Sound pressure or acoustic pressure is the local pressure deviation from the ambient
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 for sound pressure p is the pascal.
Sound pressure level or sound level is a logarithmic measure of the effective sound pressure of
a sound relative to a reference value. It is measured in decibels above a standard reference
level. The standard reference sound pressure in air or other gases is 20 µPa, which is
usually considered the threshold of human hearing.
Examples of sound pressure and sound pressure levels
*All values listed are the effective sound pressure unless otherwise stated.
Instantaneous sound pressure The instantaneous sound pressure is the deviation
from the local ambient pressure 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.
Total pressure is given by:
where: = local ambient atmospheric pressure,
= sound pressure deviation. Intensity
In a sound wave, the complementary variable to sound pressure is the acoustic particle
velocity. Together they determine the acoustic intensity of the wave. The local instantaneous
sound intensity is the product of the sound pressure and the acoustic particle velocity.
Acoustic impedance For small amplitudes, sound pressure and volume
velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance
depends on both the characteristics of the wave and the transmission medium.
The acoustic impedance is given by
where Z is acoustic impedance or sound impedance
p is sound pressure U is volume velocity
Particle displacement Sound pressure p is connected to particle
displacement ξ by .
Sound pressure p is ,
normally in units of N/m² = Pa. where:
Distance law 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:.
The distance law for the sound pressure p in 3D is inversely proportional to the distance
r of a punctual sound source.
If sound pressure , is measured at a distance , one can calculate the sound pressure at
another position ,
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 or sound level is a logarithmic
measure of the effective sound pressure of a sound relative to a reference value. It
is measured in decibels above a standard reference level.
where is the reference sound pressure and is the rms sound pressure being measured.
Sometimes variants are used such as dB, dBSPL, or dBSPL. These variants are not recognized
as units in the SI. The unit dB 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 = 20 µPa or 0.0002 dynes/cm2, which
is usually considered the threshold of human hearing. Most sound level measurements will
be made relative to this level, meaning 1 pascal 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 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
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. Distance
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 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 is measured at a distance , the sound level at the distance is
Multiple sources 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 Acoustics
Phon Loudness
Sone Sound level meter
Stevens' power law Weber–Fechner law, especially The case of
sound Notes
^ Sometimes reference sound pressure is denoted p0, not to be confused with the ambient pressure.
References
Beranek, Leo L, "Acoustics" Acoustical Society of America. ISBN 0-88318-494-X
Daniel R. Raichel, "The Science and Applications of Acoustics", Springer New York, ISBN 1441920803
External links 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 comparison chart