4.9 APPROXIMATE METHOD FOR ESTIMATING THE TL

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In preliminary design, it is often required to estimate the transmission loss

spectrum for a panel. This section presents an outline of an approximate

method for calculating the transmission loss curve for Regions II and III

(Watters, 1959). If the panel dimensions a and b are at least 20 times the

panel thickness h, the first resonant frequency for the panel is usually less

than 125 Hz, so the major portion of the transmission loss curve will involve

Regions II and III. In addition, the application of the Region II equations

for Region I results in a conservative estimate for the transmission loss.

When using the approximate method, one should check the importance of

the Region I behavior, however.

In Region II, the mass-controlled region, the random-incidence transmission

loss is given by:

TL ј TLn _ 5 ј 10 log10 1 ю

_MS f

_1c1

_ _2

" #

_ 5 (4-168)

For frequencies above about 60 Hz, the term р_MS f =_1c1Ю is usually much

larger than 1; therefore, Eq. (4-168) may be approximated by the following

expression:

TL ј 10 log10

_MS f

_1c1

_ _2

_5 (4-169)

Equation (4-169) may be written in the following alternative form:

TL ј 20 log10рMSЮ ю 20 log10р fЮ _ 20 log10р_1c1=_Ю _ 5 (4-170)

Transmission of Sound 117

Copyright © 2003 Marcel Dekker, Inc.

For the case of air at 101.3 kPa (14.7 psia) and 228C (728F), the density and

sonic velocity are:

_1 ј 1:196 kg=m3 and c1 ј 344m=s

Using these values, we find the following value for the third term in Eq.

(4-170):

20log10Ѕр1:196Юр344Ю=__ ј 42:3 dB

For frequencies below the plateau (Region II), the transmission loss

may be approximated by the following:

TL ј 20log10рMSЮю20log10р f Ю_47:3 (4-171)

The specific mass MS is in kg/m2 and the frequency f is in Hz. We note from

Eq. (4-171) that a doubling of the frequency (a frequency change of one

octave) results in a change of the transmission loss of:

_TL ј 20 log10р2Ю ј 6:02dB=octave _ 6dB=octave

The approximate method replaces the transition ‘‘peaks-and-valleys’’

between Region II and Region III by a horizontal line or plateau, as shown

in Fig. 4-12. The height of the plateau (TLP) and the width of the plateau

р_fPЮ depend on the material. Some typical values of these quantities are

given in Table 4-1.

For the damping-controlled region, the only term in Eq. (4-166) that

contains the frequency is the following:

33:22 log10р f =fcЮ

118 Chapter 4

FIGURE 4-12 Schematic of the approximate curve for the transmission loss of a

panel.

Copyright © 2003 Marcel Dekker, Inc.

For a frequency ratio of 2 (1 octave), we find the following value for this

term:

33:22 log10р2Ю ј 10:0dB=octave

In Region III, the slope of the transmission loss curve is 10 dB/octave. To be

on the ‘‘safe’’ side or for a conservative estimate of the transmission loss, it is

recommended that the TL curve in Region III be drawn with a slope of the

10 dB/octave for the first 2 octaves above the plateau. The remainder of the

curve should be drawn with a slope of 6 dB/octave (Beranek, 1960).

The application of the approximate method for estimating the transmission

loss curve is illustrated in the following example.

Example 4-6. Estimate the transmission loss curve for a steel plate having

a thickness of 3mm (0.118 in), using the approximate method.

The specific mass for the plate is found as follows:

MS ј _wh ј р7700Юр0:003Ю ј 23:1kg=m2

Let us start by calculating the transmission loss at 125 Hz, using Eq. (4-171):

TL ј 20 log10р23:1Ю ю 20 log10р125Ю _ 47:3

TL ј 27:27 ю 41:94 _ 47:3 ј 21:9 dB (at 125 Hz)

The plateau transmission loss for steel is TLP ј 40 dB, from Table 4-1.

Using Eq. (4-171), we find the frequency at which the plateau begins:

Transmission of Sound 119

TABLE 4-1 Values of the Plateau Height (TLP) and

Plateau Width р_fP) for the Approximate Method of

Calculation of the Transmission Loss for Panels.

Material TLP, dB _fP

ј f2

_ f1, octaves f2=f1

Aluminum 29 3.5 11

Brick 37 2.2 4.5

Concrete 38 2.2 4.5

Glass 27 3.3 10

Lead 56 2.0 4

Masonry block

Cinder 30 2.7 6.5

Dense 32 3.0 8

Plywood 19 2.7 6.5

Sand plaster 30 3.0 8

Steel 40 3.5 11

Source: Watters (1959).

Copyright © 2003 Marcel Dekker, Inc.

20log10р f1Ю ј 40_27:27ю47:3 ј 60:03

f1 ј 1060:03=20 ј 1003Hz (beginning of plateau)

Using the frequency ratio from Table 4-1, we may find the frequency at the

end of the plateau:

f2 ј р f2=f1Ю f1 ј р11Юр1003Ю ј 11,040 Hz

The region for the transmission loss from 63Hz to 1003Hz is Region

II, the mass-controlled region. In this range, the approximate transmission

loss values may be found by adding (or subtracting) 6dB for each octave

above (or below) 125 Hz. For frequencies above 11.04 kHz, the region is

Region III, the damping-controlled region. The transmission loss at

16 kHz, may be found from the following:

TL ј TLP ю33:22log10р f =f2Ю ј 40ю33:22 log10р16,000=11,040Ю

ј 45:4dB

The values for the complete TL curve are shown in Table 4-2, and a plot of

the TL curve is given in Fig. 4-13.

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