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 of sound pressure is the
pascal (Pa).[1]
Mathematical definition
A sound wave in a
transmission medium causes a deviation (sound pressure, a dynamic pressure) in the local ambient pressure, a static pressure.
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 a spherical sound wave decreases as 1/r from the centre of the sphere (and not as 1/r2, like the sound intensity):[3]
This relationship is an inverse-proportional law.
If the sound pressure p1 is measured at a distance r1 from the centre of the sphere, the sound pressure p2 at another position r2 can be calculated:
The inverse-proportional law for sound pressure comes from the inverse-square law for sound intensity:
The sound pressure may vary in direction from the centre of the sphere as well, so measurements at different angles may be necessary, depending on the situation. An obvious example of a sound source whose spherical sound wave varies in level in different directions is a
bullhorn.[citation needed]
Sound pressure level (SPL) or acoustic pressure level (APL) is a
logarithmic measure of the effective pressure of a sound relative to a reference value.
Sound pressure level, denoted Lp and measured in
dB,[4] is defined by:[5]
The commonly used reference sound pressure in air is[7]
p0 = 20 μPa,
which is often considered as the
threshold of human hearing (roughly the sound of a mosquito flying 3 m away). The proper notations for sound pressure level using this reference are Lp/(20 μPa) or Lp (re 20 μPa), but the suffix notations dB SPL, dB(SPL), dBSPL, or 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, meaning 1 Pa will equal an SPL of 94 dB. In other media, such as
underwater, a reference level of 1 μPa is used.[9] These references are defined in
ANSIS1.1-2013.[10]
The main instrument for measuring sound levels in the environment is the
sound level meter. Most sound level meters provide readings in A, C, and Z-weighted decibels and must meet international standards such as
IEC 61672-2013.
Examples
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)[11][12] is the largest pressure variation an undistorted sound wave can have in
Earth'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 other
atmospheres or other media, such as underwater or through the Earth.[13]
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 between 3,000 and 4,000 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.
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
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 the
inverse 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 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 sound to be comparable to measurements made in a free field environment.[13]
According to the inverse proportional law, when sound level Lp1 is measured at a distance r1, the sound level Lp2 at the distance r2 is
Multiple sources
The formula for the sum of the sound pressure levels of n incoherent radiating sources is
Inserting the formulas
in the formula for the sum of the sound pressure levels yields
EPA-identified maximum to protect against hearing loss and other disruptive effects from noise, such as sleep disturbance, stress, learning detriment, etc.[28]
^Bies, David A., and Hansen, Colin. (2003). Engineering Noise Control.
^Ross Roeser, Michael Valente, Audiology: Diagnosis (Thieme 2007), p. 240.
^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), SP811
PDF.
^Morfey, Christopher L. (2001). Dictionary of Acoustics. San Diego: Academic Press.
ISBN978-0125069403.
^
abSelf, Douglas (2020-04-17).
Small Signal Audio Design. CRC Press.
ISBN978-1-000-05044-8. 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.
^
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
^
abcdeWiner, Ethan (2013). "1". The Audio Expert. New York and London: Focal Press.
ISBN978-0-240-82100-9.
^"Krakatoa Eruption - The Loudest Sound". Brüel & Kjær. Retrieved 2021-03-24. 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.
^"Microsoft lab sets new record for the world's quietest place". 2015-10-02. Retrieved 2016-09-20. 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).