Sound power
Encyclopedia
Sound power or acoustic power Pac is a measure of sonic
energy
E per time
t unit.
It is measured in watt
s and, can be computed as sound intensity
(I) times area (A):
The difference between two sound powers can be express in decibels using this equation:
where
The sound power level SWL, LW, or LPac of a source is expressed in decibel
s (dB) and is equal to 10 times the logarithm to the base 10
of the ratio of the sound power of the source to a reference sound power. It is thus a logarithmic measure
.
The reference sound power in air is normally taken to be
= 10−12 watt, that is 0 dB SWL.
Sound power is neither room dependent nor distance dependent. Sound power belongs strictly to the sound source.
Usable music sound (trumpet) and noise sound (excavator) both have the same sound power of 0.3 watts, but will be judged psychoacoustically
to be different levels.
is to measure the sound pressure level 
at some distance 
, and solve for 
:
If the source is in free space
or
if the source is on the floor or on a wall, such that it radiates into a half sphere.
The sound power estimated this does not diminish or increase with distance, unless reflections are present.
where:
of the sound power in comparison to a specified reference level. While sound pressure level is given in decibels SPL, or dB SPL, sound power is given in dB SWL. The dimensionless term "SWL" can be thought of as "sound watts level," the acoustic output power measured relative to a very low base level of watts
given as 10-12 or 0.000000000001 watts. As used by architectural acousticians
to describe noise inside a building, typical noise measurements in SWL are very small, less than 1 watt of acoustic power.
The sound power level of a signal with sound power W is:
where W0 is the 0 dB reference level:
The sound power level is given the symbol LW. This is not to be confused with dBW, which is a measure of electrical power, and uses 1 W as a reference level.
In the case of a free field sound source in air at ambient temperature, the sound power level is approximately related to sound pressure level (SPL) at distance r of the source by the equation
where
. This assumes that the acoustic impedance
of the medium equals 400 Pa·s/m.
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
E per time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
t unit.
It is measured in watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
s and, can be computed as sound intensity
Sound intensity
Sound intensity or 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.-Acoustic intensity:...
(I) times area (A):
The difference between two sound powers can be express in decibels using this equation:
where
- P1, P0 are the sound powers.
The sound power level SWL, LW, or LPac of a source is expressed in decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s (dB) and is equal to 10 times the logarithm to the base 10
Common logarithm
The common logarithm is the logarithm with base 10. It is also known as the decadic logarithm, named after its base. It is indicated by log10, or sometimes Log with a capital L...
of the ratio of the sound power of the source to a reference sound power. It is thus a logarithmic measure
Logarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...
.
The reference sound power in air is normally taken to be
= 10−12 watt, that is 0 dB SWL.Sound power is neither room dependent nor distance dependent. Sound power belongs strictly to the sound source.
Table of some sound sources
| Situation and sound source | sound power Pac watts | sound power level Lw dB re 10−12 W |
|---|---|---|
| Rocket engine Rocket engine A rocket engine, or simply "rocket", is a jet engineRocket Propulsion Elements; 7th edition- chapter 1 that uses only propellant mass for forming its high speed propulsive jet. Rocket engines are reaction engines and obtain thrust in accordance with Newton's third law... |
1,000,000 W | 180 dB |
| Turbojet engine | 10,000 W | 160 dB |
| Siren Siren (noisemaker) A siren is a loud noise making device. Most modern ones are civil defense or air raid sirens, tornado sirens, or the sirens on emergency service vehicles such as ambulances, police cars and fire trucks. There are two general types: pneumatic and electronic.... |
1,000 W | 150 dB |
| Heavy truck engine or loudspeaker rock concert Rock concert The term rock concert refers to a musical performance in the style of any one of many genres inspired by "rock and roll" music. While a variety of vocal and instrumental styles can constitute a rock concert, this phenomenon is typically characterized by bands playing at least one electric guitar,... |
100 W | 140 dB |
| Machine gun Machine gun A machine gun is a fully automatic mounted or portable firearm, usually designed to fire rounds in quick succession from an ammunition belt or large-capacity magazine, typically at a rate of several hundred rounds per minute.... |
10 W | 130 dB |
| Jackhammer Jackhammer A jackhammer is a pneumatic tool that combines a hammer directly with a chisel that was invented by Charles Brady King. Hand-held jackhammers are typically powered by compressed air, but some use electric motors. Larger jackhammers, such as rig mounted hammers used on construction machinery, are... |
1 W | 120 dB |
| Excavator Excavator Excavators are heavy construction equipment consisting of a boom, stick, bucket and cab on a rotating platform . The house sits atop an undercarriage with tracks or wheels. A cable-operated excavator uses winches and steel ropes to accomplish the movements. They are a natural progression from the... , trumpet Trumpet The trumpet is the musical instrument with the highest register in the brass family. Trumpets are among the oldest musical instruments, dating back to at least 1500 BCE. They are played by blowing air through closed lips, producing a "buzzing" sound which starts a standing wave vibration in the air... |
0.3 W | 115 dB |
| Chain saw | 0.1 W | 110 dB |
| Helicopter Helicopter A helicopter is a type of rotorcraft in which lift and thrust are supplied by one or more engine-driven rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forwards, backwards, and laterally... |
0.01 W | 100 dB |
| Loud speech, vivid children |
0.001 W | 90 dB |
| Usual talking, Typewriter Typewriter A typewriter is a mechanical or electromechanical device with keys that, when pressed, cause characters to be printed on a medium, usually paper. Typically one character is printed per keypress, and the machine prints the characters by making ink impressions of type elements similar to the pieces... |
10−5 W | 70 dB |
| Refrigerator Refrigerator A refrigerator is a common household appliance that consists of a thermally insulated compartment and a heat pump that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the ambient temperature of the room... |
10−7 W | 50 dB |
Usable music sound (trumpet) and noise sound (excavator) both have the same sound power of 0.3 watts, but will be judged psychoacoustically
Psychoacoustics
Psychoacoustics is the scientific study of sound perception. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound...
to be different levels.
Sound power measurement
A frequently used method of estimating the sound power level by Daniel is to measure the sound pressure level at some distance , and solve for : If the source is in free spaceor
if the source is on the floor or on a wall, such that it radiates into a half sphere.The sound power estimated this does not diminish or increase with distance, unless reflections are present.
Sound power with plane sound waves
Between sound power and other important acoustic values there is the following relationship:where:
| Symbol | Units | Meaning |
|---|---|---|
| p | Pa Pascal (unit) The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre... |
sound pressure Sound pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water... |
| f | Hz Hertz The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications.... |
frequency Frequency Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency... |
| ξ | m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... |
particle displacement Particle displacement Particle displacement or particle amplitude is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a wave.... |
| c | m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... /s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... |
speed of sound Speed of sound The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds.... |
| v | m/s | particle velocity Particle velocity Particle velocity is the velocity v of a particle 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.... |
| ω = 2πf | rad Radian Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit... /s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... |
angular frequency Angular frequency In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity... |
| ρ | kg Kilogram The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water... /m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... 3 |
density of air Density of air The density of air, ρ , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity... |
| Z = c · ρ | N·s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... /m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... ³ |
acoustic impedance Acoustic impedance The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments... |
| a | m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... /s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... ² |
particle acceleration Particle acceleration In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre/second². In acoustics or physics, acceleration is defined as the rate of change of velocity. It is thus a vector... |
| I | W Watt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:... /m² |
sound intensity Sound intensity Sound intensity or 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.-Acoustic intensity:... |
| E | W Watt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:... ·s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... /m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... ³ |
sound energy density Sound energy density The sound energy density or sound density is an adequate measure to describe the sound field at a given point as a sound energy value... |
| Pac | W Watt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:... |
sound power or acoustic power |
| A | m Metre The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... ² |
area Area Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat... |
Sound power level
Sound power level or acoustic power level is a logarithmic measureLogarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...
of the sound power in comparison to a specified reference level. While sound pressure level is given in decibels SPL, or dB SPL, sound power is given in dB SWL. The dimensionless term "SWL" can be thought of as "sound watts level," the acoustic output power measured relative to a very low base level of watts
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
given as 10-12 or 0.000000000001 watts. As used by architectural acousticians
Architectural acoustics
Architectural acoustics is the science of noise control within buildings. The first application of architectural acoustics was in the design of opera houses and then concert halls. More widely, noise suppression is critical in the design of multi-unit dwellings and business premises that generate...
to describe noise inside a building, typical noise measurements in SWL are very small, less than 1 watt of acoustic power.
The sound power level of a signal with sound power W is:
where W0 is the 0 dB reference level:
The sound power level is given the symbol LW. This is not to be confused with dBW, which is a measure of electrical power, and uses 1 W as a reference level.
In the case of a free field sound source in air at ambient temperature, the sound power level is approximately related to sound pressure level (SPL) at distance r of the source by the equation
where
. This assumes that the acoustic impedanceAcoustic impedance
The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...
of the medium equals 400 Pa·s/m.