5.1 SOUND TRANSMISSION INDOORS AND OUTDOORS

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The most useful correlation for noise emitted from a system is the correlation

of the sound power level LW as a function of known or measurable

Copyright © 2003 Marcel Dekker, Inc.

characteristics of the system. The corresponding sound pressure level Lp

produced by the noise emission depends on distance from the source,

whether the source is located indoors or outdoors, and other factors. Let

us develop two general relationships that are needed for prediction of the

sound pressure level when the sound power level can be determined.

For sound transmission outdoors, the acoustic intensity for a sound

wave, not necessarily a spherical wave, is given by Eq. (4-128) with the

directivity factor Q included:

I ј

QWo

4_r2 e_2_r ј

p2

_oc

(5-1)

If we solve for the rms acoustic pressure (or p2Ю and include the reference

pressure and power terms, we obtain the following expression, where

m ј 2_:

p2

р pref Ю2 ј

WoQe_mr _ocWref

Wref r2р4_Юр pref Ю2 (5-2)

Taking log base 10 of both sides of Eq. (5-2) and multiplying by 10, we

obtain the following relationship in terms of levels:

Lp ј LW ю 10 log10рQЮ _ 10 log10рr2Ю ю 10 log10рe_mrЮ

ю 10 log10

_ocWref

4_p2

ref

_ _

(5-3)

If we introduce the definition of the directivity index DI from Eq. (2-41), we

obtain the following expression:

Lp ј LW ю DI _ 20 log10рrЮ ю 10 log10рe_mrЮ _ 10 log10

4_p2

ref

_ocWref

!

р5-4)

The characteristic impedance for atmospheric air at 300K (278C or

808F) and 101.325 kPa (14.696 psia) is Zo ј _oc ј 408:6 rayl. This value

may be used to evaluate the last term in Eq. (5-4):

4_p2

ref

_ocWref ј р4_Юр20 _ 10_6Ю2

р408:6Юр10_12Ю ј 12:30m_2

10 log10р12:30Ю ј 10:9dB

This constant value may be used for 0.1 dB accuracy if the air temperature

is between about 293K (208C or 688F) and 307K (348C or 938F). For air

temperatures outside this range or for materials other than air, the value of

the constant must be calculated.

Noise Sources 163

Copyright © 2003 Marcel Dekker, Inc.

For sound transmitted outdoors in air around 300K, the following

expression may be used to estimate the sound pressure level Lp for a

noise source having a sound power level LW:

Lp ј LW юDI_20log10рrЮ_4:343mr_10:9 (5-5)

The distance fromthe sound source r must be expressed in meters in Eq. (5-5),

and the energy attenuation coefficient must have units of m_1. The term

involving the energy attenuation coefficient is usually negligible for lower

frequencies and smaller distances, as discussed in Sec. 4.13.

For sound transmission indoors, the sound pressure level and sound

power level are related by the following expression (developed in Chapter 7):

Lp ј LW ю10 log10

4

Rю

Q

4_r2

_ _

ю10 log10

_ocWref

p2

ref

_ _

(5-6)

The quantity R is called the room constant and is given by:

R ј

SoЅ__юр4mV=SoЮ_

1____р4mV=SoЮ

(5-7)

where So is the total surface area of the room, m2; __ is the average surface

absorption coefficient; and V is the volume of the room, m3.

For the special case of air at 101.325kPa (14.696 psia) and 300K(278C

or 808F), the numerical value of the last term in Eq. (5-6) may be evaluated:

_ocWref

p2

ref ј р408:6Юр10_12Ю

р20_10_6Ю2 ј 1:0215

10log10р1:0215Ю ј 0:1 dB

In the following sections, we will consider techniques for estimation of

the sound power level that may be used in Eqs (5-4) and (5-6) to estimate the

sound pressure level generated by various noise sources.

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