|Sound pressure||p · SPL|
|Particle velocity||v · SVL|
|Sound intensity||I · SIL|
|Sound power||P · SWL|
|Sound energy density||w|
|Sound exposure||E · SEL|
|Sound energy flux||Q|
|Speed of sound||c|
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.
A sound wave in a transmission medium causes a deviation (sound pressure, a dynamic pressure) in the local ambient pressure, a static pressure.
Sound pressure, denoted p and measured in Pa, is given by:
- ptotal is the total pressure, measured in Pa;
- pstat is the static pressure, measured in Pa.
In a sound wave, the complementary variable to sound pressure is the particle velocity. Together they determine the sound intensity of the wave.
Sound intensity, denoted I and measured in W·m−2, is given by:
- is the Laplace transform of sound pressure, measured in Pa;
- is the Laplace transform of sound volume flow rate, measured in m3·s−1.
- is the Laplace transform of sound pressure, measured in Pa;
- is the Laplace transform of particle velocity, measured in m·s−1.
so particle velocity and sound pressure are equal to:
where x is the space variable along the direction of propagation of the sound wave.
Taking the Laplace transforms of v and p with respect to time yields:
Since , the amplitude of the specific acoustic impedance is equal to:
Consequently, the amplitude of the sound pressure is connected to the amplitude of the particle displacement:
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 1/r2, like sound intensity).
The distance law of sound pressure p for a spherical sound wave at a distance r from a punctual sound source is given by:
If the sound pressure p1 is measured at a distance r1, the sound pressure p2 at another position r2 can be calculated:
The sound pressure may vary in direction from the source, as well, so measurements at different angles 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 level
Sound pressure level (SPL) or acoustic pressure level is a logarithmic measure of the effective sound pressure of a sound relative to a reference value.
Sound pressure level, denoted Lp and measured in dB, above a standard reference level, is given by:
- prms is the root mean square sound pressure, measured in Pa;
- p0 is the reference sound pressure, measured in Pa.
Sometimes variants are used such as dB (SPL), dBSPL, or dBSPL. These variants are not recognized as units in the SI. 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.
The commonly used reference sound pressure in air is p0 = 20 μPa (RMS) or 0.0002 dynes/cm2, 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 Pa will equal an SPL of 94 dB. In other media, such as underwater, a reference level of 1 μPa is used. These references are defined in ANSI S1.1-1994.
The lower limit of audibility is defined as SPL of 0 dB, but the upper limit is not as clearly defined. While 1 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 atmospheres or other media such as under water, or through the Earth.
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.
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.
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.
When sound level Lp1 is measured at a distance r1, the sound level Lp2 at the distance r2 is
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
Examples of sound pressure
|This table needs additional citations for verification. (March 2009)|
|Source of sound||Sound pressure*
|Sound pressure level
|Shockwave (distorted sound waves > 1 atm; waveform valleys are clipped at zero pressure)||>101,325||>194|
|Theoretical limit for undistorted sound at 1 atmosphere environmental pressure||101,325||194|
|Simple open-ended thermoacoustic device||12,619||176|
|.30-06 rifle being fired 1 m to shooter's side||7,265||171|
|Rocket launch equipment acoustic tests||4000||165|
|LRAD 1000Xi Long Range Acoustic Device at 1 m||893||153|
|Jet engine at 1 m||632||150|
|Threshold of pain||63.2||130|
|Vuvuzela horn at 1 m||20||120|
|Risk of instantaneous noise-induced hearing loss||20||120|
|Jet engine at 100 m||6.32–200||110–140|
|Non-electric chainsaw at 1 m||6.32||110|
|Jack hammer at 1 m||2||100|
|Traffic on a busy roadway at 10 m||0.2–0.632||80–90|
|Hearing damage (over long-term exposure, need not be continuous)||0.356||85|
|Passenger car at 10 m||(2–20)×10−2||60–80|
|EPA-identified maximum to protect against hearing loss and other disruptive effects from noise, such as sleep disturbance, stress, learning detriment, etc.||6.32×10−2||70|
|Handheld electric mixer||65|
|TV (set at home level) at 1 m||2×10−2||60|
|Washing machine, dishwasher||42–53|
|Normal conversation at 1 m||(2–20)×10−3||40–60|
|Very calm room||(2–6.32)×10−4||20–30|
|Light leaf rustling, calm breathing||6.32×10−5||10|
|Auditory threshold at 1 kHz||2×10−5||0|
*All values listed are the effective sound pressure unless otherwise stated.
- Phon (unit)
- Sone (unit)
- Sound level meter
- Stevens' power law
- Weber–Fechner law, especially The case of sound
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- Sound pressure and Sound power – Effect and Cause
- Conversion of sound pressure to sound pressure level and vice versa
- Table of Sound Levels - Corresponding Sound Pressure and Sound Intensity
- 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
- How many decibels is twice as loud? Sound level change and the respective factor of sound pressure or sound intensity
- Decibel (loudness) comparison chart