Sound intensity
Encyclopedia
Sound intensity or acoustic intensity (I) 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.
Notice that both v and I are vectors, which means that both have a direction as well as a magnitude. The direction of the intensity is the average direction in which the energy is flowing. For instantaneous acoustic pressure pinst(t) and particle velocity
v(t) the average acoustic intensity during time T is given by
The SI
units of intensity are W/m2 (watt
s per square metre
). For a plane progressive wave we have:
where:
Here, Pac (upper case) is the sound power and A the surface area of a sphere of radius r. Thus the sound intensity decreases with 1/r2 the distance from an acoustic point source, while the sound pressure decreases only with 1/r from the distance from an acoustic point source after the 1/r-distance law.
= sound intensity at close distance 
= sound intensity at far distance 
Hence
where p (lower case) is the RMS
sound pressure (acoustic pressure).
ic measure of the sound intensity (measured in W/m2), in comparison to a reference level.
The measure of a ratio of two sound intensities is
where I1 and I0 are the intensities.
The sound intensity level is given the letter "LI" and is measured in "dB". The decibel is a dimensionless quantity.
If I0 is the standard reference sound intensity
(W = watt), then instead of "dB SPL" we use "dB SIL". (SIL = sound intensity level).
Note 1: The term "intensity" is used exclusively for the measurement of sound in watts per unit area.
To describe the strength of sound in terms other than strict intensity, one can use "magnitude
" "strength", "amplitude
", or "level
" instead.
Sound intensity is not the same physical quantity as sound pressure
. Hearing is directly sensitive to sound pressure which is related to sound intensity. In consumer audio electronics, the level differences are called "intensity" differences, but sound intensity is a specifically defined quantity and cannot be sensed by a simple microphone. Sound intensity is not valuable in music recording.
Intensity (physics)
In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...
in the air at a listener's location.
Acoustic intensity
The intensity is the product of the sound pressure and the particle velocityNotice that both v and I are vectors, which means that both have a direction as well as a magnitude. The direction of the intensity is the average direction in which the energy is flowing. For instantaneous acoustic pressure pinst(t) and 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....
v(t) the average acoustic intensity during time T is given by
The SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units of intensity are W/m2 (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 per square metre
Square metre
The square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...
). For a plane progressive wave we have:
where:
| Symbol | Units | Meaning |
|---|---|---|
| p | pascal 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... s |
RMS Root mean square In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids... 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 | hertz 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 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 |
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 | radians/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 |
characteristic 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 |
| 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 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 |
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... |
Spatial expansion
For a spherical sound source, the intensity in the radial direction as a function of distance r from the centre of the source is:Here, Pac (upper case) is the sound power and A the surface area of a sphere of radius r. Thus the sound intensity decreases with 1/r2 the distance from an acoustic point source, while the sound pressure decreases only with 1/r from the distance from an acoustic point source after the 1/r-distance law.
= sound intensity at close distance = sound intensity at far distance Hence
where p (lower case) is the RMS
Root mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
sound pressure (acoustic pressure).
Sound intensity level
Sound intensity level or acoustic intensity level is a logarithmLogarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
ic measure of the sound intensity (measured in W/m2), in comparison to a reference level.
The measure of a ratio of two sound intensities is
where I1 and I0 are the intensities.
The sound intensity level is given the letter "LI" and is measured in "dB". The decibel is a dimensionless quantity.
If I0 is the standard reference sound intensity
(W = watt), then instead of "dB SPL" we use "dB SIL". (SIL = sound intensity level).
Note 1: The term "intensity" is used exclusively for the measurement of sound in watts per unit area.
To describe the strength of sound in terms other than strict intensity, one can use "magnitude
Magnitude (mathematics)
The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
" "strength", "amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
", or "level
Level
Level or levels may refer to:-Places:*Levél, Győr-Moson-Sopron, Hungary*Level, Ohio, United States*Level Valley*Levels, West Virginia-Engineering-related:*Floor, or storey, of a building or a mine...
" instead.
Sound intensity is not the same physical quantity as 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...
. Hearing is directly sensitive to sound pressure which is related to sound intensity. In consumer audio electronics, the level differences are called "intensity" differences, but sound intensity is a specifically defined quantity and cannot be sensed by a simple microphone. Sound intensity is not valuable in music recording.
External links
- How many decibels is twice as loud? Sound level change and the respective factor of sound pressure or sound intensity
- Acoustic Intensity
- Conversion: Sound intensity level to sound intensity and vice versa
- Ohm's law as acoustic equivalent - calculations
- Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf
- Table of Sound Levels - Corresponding Sound Intensity and Sound Pressure