave decreases as 1/r from the centre of the sphere (and not as 1/r2, like thesound intensity):[3]p(r)∝1r.{\displaystyle p(r)\propto {\frac {1}{r}}.}

This relationship is aninverse-proportional law.

If the sound pressurep1 is measured at a distancer1 from the centre of the sphere, the sound pressurep2 at another positionr2 can be calculated:p2=r1r2p1.{\displaystyle p_{2}={\frac {r_{1}}{r_{2}}}\,p_{1}.}

The inverse-proportional law for sound pressure comes from the inverse-square law forsound intensity:I(r)∝1r2.{\displaystyle I(r)\propto {\frac {1}{r^{2}}}.}Indeed,I(r)=p(r)v(r)=p(r)[p∗z−1](r)∝p2(r),{\displaystyle I(r)=p(r)v(r)=p(r)\left[p*z^{-1}\right](r)\propto p^{2}(r),}where

hence the inverse-proportional law:p(r)∝1r.{\displaystyle p(r)\propto {\frac {1}{r}}.}

Sound pressure level

[edit]
For other uses, seeSound level.

Sound pressure level (SPL) oracoustic pressure level (APL) is alogarithmic measure of the effective pressure of a sound relative to a reference value.

Sound pressure level, denotedLp and measured indB,[4] is defined by:[5]Lp=ln⁡(p2p02) Np=2log10⁡(pp0) B=20log10⁡(pp0) dB,{\displaystyle L_{p}=\ln \left({\frac {p^{2}}{p_{0}^{2}}}\right)~{\text{Np}}=2\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{B}}=20\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{dB}},}where

  • p is theroot mean square sound pressure,[6]
  • p0 is areference sound pressure,
  • 1 Np is theneper,
  • 1 B = (⁠1/2⁠ ln 10) Np is thebel,
  • 1 dB = (⁠1/20⁠ ln 10) Np is thedecibel.

The commonly used reference sound pressure in air is[7]

p0 = 20 μPa,

which is often considered as thethreshold of human hearing (roughly the sound of a mosquito flying 3 m away). The proper notations for sound pressure level using this reference areLp/(20 μPa) orLp (re 20 μPa), but the suffix notationsdB SPL,dB(SPL), dBSPL, and dBSPL are very common, even if they are not accepted by the SI.[8]

Most sound-level measurements will be made relative to this reference, meaning1 Pa will equal an SPL of20log10⁡(12×10−5) dB≈94 dB{\displaystyle 20\log _{10}\left({\frac {1}{2\times 10^{-5}}}\right)~{\text{dB}}\approx 94~{\text{dB}}}. In other media, such asunderwater, a reference level of1 μPa is used.[9] These references are defined inANSIS1.1-2013.[10]

The main instrument for measuring sound levels in the environment is thesound level meter. Most sound level meters provide readings in A, C, and Z-weighted decibels and must meet international standards such asIEC 61672-2013.

Examples

[edit]

The lower limit of audibility is defined as SPL of0 dB, but the upper limit is not as clearly defined. While1atm (194 dB peak or191 dB SPL)[11][12] is the largest pressure variation an undistorted sound wave can have inEarth's atmosphere (i. e., if the thermodynamic properties of the air are disregarded; in reality, the sound waves become progressively non-linear starting over 150 dB), larger sound waves can be present in otheratmospheres or other media, such as underwater or through the Earth.[13]

Equal-loudness contour, showing sound-pressure-vs-frequency at different perceived loudness levels

Ears detect changes in sound pressure. Human hearing does not have a flatspectral sensitivity (frequency response) relative to frequency versusamplitude. Humans do not perceive low- and high-frequency sounds as well as they perceive sounds between 3,000 and 4,000 Hz, as shown in theequal-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.

In order to distinguish the different sound measures, a suffix is used: A-weighted sound pressure level is written either as dBA or LA, B-weighted sound pressure level is written either as dBB or LB, and C-weighted sound pressure level is written either as dBC or LC. Unweighted sound pressure level is called "linear sound pressure level" and is often written as dBL or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL.[13]

Distance

[edit]

The distance of the measuring microphone from a sound source is often omitted when SPL measurements are quoted, making the data useless, due to the inherent effect of theinverse proportional law. 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 onemetre (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 ananechoic chamber allows sound to be comparable to measurements made in a free field environment.[13]

According to the inverse proportional law, when sound levelLp1 is measured at a distancer1, the sound levelLp2 at the distancer2 isLp2=Lp1+20log10⁡(r1r2) dB.{\displaystyle L_{p_{2}}=L_{p_{1}}+20\log _{10}\left({\frac {r_{1}}{r_{2}}}\right)~{\text{dB}}.}

Multiple sources

[edit]

The formula for the sum of the sound pressure levels ofn incoherent radiating sources isLΣ=10log10⁡(p12+p22+⋯+pn2p02) dB=10log10⁡[(p1p0)2+(p2p0)2+⋯+(pnp0)2] dB.{\displaystyle L_{\Sigma }=10\log _{10}\left({\frac {p_{1}^{2}+p_{2}^{2}+\dots +p_{n}^{2}}{p_{0}^{2}}}\right)~{\text{dB}}=10\log _{10}\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2}+\left({\frac {p_{2}}{p_{0}}}\right)^{2}+\dots +\left({\frac {p_{n}}{p_{0}}}\right)^{2}\right]~{\text{dB}}.}

Inserting the formulas(pip0)2=10Li10 dB,i=1,2,…,n{\displaystyle \left({\frac {p_{i}}{p_{0}}}\right)^{2}=10^{\frac {L_{i}}{10~{\text{dB}}}},\quad i=1,2,\ldots ,n}in the formula for the sum of the sound pressure levels yieldsLΣ=10log10⁡(10L110 dB+10L210 dB+⋯+10Ln10 dB) dB.{\displaystyle L_{\Sigma }=10\log _{10}\left(10^{\frac {L_{1}}{10~{\text{dB}}}}+10^{\frac {L_{2}}{10~{\text{dB}}}}+\dots +10^{\frac {L_{n}}{10~{\text{dB}}}}\right)~{\text{dB}}.}

Examples of sound pressure

[edit]
Examples of sound pressure in air atstandard atmospheric pressure
Source of soundDistanceSound pressure level[a]
(Pa)(dBSPL)
Shock wave (distorted sound waves > 1atm; waveform valleys are clipped at zero pressure)[11][12]>1.01×105>191
Simple open-endedthermoacoustic device[14][clarification needed]1.26×104176
1883 eruption of Krakatoa[15][16]165 km172
.30-06 rifle being fired1 m to
shooter's side		7.09×103171
Firecracker[17]0.5 m7.09×103171
Stun grenade[18]Ambient1.60×103
...8.00×103		158–172
9-inch (23 cm) party balloon inflated to rupture[19]At ear4.92×103168
9-inch (23 cm) diameter balloon crushed to rupture[19]At ear1.79×103159
9-inch (23 cm) party balloon inflated to rupture[19]0.5 m1.42×103157
9-inch (23 cm) diameter balloon popped with a pin[19]At ear1.13×103155
LRAD 1000XiLong Range Acoustic Device[20]1 m8.93×102153
9-inch (23 cm) party balloon inflated to rupture[19]1 m731151
Jet engine[13]1 m632150
9-inch (23 cm) diameter balloon crushed to rupture[19]0.95 m448147
9-inch (23 cm) diameter balloon popped with a pin[19]1 m282.5143
Loudesthuman voice[21]1 inch110135
Trumpet[22]0.5 m63.2130
Vuvuzela horn[23]1 m20.0120
Threshold of pain[24][25][21]At ear20–100120–134
Risk of instantaneousnoise-induced hearing lossAt ear20.0120
Jet engine100–30 m6.32–200110–140
Two-strokechainsaw[26]1 m6.32110
Jackhammer1 m2.00100
Hearing damage (over long-term exposure, need not be continuous)[27]At ear0.3685
EPA-identified maximum to protect against hearing loss and other disruptive effects from noise, such as sleep disturbance, stress, learning detriment, etc.[28]Ambient0.0670
Passenger car at 30 kph (electric andcombustion engines)[29]10 m0.045–0.06367–70
TV (set at home level)1 m0.0260
Normal conversation1 m2×10−3–0.0240–60
Passenger car at 10 kph (combustion)[29]10 m12.6×10−356
Passenger car at 10 kph (electric)[29]10 m6.32×10−350
Very calm roomAmbient2.00×10−4
...6.32×10−4		20–30
Light leaf rustling, calm breathing[13]Ambient6.32×10−510
Auditory threshold at 1 kHz[27]At ear2.00×10−50
Anechoic chamber, Orfield Labs,A-weighted[30][31]Ambient6.80×10−6−9.4
Anechoic chamber,University of Salford,A-weighted[32]Ambient4.80×10−6−12.4
Anechoic chamber, Microsoft,A-weighted[33][34]Ambient1.90×10−6−20.35
  1. ^All values listed are the effective sound pressure unless otherwise stated.

See also

[edit]
  • Acoustics – Branch of physics involving mechanical waves
  • Phon – Logarithmic unit of loudness level
  • Loudness – Subjective perception of sound pressure
  • Sone – Unit of perceived loudness
  • Sound level meter – Device for acoustic measurements
  • Stevens's power law – Empirical relationship between actual and perceived changed intensity of stimulus
  • Weber–Fechner law – Related laws in the field of psychophysics

References

[edit]
  1. ^"Sound Pressure Is the Force of Sound on a Surface Area Perpendicular to the Direction of the Sound". Retrieved22 April 2015.
  2. ^abWolfe, J."What is acoustic impedance and why is it important?". University of New South Wales, Dept. of Physics, Music Acoustics. Retrieved1 January 2014.
  3. ^Longhurst, R. S. (1967).Geometrical and Physical Optics. Norwich: Longmans.
  4. ^"Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units",IEC 60027-3 Ed. 3.0, International Electrotechnical Commission, 19 July 2002.
  5. ^Attenborough K, Postema M (2008).A Pocket-Sized Introduction to Acoustics. Kingston upon Hull: The University of Hull.doi:10.5281/zenodo.7504060.ISBN 978-90-812588-2-1.
  6. ^Bies, David A.; Hansen, Colin (2003).Engineering Noise Control.
  7. ^Ross Roeser, Michael Valente,Audiology: Diagnosis (Thieme 2007), p. 240.
  8. ^Thompson, A. and Taylor, B. N. Sec. 8.7: "Logarithmic quantities and units: level, neper, bel",Guide for the Use of the International System of Units (SI) 2008 Edition, NIST Special Publication 811, 2nd printing (November 2008), SP811PDF.
  9. ^Morfey, Christopher L. (2001).Dictionary of Acoustics. San Diego: Academic Press.ISBN 978-0125069403.
  10. ^"Noise Terms Glossary". Retrieved2012-10-14.
  11. ^abSelf, Douglas (2020-04-17).Small Signal Audio Design. CRC Press.ISBN 978-1-000-05044-8.this limit is reached when the rarefaction creates a vacuum, because you can't have a lower pressure than that. This corresponds to about +194 dB SPL.
  12. ^abGuignard, J. C.; King, P.F.; North Atlantic Treaty Organization Advisory Group for Aerospace Research and Development Aerospace Medical Panel (1972).Aeromedical Aspects of Vibration and Noise. North Atlantic Treaty Organization, Advisory Group for Aerospace Research and Development.In air at an assumed atmospheric pressure of 1 bar (100,000 N/m2) this occurs theoretically at approximately 191 dB SPL (working with rms values
  13. ^abcdeWiner, Ethan (2013). "1".The Audio Expert. New York and London: Focal Press.ISBN 978-0-240-82100-9.
  14. ^HATAZAWA, Masayasu; SUGITA, Hiroshi; OGAWA, Takahiro; SEO, Yoshitoki (2004-01-01)."Performance of a Thermoacoustic Sound Wave Generator driven with Waste Heat of Automobile Gasoline Engine".Transactions of the Japan Society of Mechanical Engineers B.70 (689):292–299.doi:10.1299/kikaib.70.292.ISSN 0387-5016.
  15. ^"Krakatoa Eruption – The Loudest Sound".Brüel & Kjær. Retrieved2021-03-24.160 km (99 miles) away from the source, registered a sound pressure level spike of more than 2½ inches of mercury (8.5 kPa), equivalent to 172 decibels.
  16. ^Winchester, Simon (2003).Krakatoa: The Day the World Exploded, August 27, 1883. Penguin/Viking. p. 218.ISBN 978-0-670-91430-2.
  17. ^Flamme, Gregory A.; Liebe, Kevin; Wong, Adam (2009)."Estimates of the auditory risk from outdoor impulse noise I: Firecrackers".Noise and Health.11 (45):223–230.doi:10.4103/1463-1741.56216.ISSN 1463-1741.PMID 19805932.
  18. ^Brueck, Scott E.; Kardous, Chuck A.; Oza, Aalok; Murphy, William J. (2014)."NIOSH HHE Report No. 2013-0124-3208. Health hazard evaluation report: measurement of exposure to impulsive noise at indoor and outdoor firing ranges during tactical training exercises"(PDF). Cincinnati, OH: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health.
  19. ^abcdefg"Did You Know How Loud Balloons Can Be?".Canadian Audiologist.3 (6). 9 January 2014. Retrieved8 June 2018.
  20. ^"LRAD Corporation Product Overview for LRAD 1000Xi". Archived fromthe original on 16 March 2014. Retrieved29 May 2014.
  21. ^abRealistic Maximum Sound Pressure Levels for Dynamic Microphones –Shure.
  22. ^Recording Brass & Reeds.
  23. ^Swanepoel, De Wet; Hall III, James W.; Koekemoer, Dirk (February 2010)."Vuvuzela – good for your team, bad for your ears"(PDF).South African Medical Journal.100 (4):99–100.doi:10.7196/samj.3697 (inactive 12 July 2025).hdl:2263/13136.PMID 20459912.{{cite journal}}: CS1 maint: DOI inactive as of July 2025 (link)
  24. ^Nave, Carl R. (2006)."Threshold of Pain".HyperPhysics. SciLinks. Retrieved2009-06-16.
  25. ^Franks, John R.; Stephenson, Mark R.; Merry, Carol J., eds. (June 1996).Preventing Occupational Hearing Loss – A Practical Guide(PDF).National Institute for Occupational Safety and Health. p. 88. Retrieved2009-07-15.
  26. ^"Decibel Table – SPL – Loudness Comparison Chart".sengpielaudio. Retrieved5 Mar 2012.
  27. ^abHamby, William."Ultimate Sound Pressure Level Decibel Table".Archived from the original on 2005-10-19.
  28. ^"EPA Identifies Noise Levels Affecting Health and Welfare" (Press release).Environmental Protection Agency. April 2, 1974. RetrievedMarch 27, 2017.
  29. ^abcMisdariis, Nicolas; Pardo, Louis-Ferdinand (August 2017)."The sound of silence of electric vehicles – Issues and answers".Inter.noise (International Congress & Exposition on Noise Control Engineering). Hong-Kong, China.Figure 1 shows the noise level generated when three vehicles go by, according to their speed. At low speed, the difference between a vehicle with an engine and an electric vehicle can be significant (over 10 dB(A)). Above 20 to 30 km/h, the noise made by the tyres on the road surface becomes dominant and the differences become less pronounced.
  30. ^"'The Quietest Place on Earth' – Guinness World Records Certificate, 2005"(PDF). Orfield Labs.
  31. ^Middlemiss, Neil (December 18, 2007)."The Quietest Place on Earth – Orfield Labs".Audio Junkies. Archived fromthe original on 2010-11-21.
  32. ^Eustace, Dave."Anechoic Chamber". University of Salford. Archived fromthe original on 2019-03-04.
  33. ^"Microsoft Lab Sets New Record for the World's Quietest Place". 2015-10-02. Retrieved2016-09-20.The computer company has built an anechoic chamber in which highly sensitive tests reported an average background noise reading of an unimaginably quiet −20.35 dBA (decibels A-weighted).
  34. ^"Check Out the World's Quietest Room".Microsoft: Inside B87. Retrieved2016-09-20.
General
  • Beranek, Leo L.,Acoustics (1993), Acoustical Society of America,ISBN 0-88318-494-X.
  • Daniel R. Raichel,The Science and Applications of Acoustics (2006), Springer New York,ISBN 1441920803.

External links

[edit]
Quantity
See also
Related
International
National
Other
Retrieved from "https://en.wikipedia.org/w/index.php?title=Sound_pressure&oldid=1336957121"
Categories:
Hidden categories:
[8]ページ先頭
©2009-2026 Movatter.jp