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5.11 AIR DISTRIBUTION SYSTEMNOISE

Back

Noise generated in air distribution systems is one of the concerns in design

of heating, ventilating, and air conditioning (HVAC) systems. Noise is

transmitted from the air-handling unit (fan) into the duct system. Sound

may also be generated as the air flows through elbows, fittings, and the grill

or diffuser at the duct outlet into the room. The location of these components

in an air distribution systemis illustrated in Fig. 5-4. The sound power

level of the noise introduced into the duct by the fan is given by Eq. (5-8).

192 Chapter 5

LWрfan outletЮ ј LW _ 3 dB (5-58)

For industrial air distribution systems that utilize high air velocities, the

noise generated by the air flowing through the distribution system is a

particular concern.

Energy transmitted along the duct may be attenuated or dissipated by

the interaction with the duct wall, or acoustic material may be placed inside

the duct to reduce the noise transmission.

5.11.1 Noise Attenuation in Air Distribution

Systems

There are three primary mechanisms responsible for noise attenuation in air

distribution systems:

(a) Acoustic energy is absorbed by interaction with the duct walls.

(b) Acoustic energy is reflected at the open end of the duct.

Noise Sources 193

FIGURE 5-4 Air distribution system. _LW is the attenuation in the element, and LW

is the noise generation within the element.

The attenuation of sound by each of these mechanisms has been correlated

in terms of the change in the sound power level produced by each element in

the HVAC system (ASHRAE, 1991).

At the junction where a duct divides or has side branches or outlets,

the acoustic power moving down the duct is divided at the duct branch. The

acoustic power from the fan into the duct divides in proportion to the ratio

of the total cross-sectional area of all branches leaving the junction to the

specific branch cross-sectional area. The sound power level for the acoustic

energy transmitted to a specific branch is given by the following expression:

LWрith branchЮ ј LW _ 10 log10

_Sj

_ _

(5-59)

If the duct has no external or internal lining material (a ‘‘bare’’ duct),

the attenuation per unit length for the duct is given in Table 5-15. If the duct

is externally insulated, the attenuation is approximately two times that given

in Table 5-15 for the base duct. If the duct is lined internally with an

absorbent material having an acoustic absorption coefficient _, the attenuation

by the lining material may be estimated, as follows:

(a) For 63 Hz _ f _ 2000 Hz:

_LW ј 4:20_1:4рL=DeЮ (5-60)

The quantity De is the equivalent or hydraulic diameter of the duct and L is

the length of the duct section:

De ј 4S=PW (5-61)

The quantity S is the cross-sectional area of the duct and PW is the perimeter

of the duct cross section.

194 Chapter 5

TABLE 5-15 Attenuation per Unit Length in Bare Ducts,

_LW=L, dB/m

ј 4S=Pw, ma

Octave band center frequency, Hz

63 125 250 500 1,000 and greater

0.075 0.59 0.59 0.57 0.53 0.47

0.15 0.59 0.57 0.53 0.47 0.37

0.30 0.57 0.53 0.47 0.37 0.23

0.60 0.53 0.47 0.37 0.23 0.16

1.20 0.47 0.37 0.23 0.085 0.084

2.40 0.42 0.29 0.14 0.033 0.033

aS is the cross-sectional area of the duct and Pw is the perimeter

of the duct.

(b) For 2000Hz < f < 8000 Hz:

_LW ј 1

2 Ѕ10ю_LWрEq: 5-60Ю_ (5-62)

_LW ј 10 dB (5-63)

The attenuation in the 8kHz and higher octave bands is limited to about

10dB because of line-of-sight propagation of sound through the lined

portion of the duct.

The attenuation due to reflection of the acoustic energy at the open

end of the duct is presented in Table 5-16. The data apply for ducts terminating

flush with the wall or ceiling.

The attenuation of elbows in the systemis given in Table 5.17 (circular

duct) and Table 5-18 (rectangular duct). The data presented in the tables are

for unlined ducts. Using acoustic lining before or after the elbow, or both,

will increase the attenuation by 7 dB to 12 dB in the 4 kHz to 8 kHz octave

bands (Faulkner, 1976, p. 404).

5.11.2 Noise Generation in Air Distribution

System Fittings

In addition to attenuation or dissipation of acoustic energy in fittings, flow

energy may also be converted to acoustic energy in the fittings. Flow-

Noise Sources 195

TABLE 5-16 Octave Band Attenuation (dB) Due to Reflection at the Open

End of the Ducta

foD, Hz-m Attenuation, _LW, dB foD, Hz-m Attenuation, _LW, dB

5 20.6 70 3.7

10 15.3 80 3.1

15 12.4 90 2.6

20 10.5 100 2.2

25 9.1 120 1.6

30 8.1 140 1.0

35 7.2 160 0.6

40 6.4 180 0.3

50 5.3 200 and greater 0.0

60 4.4

aD is the inner diameter for a circular duct and D ј S1=2 for a rectangular duct, where S

is the duct cross-sectional area; fo is the octave band center frequency.

induced noise generated in elbows may be estimated from the following

expression (Bullock, 1970):

LW ј Fs ю10log10 fo ю10log10 S ю44:4log10 u_54 (5-64)

The quantity fo is the octave band center frequency, Hz; S is the duct crosssectional

area, m2; and u is the velocity of the air upstream of the elbow,

m/s. The spectrum function Fs is given in Table 5-19. The Strouhal number

Ns is defined by the following expression:

196 Chapter 5

TABLE 5-17 Attenuation of Sound by Circular 908 Elbowsa

foD, Hz-m Attenuation, _LW, dB foD, Hz-m Attenuation, _LW, dB

40 or less 0.0 500 2.2

50 0.2 600 2.4

100 0.7 700 2.5

150 1.1 800 2.6

200 1.3 1,000 2.7

250 1.6 1,500 2.8

300 1.8 2,000 2.9

400 2.0 3,000 and greater 3.0

aThe quantity D is the inner diameter of the elbow and fo is the octave band center

frequency.

TABLE 5-18 Attenuation of Sound by Rectangular 908 Elbowsa

foS1=2, Hz-m Attenuation, LW, dB foS1=2, Hz-m Attenuation, _LW, dB

40 or less 0.0 300 6.8

50 0.4 350 6.5

60 1.0 400 5.9

70 1.6 450 5.4

80 2.4 500 5.0

100 3.6 600 4.5

120 4.8 700 4.1

140 5.6 800 3.8

160 6.2 1,000 3.4

200 6.8 1,200 3.2

250 7.0 1,500 or greater 3.0

aThe quantity S is the cross-sectional area of the duct before the elbow and fo is the octave

band center frequency. The data apply to rectangular ducts with aspect ratios between 0.8

and 1.2.

NS ј

foD

(5-65)

where D ј р4S=_Ю1=2.

The aerodynamic noise generation produced by 908 branch tees has

been correlated in a manner similar to that used for elbows (Bullock, 1970).

The noise generated and transmitted to the side branch, having a crosssectional

area S3, m2, may be estimated from the following expression:

LW ј Fsb ю10log10 fo ю10log10 S3 юLbr _1:5 (5-66)

For the noise generated and transmitted into the main straight branch, use

the area S2 instead of S3 in Eq. (5-66). The spectrum function for branch

tees is given in Table 5-20. The quantity Lbr is calculated fromthe velocity in

the main straight branch of the tee, u2, and the velocity in the side branch of

the tee, u3, where both velocities are expressed in units of m/s:

Lbr ј 10log10р10L2=10 ю10L3=10Ю (5-67)

L2 ј 46log10 u2 _70 (5-68)

L3 ј 23log10 u3 _20 (5-69)

Noise Sources 197

TABLE 5-19 Spectrum Function Fs for Noise Generation in Elbowsa

ј foD=u 908 elbow, without turning vanes 908 elbow, with turning vanes

0.6 79 49

0.8 67 48

1.0 65 47

2 56 45

4 46 42

6 42 40

8 40 38

10 38 37

20 34 33

40 31 27

60 29 22

100 27 14

200 23 0

aThe Strouhal number is NS ј foD=u, where D ј р4S=_Ю1=2; fo is the octave band center

frequency, Hz; and u is the velocity of the air before the elbow, m/s.

Note: Use logarithmic interpolation with this table;

F _ F1

F2 _ F1 ј

log10рNS=NS1Ю

log10рNS2=NS1Ю

The attenuation values are subtracted directly from the sound power

level, in decibels, because the attenuation is an exponential function. On the

other hand, the acoustic energy generation in fittings must be combined by

‘‘decibel addition’’ with the existing sound power. The energy or power is

additive, but the decibel values are not directly additive. This procedure is

illustrated in the example at the end of this section.

5.11.3 Noise Generation in Grilles

Most air distribution systems are terminated by grilles or diffusers. Noise is

generated by the flow of air over the grille or diffuser elements. The following

correlation (Beranek and Veґ r, 1992) may be used to estimate the noise

generated in a grille:

LWрgrilleЮ ј 10 ю 10 log10 S ю 30 log10 CD ю 60 log10 u (5-70)

where S is the cross-sectional area, m2; u is the velocity of the air before

entering the grille, m/s; and CD is the dimensionless grille pressure drop

coefficient, defined by the following expression:

_P ј 1

2CD_u2 (5-71)

198 Chapter 5

TABLE 5-20 Spectrum Function Fsb for Noise

Generated in Branch Duct Take-offsa

ј foD=u1 Fsb, dB NS

ј foD=u1 Fsb, dB

1 80 50 42

2 74 100 35

5 64 200 26

10 57 500 11

20 51 1,000 0

aThe Strouhal number is defined by NS ј foD=u1,

where D ј р4S1=_Ю1=2; fo is the octave band center

frequency, Hz; and u1 is the velocity of the air before

the branch, m/s:

" u3

u2 ? u1

Note: Use logarithmic interpolation with this table:

F _ F1

F2 _ F1 ј

log10рNS=NS1Ю

log10рNS2=NS1Ю

The quantity _P is the pressure drop across the grille due to the flowing air

and _ is the density of the air. Specific values for the grille pressure drop

coefficient may be obtained from the grille manufacturer. Some representative

values for CD are given in Table 5-21 for various grille configurations.

The sound generated by air flow through a grille is usually broadband

noise; however, some discrete frequency noise, due to vortex shedding from

the solid elements of the grille, is also present. The peak in the grille noise

spectrumfor HVAC systems occurs at a frequency fm given by the following

dimensional relationship:

fm ј 150u рm=sЮ (5-72)

The octave band sound power levels may be obtained from the following

expression:

LWрoctave bandЮ ј LWрgrilleЮ_CFg (5-73)

Values for the conversion factor CFg are given in Table 5-22.

The directivity factor is not unity for acoustic radiation from a grille,

because the sound is not radiated as spherical waves. The value of the

directivity factor is a function of the dimensionless ratio, f рSЮ1=2=c. Values

for the directivity factor Q and the directivity index, DI ј 10log10 Q, are

given in Table 5-23.

Example 5-7. In the air distribution system shown in Fig. 5-5, the ducts

have a square cross section and are uninsulated. There is one elbow in the

Noise Sources 199

TABLE 5-21 Grille Pressure Drop Coefficient,

Grille type CD

Rectangular grille with no dampers:

parallel louvers 2.9

inclined louvers 2.7

Rectangular grille with dampers:

parallel louvers, open damper 4.8

parallel louvers, partially closed damper 7.3

Circular ceiling diffuser 1.59

High side-wall diffuser (rectangular):

zero angle of deflection of exit air 0.73

458 angle of deflection of exit air 1.93

Source: Hubert (1970) and McQuiston and Parker

(1994).

600mm (23.6 in) branch duct and one elbow in the 900mm (35.4 in) main

duct. The grille at the duct outlet has parallel louvers and no dampers. The

volumetric flow rate out of the grille (and through the 600mm branch duct)

is 1440 dm3/s (3051 cfm), and the volumetric flow rate in the 900mm main

duct from the fan is 5050 dm3/s (10,680 cfm). The internal fan sound power

level spectrum is given in Table 5-24. The air in the room is at 258C (778F),

at which condition the sonic velocity is 346.1 m/s (1136 ft/sec). Determine

the steady-state sound pressure level in the roomat a distance of 5m(16.4 ft)

directly in front of the grille р_ ј 08Ю.

200 Chapter 5

TABLE 5-22 Conversion Factors CFg to Convert from

the Overall Sound Power Level for Grille Noise to the

Octave Band Sound Power Levels

Octave band center frequency, Hz

fm=16 fm=8a fm=4 fm=2 fm 2fm 4fm 8fm 16fm

CFg, dB 23 17 11 6 5 7 12 18 24

aThe table entry fm=8, for example, refers to the octave band that

includes the frequency fm=8, where fm is given by Eq. (5-73).

TABLE 5-23 Directivity Factor Q and Directivity Index DI

(dB) for a Duct Opening Flush with the Walla

fS1=2=c Qр_ ј 08Ю DI(08), dB Qр_ ј 458Ю DI(458), dB

0.04 2.0 3.0 2.0 3.0

0.06 2.2 3.4 2.0 3.0

0.08 2.5 4.0 2.0 3.1

0.10 2.7 4.3 2.0 3.1

0.20 3.6 5.6 2.2 3.4

0.40 4.6 6.6 2.7 4.3

0.60 5.3 7.2 3.0 4.8

0.80 5.9 7.7 3.2 5.1

1.0 6.3 8.0 3.3 5.2

2.0 7.2 8.6 3.7 5.7

4.0 7.8 8.9 3.9 5.9

1 8.0 9.0 4.0 6.0

aThe quantity S is the opening cross-sectional area and c is the sonic

velocity in the air. The angle _ is the angle between the desired

direction and the normal to the grille opening.

Asample calculation for the 125Hz octave band is given in the following

material. The calculations for the other octave bands are summarized in

Table 5-24. The calculation procedure involves beginning with the sound

power level at the duct inlet and proceeding along the duct system to the

outlet grille in each branch. The attenuation values are subtracted, and the

noise generation values are combined by energy addition at each point

where the energy is generated.

The sound power level produced internally at the fan in the 125 Hz

octave band is given as 71dB. The acoustic energy transmitted through the

fan outlet into the duct system is given by Eq. (5-8):

LWрto ductЮ ј 71_3 ј 68 dB

For a square duct рa ј bЮ, the quantity De ј 4S=PWј р4ЮрabЮ=

2рaюbЮ ј a, the side length of the duct cross section. For the 10m long,

900mm square duct, the attenuation is found from Table 5-15:

_LW ј р0:42 dB=mЮр10mЮ ј 4:2dB

The sound power level before the elbow in the main duct is:

LWрaЮ ј 68 _ 4:2 ј 63:8dB

Noise Sources 201

FIGURE 5-5 Diagram for Example 5-7.

202 Chapter 5

TABLE 5-24 Solution for Example 5-7

Item

Octave band center frequency, Hz

63 125 250 500 1,000 2,000 4,000 8,000

LW(fan) 73 71 71 69 61 57 54 48

LW(to duct) 70 68 68 66 58 54 51 45

_LW(10m duct) 5.0 4.2 3.0 3.6 1.2 1.2 1.2 1.2

рaЮ before ell 65.0 63.8 65.0 62.4 56.8 52.8 49.8 43.8

NS 10.2 20.4 40.8 81.6 163 326 652 1,304

Fs 37.8 33.9 30.9 27.8 24.2 20.2 16.2 12.2

LW(elbow) 36.1 35.2 35.2 35.1 34.5 33.5 32.6 31.6

рbЮ in ell 65.0 63.8 65.0 62.4 56.8 52.9 49.9 44.1

foD, Hz-m 56.3 112.5 225 450 900 1,800 3,600 7,200

_LW(elbow) 0.8 4.4 6.9 5.4 3.6 3.0 3.0 3.0

LW to tee 64.2 59.4 58.1 57.0 53.2 49.9 46.9 41.1

Fsb 56.9 50.8 44.0 37.1 28.6 18.0 6.8 _4.2

LW(tee) 62.8 59.7 55.9 52.0 46.5 38.9 30.7 22.7

LW in tee 66.6 62.6 60.1 58.2 54.0 50.2 47.0 41.2

_LW(branch) 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1

LW(branch) 61.5 57.5 55.0 53.1 48.9 45.1 41.9 36.1

_LW(12m duct) 6.4 5.6 4.4 2.8 1.9 1.9 1.9 1.9

LW before ell 55.1 51.9 50.6 50.3 47.0 43.2 40.0 34.2

NS 10.7 21.2 42.3 84.6 169 339 677 1,354

Fs 37.6 33.7 30.6 27.7 24.0 20.0 16.0 12.0

LW(elbow) 23.9 23.0 22.9 23.0 22.3 21.3 20.3 19.3

LW in elbow 55.1 51.9 50.6 50.3 47.0 43.2 40.0 34.3

foD, Hz-m 37.8 75 150 300 600 1,200 2,400 4,800

_LW(elbow) 0.0 2.0 5.9 6.8 4.5 3.2 3.0 3.0

_LW(reflect.) 6.8 3.4 0.8 0.0 0.0 0.0 0.0 0.0

_Lw(8m duct) 4.2 3.8 3.0 1.8 1.3 1.3 1.3 1.3

Total attenuation 11.0 9.2 9.7 8.6 5.8 4.5 4.3 4.3

LW(before grille) 44.1 42.7 41.9 41.7 41.2 38.7 35.8 30.0

LW(grille) 55.6 55.6 55.6 55.6 55.6 55.6 55.6 55.6

CFg 17 11 6 5 7 12 18 24

LW(grille, octave band) 38.6 44.6 49.6 50.6 48.6 43.6 37.6 31.6

LW to room 45.2 46.8 50.3 51.1 49.3 44.8 39.8 33.9

The quantity D for the 900mm main duct is, as follows:

D ј р4S=_Ю1=2 ј Ѕр4Юр0:810Ю=__1=2 ј 1:016m

The velocity of the air before the elbow in the 900mmmain duct is found as

follows:

u ј Qg=S ј р5:040m3=sЮ=р0:810m2Ю ј 6:22m=s

The Strouhal number for the 125Hz octave band is calculated from its

definition:

NS ј foD=u ј р125Юр1:016Ю=р6:22Ю ј 20:4

The corresponding spectrum function is found in Table 5-19:

Fs ј 33:9

The sound power generated by flow noise through the elbow is found from

Eq. (5-64):

LWрelbowЮ ј33:9ю10log10р125Юю10 log10р0:810Ю

ю44:4 log10р6:22Ю_54

LWрelbowЮ ј 33:9ю21:0юр_0:9Юю35:2_54 ј 35:2dB

The total sound power level at the elbow is found as follows:

LWрbЮ ј 10log10р106:38 ю103:52Ю ј 63:8 dB

For a square duct рa ј bЮ, the quantity S1=2 ј рabЮ1=2 ј a, the side

length of the duct cross section. For the 125Hz octave band, the quantity

foS1=2 ј foa ј р125Юр0:900Ю ј 112:5Hz-m. The attenuation for the elbow is

found fromTable 5-18 to be _LW ј 4:4dB. The sound power level fromthe

elbow to the tee is as follows:

LW (to tee) ј 63:8_4:4 ј 59:4dB

The spectrum function for the side-branch energy generation is found

from Table 5-20 at a Strouhal number, NS ј foD=u1 ј 20:4, or Fsb ј 50:8.

The air velocity in the two branches may be determined as follows:

u2 ј Qg2=S2 ј р5:040 _ 1:440Ю=р0:810Ю ј 4:44m=s

u3 ј Qg3=S3 ј р1:440Ю=р0:360Ю ј 4:00m=s

The branch functions given in Eqs. (5-68) and (5-69) may be determined:

L2 ј 46 log10р4:44Ю _ 70 ј _40:2dB

L3 ј 23 log10р4:00Ю _ 20 ј _6:2dB

Noise Sources 203

These values may be combined according to Eq. (5-67):

Lbr ј 10log10р10_4:02 ю10_0:62Ю ј _6:2 dB

The acoustic energy generated within the tee in the 125Hz octave band

is determined from Eq. (5-66):

LWрteeЮ ј 50:8ю10 log10р125Юю10log10р0:810Ююр_6:2Ю_1:5

ј 59:7 dB

The acoustic power in the tee is found by combining the energy before the

tee and the energy generated within the tee:

LW (in tee) ј 10log10р105:94 ю105:97Ю ј 62:6 dB

The energy delivered to the 600mm branch duct is found from Eq.

(5-59):

LW _LWрbranchЮ ј 10 log10

0:810ю0:360

0:360

_ _

ј 5:1dB

The sound power level delivered to the 600mm side branch in the 250 Hz

octave band is:

LWрbranchЮ ј 62:6_5:1 ј 57:5dB

The attenuation in the 12m long run of the side branch may be calculated

as follows. The attenuation per unit length is found from Table 5-15,

with De ј 0:600m for the square cross section:

_LWр12 m ductЮ ј р0:47dB=mЮр12mЮ ј 5:6 dB

The sound power level to the elbow in the 125Hz octave band is as follows:

LW (before elbow) ј 57:5_5:6 ј 51:9dB

The energy generated in the elbow in the 600mm duct may be determined

by the same procedure as that for the previous elbow. The quantity D

for the smaller duct is as follows:

D ј р4S=_Ю1=2 ј Ѕр4Юр0:360Ю=__1=2 ј 0:677m

The Strouhal number is calculated from its definition:

NS ј foD=u3 ј р125Юр0:667Ю=р4:00Ю ј 21:2

The spectrum function is found from Table 5-19, Fs ј 33:7. The noise

generated in the elbow is found from Eq. (5-64):

204 Chapter 5

LWрelbowЮ ј Fs ю10log10 fo ю10log10 S ю44:4log10 u3 _54

LWрelbowЮ ј33:7ю10log10р125Юю10 log10р0:360Юю44:4 log10р4:00Ю

_54

LWрelbowЮ ј 33:7ю21юр_4:4Юю26:7_54 ј 23:0dB

The sound power level in the elbow in the 600mmbranch run is found

by combining the energy generated and the energy to the elbow:

LW (in elbow) ј 10 log10р105:19 ю102:30Ю ј 51:9dB

It is noted that the noise generated in the smaller elbow is negligible in this

example.

The attenuation in the elbow is found as follows. The quantity

foS1=2 ј р125Юр0:600Ю ј 75 Hz-m. The attenuation of the elbow in the

125Hz octave band is found from Table 5-18, _LWрelbowЮ ј 2:0dB.

The attenuation due to reflection at the open end of the 600mmsquare

duct is found from Table 5-16 at a value foD ј 75Hz-m for the 125 Hz

octave band, _LWрreflectionЮ ј 3:4dB.

The attenuation in the 8m long section of the branch is as follows:

_LWр8m ductЮ ј р0:47dB=mЮр8mЮ ј 3:8dB

The total attenuation from the elbow to the open end of the duct in the

125Hz octave band is found by adding the three contributions (elbow,

straight length, and reflection):

_LWрtotalЮ ј 2:0ю3:4ю3:8 ј 9:2dB

The sound power level before the grille is as follows:

LW (before grille) ј 51:9_9:2 ј 42:7dB

The grille pressure drop coefficient, from Table 5-21, is CD ј 2:9. The

overall power level generated by the flow through the grille may be found

from Eq. (5-70):

LWрgrilleЮ ј 10ю10 log10 S ю30 log10 CD ю60log10 u

LWрgrilleЮ ј 10ю10 log10р0:360Юю30log10р2:9Юю60log10р4:00Ю

LWрgrilleЮ ј 10юр_4:4Юю13:9ю36:1 ј 55:6dB рoverallЮ

The peak frequency of the grille power level spectrum occurs at the following

frequency, according to Eq. (5-72):

fm ј р150Юр4:00Ю ј 600 Hz

This frequency falls in the 500Hz octave band, so the frequency 125 Hz

corresponds to fm=4, and CFg ј 11, from Table 5-22. The sound power

Noise Sources 205

level generated by the flow through the grille for the 125Hz octave band is

found from Eq. (5-73):

LWрgrille, octave bandЮ ј 55:6_11 ј 44:6dB (125 Hz octave band)

The sound power level delivered from the grille to the room may be

determined by combining the sound power level before the grille and the

power level generated in the grille:

LW (to room) ј 10log10р104:27 ю104:46Ю ј 46:8dB

This calculation completes the first part of the problem, which is to

determine the sound power level input to the room. Next, let us use this data

to determine the steady-state sound pressure level in the room. We will

continue to present a sample calculation for the 125Hz octave band and

present the results for the other octave bands in Table 5-25.

Values for the room constant in each octave band are given in Table

5-25. The dimensionless parameter needed to determine the directivity factor

for the grille opening is as follows:

foS1=2

c ј р125Юр0:360Ю1=2

р346:1Ю ј 0:217

The directivity factor is found from Table 5-23, Qр_ ј 08Ю ј 3:7.

The second term in Eq. (5-6) may be calculated:

10 log10

R ю

4_r2

_ _

ј 10 log10

7:1 ю р3:7Ю

р4_Юр5:00Ю2

_ _

ј _2:4dB

206 Chapter 5

TABLE 5-25 Solution for Overall Sound Pressure Level in Example 5-7

Item

Octave band center frequency, Hz

63 125 250 500 1,000 2,000 4,000 8,000

Lw to room 45.2 46.8 50.3 51.1 49.3 44.8 39.8 33.9

R, m2 (given) 4.2 7.1 8.6 11.8 15.1 17.8 19.1 22.0

foS1=2=c 0.109 0.217 0.433 0.867 1.73 3.47 6.93 13.87

Qр_ ј 08Ю 2.8 3.7 4.8 6.0 7.0 7.7 7.9 8.0

10 log10

ю Q

4_r2

_ _

_0.2 _2.4 _3.2 _4.5 _5.4 _6.0 _6.3 _6.8

Lp, dB 45.1 44.5 47.2 46.7 44.0 38.9 33.6 27.2

Background Lp 55 50 45 40 35 30 28 28

Total Lp, dB 55.4 51.1 49.2 47.5 44.5 39.4 34.7 30.6

The sound pressure level in the 125Hz octave band may be found from Eq.

(5-6) for sound propagated indoors:

Lp ј 46:8юр_2:4Юю0:1 ј 44:5 dB

The background sound pressure level in the 125Hz octave band is

given as 50 dB in Table 5-25. The total octave band sound pressure level

may be found by combining the noise from the grille and the background

noise.

Total Lpрoctave bandЮ ј 10 log10р104:45 ю 105:00Ю ј 51:1dB

The overall sound pressure level is found by combining the octave

band sound pressure level values:

LpрoverallЮ ј 10 log10р105:54 ю 105:11 ю_ _ _ю103:06Ю ј 58:2dB

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