Sound power

Sound quantities

Sound deflection ${\displaystyle \xi }$ Sound pressure ${\displaystyle p}$ Sound pressure level ${\displaystyle L_{p}}$ Sound energy density ${\displaystyle E}$ Sound energy ${\displaystyle W}$ Sound flow ${\displaystyle q}$ Speed ​​of sound ${\displaystyle c_{\text{S}}}$ Acoustic impedance ${\displaystyle Z}$ Sound intensity ${\displaystyle I}$ Sound power ${\displaystyle P_{\text{ak}}}$ Speed ​​of sound ${\displaystyle v}$ Fast sound amplitude ${\displaystyle v}$ Sound radiation pressure

The sound power (symbol  P _ak ) of a sound source is an acoustic quantity. It describes the sound energy emitted by a sound source per unit of time . It is one of the sound energy quantities and is a mechanical achievement . Your unit is watt (W). The associated logarithmic quantity is the sound power level .

The sound power describes the source strength of a sound generator and not the sound field . Neglecting attenuation within the surrounding medium, the same sound energy must pass through every closed envelope around the sound source, regardless of its shape and distance from the sound source.

In emission measurement , this is an important sound energy variable for evaluating a sound source, since the sound power of a sound source, in contrast to the sound pressure , the sound velocity and the sound intensity, is independent of the location of the source or the receiver.

The sound immission at a receiving location can be calculated from the sound power if the sound power of the sound sources relevant at this location, their distance from the receiving location and their radiation characteristics are known. So it is with knowledge of the sound power of the individual components z. B. possible to determine the noise exposure of the operating personnel of a machine or system before its completion and to initiate any necessary noise protection measures.

definition

If an imaginary enveloping surface A is chosen so that the sound intensity is evenly distributed on the enveloping surface and is aligned perpendicular to the enveloping surface, the sound power is obtained as the product of the sound intensity  I and the area  A or as the product of sound pressure  p , sound velocity  v and the sounded area  A :

${\displaystyle P_{\text{ak}}=I\cdot A=p\cdot v\cdot A}$

The sound power can also be determined from the integral of the sound intensity  I over a sounded area  A or from the integral over the product of sound pressure  p and sound velocity  v over a sounded area  A , with only the parts of sound intensity directed perpendicular to the surface for each area or sound velocity have an influence on the determination of the sound power.
Mathematically, this relationship corresponds to the scalar product of a sound intensity or sound velocity vector with an area vector, the area vector being oriented perpendicular to the respective area piece.

${\displaystyle P_{\text{ak}}=\int {\vec {I}}\cdot {\overrightarrow {\mathrm {d} A}}=\int p\cdot {\vec {v}}\cdot {\overrightarrow {\mathrm {d} A}}\,}$

Sound power level

The sound power level L _W in decibels  (dB) is more common than specifying the sound power :

${\displaystyle L_{W}=10\lg \left({\frac {P_{\text{ak}}}{P_{0}}}\right)\,\mathrm {dB} }$

with for airborne sound standardized reference value P ₀ = 10 ^-12 W.

Measurement

General

If the sound power emitted by a sound source is to be determined (e.g. for emission measurements), area A is selected so that the entire sound source is enveloped and the sound field is measured on this enveloping area. It does not matter at what distance from the sound source this enveloping surface is located. (In very rare individual cases, the sound power recorded by a sound receiver is also determined; then area A is selected so that all paths to the receiver are covered, e.g. the area of ​​the ear canal for the ear.)

There are several measurement methods for measuring the radiated sound power of a sound source:

• Measurement in an anechoic room with an anechoic lining on all sides: measurements over the entire envelope of the sound source (only possible with hanging sound sources).
• Measurement in an anechoic half-space (firm, reverberant floor, anechoic walls): Measurements over an envelope above the floor (e.g. with heavy sound sources).
• Measurements in the reverberation room: Since a diffuse field is formed here, in which ideally the same sound pressure prevails everywhere, after a calibration of the room (with a source of known sound power or by measuring the reverberation time), the sound power of the sound source can theoretically be determined from a single sound pressure measurement.
• In any environment with extraneous sound or reflections: in order to determine the sound power, the sound intensity passing through an enveloping surface around the source must be measured here. This measurement detects both the radiated sound to the outside, as well as to be irradiated by the volume enveloped interference noise . This can thus be eliminated.

Sound intensity probes or microphones (which are actually sound pressure receivers) can be used to measure the sound power. However, microphones only deliver a correct result if the sound passes perpendicularly through the enveloping surface and no interfering sound is present.

Usually the emitted sound power is given in the form of the sound power level .

The sound power emitted by a sound source is independent of location and room. It is the same for all distances from the sound source. Specifying a distance here only creates confusion. The location-independent sound power level is often confused with the location-dependent sound pressure level (SPL) because both levels are expressed in dB.

Determination from sound pressure measurements according to DIN EN ISO 3746: 2011-03

The starting point is the measurement of the sound pressure level at specified positions on an envelope surface. Details on these items can be found in the named standard or in a suitable product standard.

The starting point is measurements with the time-averaged A-weighted sound pressure levels , from which the mean value ${\displaystyle N_{\text{M}}}$ ${\displaystyle L'_{p{\text{A}}j{\text{(ST)}}}}$

${\displaystyle {\overline {L'_{p{\text{A(ST)}}}}}=10\lg \left({\frac {1}{N_{\text{M}}}}\sum _{j=1}^{N_{\text{M}}}10^{0{,}1L'_{p{\text{A}}j{\text{(ST)}}}}\right)}$

is determined. The standard mentions the background noise correction factor and the influence of the measuring environment as correction factors with which the measuring surface sound pressure level can be calculated. The sound power level is thus ${\displaystyle K_{\text{1A}}}$ ${\displaystyle K_{\text{2A}}}$ ${\displaystyle {\overline {L_{p{\text{A}}}}}={\overline {L'_{p{\text{A(ST)}}}}}-K_{\text{1A}}-K_{\text{2A}}}$

${\displaystyle L_{W{\text{A}}}={\overline {L_{p{\text{A}}}}}+10\lg \left({\frac {S}{S_{0}}}\right)\mathrm {dB} }$

With

${\displaystyle S_{0}=1\,\mathrm {m} ^{2}}$.

With you get . So with the same mean sound pressure, the sound power is greater if the sound pressure was measured over a larger area. ${\displaystyle {\overline {L_{p{\text{A}}}}}=10\lg {\frac {p_{\text{A}}}{p_{0}}}}$ ${\displaystyle L_{W{\text{A}}}=10\lg {\frac {p_{\text{A}}}{p_{0}}}\cdot {\frac {S}{S_{0}}}}$

Table: Sound power and sound power level of various sound sources

Situation and source of sound	Sound power P ak   watt	Sound power level L w dB re 10 −12 watts
Rocket engine	1,000,000 W	180 dB
Jet engine	10,000 W	160 dB
siren	1,000 W	150 dB
Ship diesel engine	100 W	140 dB
Machine gun	10 W	130 dB
Jackhammer	1 w	120 dB
Excavator, trumpet	0.3 W	115 dB
Combustion engine chainsaw	0.1 W	110 dB
helicopter	0.01 W	100 dB
loud language , lively children	0.001 W	90 dB
Conversation language, typewriter	10 −5 W	70 dB
fridge	10 −7 W.	50 dB

Sound power with plane sound waves

The following relationship exists between the sound power in the case of flat, progressing sound waves and other important acoustic quantities:

${\displaystyle {\frac {{\text{d}}P_{\text{ak}}}{{\text{d}}A}}=I=\xi ^{2}\omega ^{2}Z=v^{2}Z={\dfrac {p^{2}}{Z}}=v\,p=E\,c}$

Where:

symbol	units	meaning
${\displaystyle {\frac {{\text{d}}P_{\text{ak}}}{{\text{d}}A}}=I}$	W / m 2	Sound power per surface element ( sound intensity )
ξ	m , meter	Sound deflection
${\displaystyle \omega }$= 2 · · f ${\displaystyle \pi }$	rad / s	Angular frequency
Z = c ρ	N · s / m 3	Characteristic acoustic impedance, acoustic field impedance
v	m / s	Speed ​​of sound
ρ	kg / m 3	Air density , density of the air (of the medium)
p	Pascal	Sound pressure
f	hertz	frequency
c	m / s	Speed ​​of sound
E.	W · s / m 3	Sound energy density

See also

• Sound field size
• Sound energy quantity
• Performance (physics)

Web links

• Correlation of the acoustic quantities in plane progressive sound waves (PDF; 109 kB)
• Sound power of musical instruments (PDF; 58 kB)
• Sound quantities, their levels and the reference value - conversions, calculations and formulas
• Sound power and sound pressure - cause and effect (PDF; 112 kB)

Individual evidence

1. ↑ Gerhard Müller, Michael Möser (ed.): Pocket book of technical acoustics . 3rd expanded and revised edition. Springer, Berlin a. a. 2004, ISBN 3-540-41242-5 , pp. 150 .
2. ↑ Werner Schirmer (Ed.): Technical noise protection. Basics and practical measures to protect against noise and vibrations from machines . 2nd revised and expanded edition. Springer, Berlin a. a. 2006, ISBN 3-540-25507-9 , pp. 26th f . (VDI book).