Sound pressure
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Sound measurements 

Sound pressure p 
Particle velocity v 
Particle velocity level (SVL) 
(Sound velocity level) 
Particle displacement ξ 
Sound intensity I 
Sound intensity level (SIL) 
Sound power P_{ac} 
Sound power level (SWL) 
Sound energy density E 
Sound energy flux q 
Surface S 
Acoustic impedance Z 
Speed of sound c

Sound pressure is the local pressure deviation from the ambient (average, or equilibrium) pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure p_{0} caused by a sound wave at a given location and given instant in time. The effective sound pressure is the root mean square of the instantaneous sound pressure over a given interval of time (or space). In a sound wave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity.
The sound pressure deviation (instantaneous acoustic pressure) p is
where
 F = force,
 A = area.
The entire pressure p_{total} is
where
 p_{0} = local ambient pressure,
 p = sound pressure deviation.
Contents 
[edit] Sound pressure level
Sound pressure level (SPL) or sound level L_{p} is a logarithmic measure of the rms sound pressure of a sound relative to a reference value. It is measured in decibels (dB).
where p_{ref} is the reference sound pressure and p_{rms} is the rms sound pressure being measured.^{[1]}
Sometimes variants are used such as dB (SPL), dBSPL, or dB_{SPL}. These variants are not permitted by SI.^{[2]}
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.^{[contradiction]}
The commonly used reference sound pressure in air is p_{ref} = 20 µPa (rms), which is usually considered the threshold of human hearing (roughly the sound of a mosquito flying 3 m away). When dealing with hearing, the perceived loudness of a sound correlates roughly logarithmically to its sound pressure. See also WeberFechner 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, a reference level of 1 µPa is more often used.^{[3]}
These references are defined in ANSI S1.11994.^{[4]}
The human ear is a sound pressure sensitive detector. It does not have a flat spectral response, so the sound pressure is often frequency weighted 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 (IEC) has defined several weighting schemes. Aweighting attempts to match the response of the human ear to pure tones, while Cweighting is used to measure peak sound levels.^{[5]} If the (unweighted) SPL is desired, many instruments allow a "flat" or unweighted measurement to be made. See also Weighting filter.
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 with 1/r (and not with 1/r^{2}, like sound intensity). 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, sound impedance, or characteristic impedance, in Pa·s/m
 v is particle velocity in m/s
 J is acoustic intensity or sound intensity, in W/m^{2}
Sound pressure p is connected to particle displacement (or particle amplitude) ξ, in m, by
 .
Sound pressure p is
 ,
normally in units of N/m² = Pa.
where:
Symbol  SI Unit  Meaning 

p  pascals  sound pressure 
f  hertz  frequency 
ρ  kg/m³  density of air 
c  m/s  speed of sound 
v  m/s  particle velocity 
ω = 2 · π · f  radians/s  angular frequency 
ξ  meters  particle displacement 
Z = c • ρ  N·s/m³  acoustic impedance 
a  m/s²  particle acceleration 
J  W/m²  sound intensity 
E  W·s/m³  sound energy density 
P_{ac}  watts  sound power or acoustic power 
A  m²  Area 
The distance law for the sound pressure p is inverseproportional 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.
Note: The often used term "intensity of sound pressure" is not correct. Use "magnitude", "strength", "amplitude", or "level" instead. "Sound intensity" is sound power per unit area, while "pressure" is a measure of force per unit area. Intensity is not equivalent to pressure.
Hence
[edit] Examples of sound pressure and sound pressure levels
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Sound pressure in air:
Source of sound  Sound pressure  Sound pressure level 

pascal  dB re 20 μPa  
Krakatoa explosion at 100 miles (160 km) in air^{[dubious – discuss]}  20,000 Pa  180 dB 
Simple openended thermoacoustic device ^{[6]}  12,619 Pa  176 dB 
.3006 carbine 1 m to shooter's left side  7,265 Pa  171 dB (peak) 
M1 Garand being fired at 1 m  5,023 Pa  168 dB 
Jet engine at 30 m  632 Pa  150 dB 
Threshold of pain  63.2 Pa  130 dB 
Hearing damage (due to shortterm exposure)  20 Pa  approx. 115 dB 
Jet at 100 m  6.32 – 200 Pa  110 – 140 dB 
Jack hammer at 1 m  2 Pa  approx. 100 dB 
Hearing damage (due to longterm exposure)  0.356 Pa  78 dB 
Major road at 10 m  2×10^{−1} – 6.32×10^{−1} Pa  80 – 90 dB 
Passenger car 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} – 6.32×10^{−4} Pa  20 – 30 dB 
Leaves rustling, calm breathing  6.32×10^{−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  dB re 1 μPa  
Pistol shrimp  218 dB^{[7]}  
Sperm Whale  163180 dB^{[8]}  
Fin Whale  160186 dB^{[9]}  
Humpback Whale  144174 dB^{[10]}  
Bowhead Whale  128189 dB^{[11]}  
Blue Whale  155188 dB^{[12]}  
Southern Right Whale  172187 dB^{[13]}  
Gray Whale  142185 dB^{[14]}  
Auditory threshold of a diver at 1 kHz  2.2 × 10^{−3} Pa  67 dB^{[15]} 
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
[edit] See also
 Acoustics
 amplitude
 decibel, especially the Acoustics section
 phon (unit)
 loudness
 sone (unit)
 sound level meter
 sound power level
 Stevens' power law
 Weber–Fechner law, especially The case of sound
[edit] Notes and References
 ^ Sometimes reference sound pressure is denoted p_{0}, not to be confused with the (much higher) ambient pressure.
 ^ Taylor 1995, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811
 ^ C. L. Morfey, Dictionary of Acoustics (Academic Press, San Diego, 2001).
 ^ Glossary of Noise Terms — Sound pressure level definition
 ^ Glossary of Terms — Cirrus Research plc.
 ^ 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. [1]
 ^ http://www.dailymail.co.uk/sciencetech/article1085398/DeadlypistolshrimpstunspreysoundloudConcordeUKwaters.html
 ^ http://www.surtasslfaeis.com/Terms/
 ^ http://www.surtasslfaeis.com/Terms/
 ^ http://www.surtasslfaeis.com/Terms/
 ^ http://www.surtasslfaeis.com/Terms/
 ^ http://www.surtasslfaeis.com/Terms/
 ^ http://www.surtasslfaeis.com/Terms/
 ^ http://www.surtasslfaeis.com/Terms/
 ^ Parvin S.J., Searle S.L. and Gilbert M.J. (2001). "Exposure of divers to underwater sound in the frequency range from to 2250 Hz". Undersea Hyperb Med. Abstract 28 (Supl). ISSN 10662936. OCLC 26915585. http://archive.rubiconfoundation.org/984. Retrieved on 20080505.
 Beranek, Leo L, "Acoustics" (1993) Acoustical Society of America. ISBN 088318494X
 Morfey, Christopher L, "Dictionary of Acoustics" (2001) Academic Press, San Diego.
[edit] External links
 Conversion of sound pressure to sound pressure level and vice versa
 Table of Sound Levels  Corresponding Sound Pressure and Sound Intensity
 William Hamby (2004) Ultimate Sound Pressure Level Decibel Table
 Ohm's law as acoustic equivalent  calculations
 Definition of sound pressure level
 A table of SPL values
 Relationships of acoustic quantities associated with a plane progressive acoustic sound wave  pdf
 Sound pressure and sound power  two commonly confused characteristics of sound