Sound power or acoustic power is the rate at which
sound energy
In physics, sound energy is a form of energy that can be heard by living things. Only those waves that have a frequency of 16 Hz to 20 kHz are audible to humans. However, this range is an average and will slightly change from individ ...
is emitted, reflected, transmitted or received, per unit time.
It is defined as "through a surface, the product of the sound pressure, and the component of the particle velocity, at a point on the surface in the direction normal to the surface, integrated over that surface." The
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
of sound power is the
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
(W).
[ It relates to the power of the sound force on a surface enclosing a sound source, in air. For a sound source, unlike ]sound pressure
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 ...
, sound power is neither room-dependent nor distance-dependent. Sound pressure is a property of the field at a point in space, while sound power is a property of a sound source, equal to the total power emitted by that source in all directions. Sound power passing through an area is sometimes called sound flux or acoustic flux through that area.
Sound power level ''L''WA
Regulations often specify a method for measurement that integrates sound pressure over a surface enclosing the source. ''L''WA specifies the power delivered to that surface in decibels relative to one picowatt. Devices (e.g., a vacuum cleaner) often have labeling requirements and maximum amounts they are allowed to produce. The A-weighting
A-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured ...
scale is used in the calculation as the metric is concerned with the loudness as perceived by the human ear. Measurements in accordance with ISO 3744 are taken at 6 to 12 defined points around the device in a hemi-anechoic space. The test environment can be located indoors or outdoors. The required environment is on hard ground in a large open space or hemi-anechoic chamber (free-field over a reflecting plane.)
Table of selected sound sources
Here is a table of some examples, from an on-line source. For omnidirectional sources in free space, sound power in ''L''wA is equal to sound pressure level in dB above 20 micropascals at a distance of 0.2821 m
Mathematical definition
Sound power, denoted ''P'', is defined by
:
where
*f is the sound force of unit vector u;
*v is the particle velocity
Particle velocity is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound, but it can ...
of projection ''v'' along u;
*''A'' is the area;
*''p'' is the sound pressure
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 ...
.
In a medium
Medium may refer to:
Science and technology
Aviation
*Medium bomber, a class of war plane
*Tecma Medium, a French hang glider design
Communication
* Media (communication), tools used to store and deliver information or data
* Medium of ...
, the sound power is given by
:
where
*''A'' is the area of the surface;
*''ρ'' is the mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
;
*''c'' is the sound velocity
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as wel ...
;
*''θ'' is the angle between the direction of propagation of the sound and the normal to the surface.
*''p'' is the sound pressure
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 ...
.
For example, a sound at SPL = 85 dB or ''p'' = 0.356 Pa in air (''ρ'' = and ''c'' = ) through a surface of area ''A'' = normal to the direction of propagation (''θ'' = 0°) has a sound energy flux ''P'' = .
This is the parameter one would be interested in when converting noise back into usable energy, along with any losses in the capturing device.
Relationships with other quantities
Sound power is related to sound intensity
Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (W/m2 ...
:
:
where
*''A'' stands for the area;
*''I'' stands for the sound intensity.
Sound power is related sound energy density
Sound energy density or sound density is the sound energy per unit volume. The SI unit of sound energy density is the pascal (Pa), which is 1 kg⋅m−1⋅s−2 in SI base units or 1 joule per cubic metre (J/m3).
Mathematical definition
S ...
:
:
where
*''c'' stands for the speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...
;
*''w'' stands for the sound energy density.
Sound power level
Sound power level (SWL) or acoustic power level is a logarithmic measure
In mathematics, the set of positive real numbers, \R_ = \left\, is the subset of those real numbers that are greater than zero. The non-negative real numbers, \R_ = \left\, also include zero. Although the symbols \R_ and \R^ are ambiguously used f ...
of the power of a sound relative to a reference value.
Sound power level, denoted ''L''''W'' and measured in dB,["Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units"]
''IEC 60027-3 Ed. 3.0'', International Electrotechnical Commission, 19 July 2002. is defined by:
:
where
*''P'' is the sound power;
*''P''0 is the ''reference sound power'';
* is the neper;
* is the bel;
* is the decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
.
The commonly used reference sound power in air is[Ross Roeser, Michael Valente, ''Audiology: Diagnosis'' (Thieme 2007), p. 240.]
:
The proper notations for sound power level using this reference are or , but the suffix notations , , dBSWL, or dBSWL are very common, even if they are not accepted by the SI.[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), SP81]
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The reference sound power ''P''0 is defined as the sound power with the reference sound intensity passing through a surface of area :
:
hence the reference value .
Relationship with sound pressure level
The generic calculation of sound power from sound pressure is as follows:
:
where:
defines the area of a surface that wholly encompasses the source. This surface may be any shape, but it must fully enclose the source.
In the case of a sound source located in free field positioned over a reflecting plane (i.e. the ground), in air at ambient temperature, the sound power level at distance ''r'' from the sound source is approximately related to sound pressure level (SPL) by[Chadderton, David V. ''Building services engineering'', pp. 301, 306, 309, 322. Taylor & Francis, 2004. ]
:
where
*''L''''p'' is the sound pressure level;
*''A''0 = 1 m2;
* defines the surface area of a hemisphere; and
*''r'' must be sufficient that the hemisphere fully encloses the source.
Derivation of this equation:
:
For a ''progressive'' spherical wave,
:
: (the surface area of sphere)
where ''z''0 is the characteristic specific acoustic impedance.
Consequently,
:
and since by definition , where is the reference sound pressure,
:
The sound power estimated practically does not depend on distance. The sound pressure used in the calculation may be affected by distance due to viscous effects in the propagation of sound unless this is accounted for.
References
External links
Sound power and Sound pressure. Cause and Effect
Relationships of Acoustic Quantities Associated with a Plane Progressive Acoustic Sound Wave
NIOSH Powertools Database
Sound Power Testing
{{Authority control
Acoustics
Sound
Sound measurements
Physical quantities
Power (physics)