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Introduction to Acoustics

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972 Part G Structural <strong>Acoustics</strong> and Noise<br />

Part G 23.2<br />

Strictly speaking, this relationship is only correct<br />

in the far field of a source radiating in<strong>to</strong> free space.<br />

Good approximations <strong>to</strong> free-space, or free-field, conditions<br />

can be achieved in properly designed anechoic<br />

or hemi-anechoic rooms, or outdoors. Hence, (23.26)<br />

is approximately correct in the far field of a source<br />

over a reflecting plane, provided that the space above<br />

the reflecting plane remains essentially a free field<br />

at distance r. Even if the free field is not perfect,<br />

and a small fraction of the sound is reflected from<br />

the walls and ceiling of the room, an environmental<br />

correction may be introduced <strong>to</strong> allow valid measurements<br />

<strong>to</strong> be taken in the room. The relations below<br />

are widely used in standards that determine the sound<br />

power of a source from a measurement of sound pressure<br />

level.<br />

If a closed measurement surface is placed around<br />

a source so that all points on the surface are in the<br />

far field, and if the intensity vec<strong>to</strong>r is assumed <strong>to</strong> be<br />

essentially normal <strong>to</strong> the surface so that I = In at all<br />

points on the surface, then (23.23) and(23.26) can be<br />

combined <strong>to</strong> yield<br />

W = 1 �<br />

p<br />

ρc<br />

i<br />

2 i Si , (23.27)<br />

here pi is the average RMS sound pressure over area<br />

segment Si.<br />

The sound power level is as expressed in (23.25). If<br />

all segments are of equal area,<br />

W = S 1 �<br />

p<br />

ρc N<br />

i<br />

2 S<br />

i =<br />

ρc 〈p2 〉 , (23.28)<br />

where S is the <strong>to</strong>tal area of the measurement surface, N<br />

is the number of area segments, and 〈p 2 〉 is the average<br />

mean square pressure over the measurement surface.<br />

In logarithmic form with reference power 10 −12 W<br />

and reference pressure 20 µPa, the sound power level is<br />

LW = Lp + 10 log S<br />

S0<br />

+ 10 log 400<br />

ρc<br />

, (23.29)<br />

where S0 = 1m 2 .<br />

For ρc = 406 MKS Rayl, the last term in (23.29) is<br />

− 0.064, and can usually be neglected.<br />

Hence, the sound power level of a source can be computed<br />

from sound pressure level measurements made in<br />

a free field. Equation (23.29) iswidelyusedinstandardized<br />

methods for the determination of sound power<br />

levels in a free field or in a free field over a reflecting<br />

plane.<br />

Sound Power Determination in a Diffuse Field<br />

The sound power level of a source can also be computed<br />

from sound pressure level measurements made in an<br />

enclosure with a diffuse sound field because in such<br />

a field the sound energy density is constant; it is directly<br />

related <strong>to</strong> the mean-square sound pressure and, therefore,<br />

<strong>to</strong> the sound power radiated by the source. The sound<br />

pressure level in the reverberant room builds up until<br />

the <strong>to</strong>tal sound power absorbed by the walls of the room<br />

is equal <strong>to</strong> the sound power generated by the source.<br />

The sound power is determined by measuring the meansquare<br />

sound pressure in the reverberant field. This value<br />

is either compared with the mean-square pressure of<br />

a source of known sound power output (comparison<br />

method) or calculated directly from the mean-square<br />

pressure produced by the source and a knowledge of<br />

the sound-absorptive properties of the reverberant room<br />

(direct method).<br />

The procedure for determining the sound power level<br />

of a noise source by the comparison method requires the<br />

use of a reference sound source of known sound power<br />

output. The procedure is essentially as follows.<br />

With the equipment being evaluated at a suitable location<br />

in the room, determine, in each frequency band,<br />

the average sound pressure level (on a mean-square basis)<br />

in the reverberant field using the microphone array<br />

or traverse described above.<br />

Replace the source under test with the reference<br />

sound source and repeat the measurement <strong>to</strong> obtain the<br />

average level for the reference sound source.<br />

The sound power level of the source under test LW<br />

for a given frequency band is calculated from<br />

LW = LWr + � �<br />

〈Lp〉−〈Lp〉r<br />

(23.30)<br />

where LW is the one-third-octave band sound power<br />

level for the source being evaluated, 〈Lp〉 is the spaceaveraged<br />

one-third octave band sound pressure level of<br />

source being evaluated, LWr is the calibrated one-thirdoctave<br />

band sound power level of the reference source,<br />

and 〈Lp〉r is the space-averaged one-third-octave band<br />

sound pressure level of the reference sound source.<br />

The direct method does not use a reference sound<br />

source. Instead, this method requires that the soundabsorptive<br />

properties of the room be determined by<br />

measuring the reverberation time in the room for each<br />

frequency band. Measurement of T60 is described in<br />

Chap. 11.<br />

With this method, the space-averaged sound pressure<br />

level for each frequency band of the source being<br />

evaluated is determined as described above for the comparison<br />

method. The sound power level of the source is

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