Information about Sound Pressure
| Sound measurements |
|---|
| Sound pressure p |
| Sound pressure level (SPL) |
| Particle velocity v |
| Particle velocity level (SVL) |
| (Sound velocity level) |
| Particle displacement ξ |
| Sound intensity I |
| Sound intensity level (SIL) |
| Sound power Pac |
| Sound power level (SWL) |
| Sound energy density E |
| Sound energy flux q |
| Acoustic impedance Z |
| Speed of sound c |
Sound pressure is the pressure deviation from the local ambient 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 p0 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. 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 p is
where
- F = force,
- A = area.
The entire pressure ptotal is
where
- p0 = local ambient pressure,
- p = sound pressure deviation.
Sound pressure level
Sound pressure level (SPL) or sound level Lp is a logarithmic measure of the rms sound pressure of a sound relative to a reference value. It is measured in decibels (dB). Sometimes variants are used such as dB (SPL), dBSPL, or dBSPL. These variants are not permitted by SI.
where
is the reference sound pressure and 
is the rms sound pressure being measured.
The commonly used reference sound pressure in air is p0 = 20 µPa (rms). In underwater acoustics, the reference sound pressure is p0 = 1 µPa (rms).
It can be useful to express sound pressure in this way when dealing with hearing, as the perceived loudness of a sound correlates roughly logarithmically to its sound pressure. See also Weber-Fechner law.
Measuring sound pressure levels
dBSPL: A measurement of sound pressure level in decibels, where 0 dBSPL is the reference to the threshold of hearing. Often the calibration is done for 1 pascal is equal to 94 dBSPL.When making measurements in air (and other gases), SPL is almost always expressed in decibels compared to a reference sound pressure of 20 µPa, which is usually considered the threshold of human hearing (roughly the sound of a mosquito flying 3 m away). Thus, most measurements of audio equipment will be made relative to this level. However, in other media, such as underwater, a reference level of 1 µPa is more often used.[1] These references are defined in ANSI S1.1-1994.[2] In general, it is necessary to know the reference level when comparing measurements of SPL. 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 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. A-weighting attempts to match the response of the human ear to pure tones, while C-weighting is used to measure peak sound levels.[3] 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/r2, 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/m2
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 |
 = 2 ·  · 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 |
| Pac | watts | sound power or acoustic power |
| A | m² | Area |
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.
Note: The often used term "intensity of sound pressure" is not correct. Use "magnitude", "", "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.
Examples of sound pressure and sound pressure levels
| Source of sound | Sound pressure | Sound pressure level[4] |
|---|---|---|
| pascal | dB SPL | |
| Theoretical limit for a sound wave at 1 atmosphere environmental pressure | 101,325 Pa | 194 dB |
| Krakatoa explosion at 100 miles (160 km) in air | 20,000 Pa | [1] 180 dB |
| Simple open-ended thermoacoustic device [5] | 12,000 Pa | 176 dB |
| M1 Garand being fired at 1 m | 5,000 Pa | 168 dB |
| Jet engine at 30 m | 630 Pa | 150 dB |
| Rifle being fired at 1 m | 200 Pa | 140 dB |
| Threshold of pain | 100 Pa | 130 dB |
| Hearing damage (due to short-term exposure) | 20 Pa | approx. 120 dB |
| Jet at 100 m | 6 – 200 Pa | 110 – 140 dB |
| Jack hammer 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 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 2 kHz | 2×10−5 Pa | 0 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
See also
- Decibel, especially the Acoustics section
- Sone
- Loudness
- Weber-Fechner law (The case of Sound)
- Stevens' power law
- Sound power level
- Amplitude
- Acoustics
References
1. ^ Underwater Acoustics — Federation of American Scientists
2. ^ Glossary of Noise Terms — Sound pressure level definition
3. ^ Glossary of Terms — Cirrus Research plc.
4. ^ Decibel level chart.
5. ^ 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. [2]
2. ^ Glossary of Noise Terms — Sound pressure level definition
3. ^ Glossary of Terms — Cirrus Research plc.
4. ^ Decibel level chart.
5. ^ 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. [2]
- Beranek, Leo L, "Acoustics" (1993) Acoustical Society of America. ISBN 0-88318-494-X
- Morfey, Christopher L, "Dictionary of Acoustics" (2001) Academic Press, San Diego.
External links
- Conversion of sound pressure to sound pressure level and vice versa
- The level of sound is dB
- Table of Sound Levels - Corresponding Sound Pressure and Sound Intensity
- SPL of many different sounds - txt
- 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
- Another Sound Pressure Level Decibel Table
- Sound pressure and sound power - two commonly confused characteristics of sound
Sound pressure is the pressure deviation from the local ambient 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).
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Particle velocity is the velocity v of a particle (real or imagined) 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.
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The particle velocity level or the sound velocity level tells the ratio of a sound incidence in comparison to a reference level of 0 dB in a medium, mostly air.
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Particle displacement or particle amplitude (represented in mathematics by the lower-case Greek letter ξ) is a measurement of distance (in metres) of the movement of a particle in a medium as it transmits a wave.
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The sound intensity, I, (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.
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Sound intensity level or acoustic intensity level is a logarithmic measure of the sound intensity in comparison to the reference level of 0 dB (decibels).
The measure of a ratio of two sound intensities is
where J1
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The measure of a ratio of two sound intensities is
where J1
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Sound power or acoustic power Pac is a measure of sonic energy E per time t unit.
It is measured in watts, or sound intensity I times area A:
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It is measured in watts, or sound intensity I times area A:
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Sound power level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level.
The measure of a ratio of two sound powers is [1] [2]
where W
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The measure of a ratio of two sound powers is [1] [2]
where W
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The sound energy density or sound density (symbol E or w) is an adequate measure to describe the sound field at a given point as a sound energy value.
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The sound energy q results from the integral particle velocity v of the surface A , whereby only the portions perpendicularly to the surface acoustic velocity are important.
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The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments.
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speed of sound describes how much distance such a wave travels in a given amount of time. In dry air, at a temperature of 21 °C (70 °F) the speed of sound is 344 m/s (1238 km/h, or 769 mph, or 1128 ft/s).
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Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.
Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves).
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wave is a mode of energy transfer from one place to another, often with little or no permanent displacement of the particles of the medium (i.e. little or no associated mass transport); instead there are oscillations around almost fixed positions.
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microphone, sometimes referred to as a mike or mic (both IPA pronunciation: [maɪk]), is an acoustic to electric transducer or sensor that converts sound into an electrical signal.
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A hydrophone is a submersible sound sensor. It is analogous to a microphone or an ear for listening to underwater sound. At its core is a piezoelectric material that generates electricity when subjected to a pressure change.
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The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Young's modulus and tensile strength). It is a measure of perpendicular force per unit area i.e. equivalent to one newton per square meter or one Joule per cubic meter.
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In mathematics, root mean square (abbreviated RMS or rms), 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. waves.
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Particle velocity is the velocity v of a particle (real or imagined) 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.
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The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments.
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A transmission medium (plural transmission media) is a material substance (solid, liquid or gas) which can propagate 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
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The sound intensity, I, (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.
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Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves).
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Level may refer to:
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- A floor of a building
- A level of a mine, see shaft mining. A level with access to the surface is an adit
- Level (computer and video games), a stage of the game
- Level up, in role-playing games
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logarithmic scale is a scale of measurement 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
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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
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In mathematics, root mean square (abbreviated RMS or rms), 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. waves.
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Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.
Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level.
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Si, si, or SI may refer to (all SI unless otherwise stated):
In language:
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In language:
- One of two Italian words:
- sì (accented) for "yes"
- si
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