# SOUND REDUCTION IN AIR-HANDLING SYSTEMS Basic Concepts

The subject of acoustics involving sound transmission is of prime impor­tance in industrial ventilation. Correct system design will ensure that the de­signer provides a system that will not give rise to complaints regarding noise levels.

Consider the continuous oscillations of a tuning fork. These oscillations generate successive compressions and rarefactions outward through the air. The human ears, when receiving these pressure variations, transfer them to the brain, where they are interpreted as sound. Therefore, the phenomenon of sound is a pressure variation in a fixed point in the air or in another elastic medium, such as water, gas, or solid.

This pressure variation can be considered as the transfer of a pressure wave in space. In the same way, when a stone is thrown into a lake, the ripples generated move radially from the point of entry of the stone. But this observa­tion is only apparent, because a floating buoy will stay in the same horizontal position. It does not move radially in the space; the perturbation, however, moves.

These phenomena can be considered as work processes. In fact, pressure is the force per surface unit, and work is the product of force and displace­ment of the force. Work is equivalent to energy, and it cannot be created or destroyed.

Therefore, when a noise is to be reduced, the sound energy must be con verted into another form of energy, such as kinetic energy of a medium or heat.

This issue must be understood in order to reduce noise problems.

In a fixed point in space, the magnitude of pressure will change according to the nature of the sound source.

A tuning fork gives a pure tone, that is, a pressure variation represented by a sinusoid curve (Fig. 9.60).

The sound speed c, m s_1, is the velocity of propagation of the pressure variations. This depends on the physical properties of the medium and in­creases with the density of the medium. In air, for example, it is 344 m s1, while in water, 1410 m s’1 and in concrete, 3000 m s-1. The elapsed time be­tween successive compressions is called the period time T.

Frequency is the repetition rate of pressure variations, and it is described by the reciprocal of the period time T:

 (9.159)

F= jIHz. l.

Its unit is hertz (s_1), corresponding one cycle per second. Pure tone consists of one frequency, but normally all sounds are a mixture of many frequencies. In the audio range, frequency varies normally from 20 Hz to 16 000 Hz. The size of the audio range depends on the sensitivity of the listener’s ears. When the frequency is below 20 Hz, it is called infrasound, while for frequencies over 16000 Hz, it is called ultrasound.

 (9.160)

W’avelength A is defined as the distance between successive compressions or rarefactions and is

A = j [m].

A sound can be periodic, hence steady, or random (Fig. 9.61 ).

 I P(A)

\ Јrn, s = VVr2

/ j Pave rage

./

T

PL R rms

 F >’

 T (a)

 T

 IN I/-) ~0 ~0 C C C Ј -D -D .O

(d)

FIGURE 9.61 Different kinds of sounds: (a) pure tone, (fa) periodic sound, (c) random noise, (d) effects overlapping principle.

A sound is generally not a pure tone, as the latter is only emitted from particular sources. It can be demonstrated that a sound can be divided into different pure tones (superposition method). The waves at different frequen­cies give the spectrum of the sound, which also describes its energy distribu­tion. In frequency analysis, the spectrum is divided into octave bands. An octave band is defined as the frequency range with its upper boundary twice the frequency of its lower boundary. For every octave band, a central band fre­quency ( Fc) is defined as follows:

(9.161)

Where Ft and Fu are the lower and upper boundary frequencies, respectively. In ventilation technology the normally interesting frequency area is 63-8000 Hz. In this area we have eight octave bands. Sometimes also the frequency band

31.5 Hz is under consideration.

For example, the lowest octave band corresponds to a frequency range be­tween 22 and 45 Hz. Its central value is

Fc JZ2~4S 31.5 Hz.

In l’able 9.13 the standardized octave band series are shown.

Octave bands are divided, on a logarithmic frequency scale, into three equally wide one-third octave bands. This is done often when more exact data of sound spectra are needed. Table 9.14 shows the standardized one-third oc­tave band series.

The sound generation mechanism involves the transmission of acoustic energy in space. Therefore, the power of a sound source is the energy emitted in time units and is measured in W.

TABLE 9.13 Standardized Octave Band Series (ISO 226)

 Octave 1 Octave 2 Octave 3 Lower 22 Central 31.5 Octave 4 Upper 45 Lower 45 Central 63 Octave 5 Upper 90 Lower 90 Central 125 Octave 6 Upper 180 Lower ISO Central 250 Octave 7 Upper 355 Lower 355 Central 500 Octave 8 Upper 710 Lower 710 Central 1000 Octave 9 Upper 1400 Lower 1400 Central 2000 Octave 10 Upper 2800 Lower 2800 Central 4000 Upper 5600 Lower 5600 Central 8000 Upper 11 200

Lower Central Upper

11 200 16 000 22 400

CHAPTER 9 AIR-HANDUNG PROCESSES TABLE 9.14 Standardized One-Third Octave Band Series (ISO 226)

 First Third of Octave 1 Second Third of Octave 1 Third Third of Octave 1 Lower 2? Central Upper 25 28 Lower 28 Central 31.5 Upper 35.5 Lower 35,5 Central Upper 40 45 First Third of Octave 2 Second Third of Octave 2 Third Third of Octave 2 Lower 45 Central Upper 50 56 Lower 56 Central 63 Upper 71 Lower 71 Central Upper 80 90 First Third of Octave 3 Second Third of Octave 3 Third Third of Octave 3 Lower 90 Central Upper 100 112 Lower 112 Central 125 Upper 140 Lower 140 Central Upper 160 iso First Third of Octave 4 Second Third of Octave 4 Third Third of Octave 4 Lower USD Central Upper 200 224 Lower 224 Central 250 Upper 280 Lower 280 Central Upper 315 35 5 First Third of Octave S Second Third of Octave S Third Third of Octave S Lower 355 Central Upper 400 450 Lower 450 Central 500 Upper 560 Lower 560 Central Upper 630 710 First Third of Octave 6 Second Third of Octave 6 Third Third of Octave 6 Lower 710 Central Upper 800 900 Lower 900 Central 1000 Upper 1120 Lower 1120 Central Upper 1250 1400 First Third of Octave 7 Second Third of Octave 7 Third Third of Octave 7 Lower 1400 Central Upper 1600 1800 Lower 1800 Central 2000 Upper 2240 Lower 2240 Central Upper 2500 2800 First Third of Octave 8 Second Third of Octave 8 Third Third of Octave 8 Lower 2800 Central Upper 3150 3550 Lower 3550 Central 4000 Upper 4500 Lower 4500 Central Upper 5000 5600 First Third of Octave 9 Second Third of Octave 9 Third Third of Octave 9 Lower 5600 Central Upper 6300 7100 Lower 7100 Central 8000 Upper 9000 Lower 9000 Central Upper 10 000 11200 First Third of Octave 10 Second Third of Octave 10 Third Third of Octave 10 Lower Central Upper 11 200 12 500 14 000 Lower 14 000 Central 16 000 Upper 18 000 Lower 18 000 Central Upper 20 000 22 400

On the basis of a sound wave equation, it is shown that the power ol a noise source is equal to

 ( 9.1621

Pc

Where

A is the orthogonal surface to the waves path (measured in m-) P is the density of the medium (kg ni"3)

<• is the sound speed in the medium (m s_I) Ft is the pressure amplitude of the sound (Pa)

If the noise source is a point source and the emission propagation is spherical (Fig. 9.62), then the source power can be written as

 (9.163)

I — 4 7Rr2

Pc

Therefore, with constant (steady-state) sound power, P decreases when R increases, not linearly, but quadratically.

Perception of sound by the human ear is not related to sound power but to sound intensity, defined as

(9.164)

That is, sound power for surface unit Wm~-. As the listener moves away from the sound-generating source, A increases and intensity decreases.

The lowest intensity audible by human ear is 10~12 Wm-3, while the max­imum value is 1 Wm~-. Therefore the scale range is very large and inconve­nient for technical calculations: it is more convenient to make use of a

 0=1
 i/
 Q = 2

 -isLd.

 (a)

Tb)

 0 = 8

 8 = 4

W

 («•)

Id)

Logarithmic unit, defined as funcdon of the ratio between the sound intensity and the intensity l0 of the hearing threshold:

 T I
 ,p = 10 log
 10 log
 Po.
 (.9.165)

/0 is fixed equal to 10“12 W nr2, and its corresponding pressure is 2 x 10’5 Pa. The new unit is decibel (symbol dB) and Lp is called the sound pressure level. In a similar way, we can define sound power level Lw/ as

 N
 N_ N0
 = 10 log
 12
 10
 Lw = 10 log
 (9.166)

This unit is also a decibel. Note that the decibel is a pure number.

When two sound sources are added, it must be remembered that the deci­bel is a logarithmic unit. Therefore, they cannot be added arithmetically but must be combined as follows:

Step 1. They must be divided by 10.

Step 2. Then the antilogarithm must be calculated.

Step 3. The obtained values are added.

Step 4. The logarithm is calculated and then multiplied by 10 to obtain the combined value.

In general, when two or more sounds reach the listener at the same time, a composed sound will be received, with pressure level L equal to

R r*nL,/l0 „„L,/10 .„Ј,/10 _L„/10,

 (.9,16′

L = 10 log[10 +10- +10 + ••• + 10 ]

Where Lj, L2, L},. . . , Ln are the pressure levels of each source. This formula can also be applied for the composition of the pressure levels at different fre­quencies for the same source.

As an alternative to the above Eq. (9.167), it is easier to add to the higher pressure level a term depending on the difference between the considered lev­els, as shown in Table 9.15.

Two noise sources produce 69.2 and 69 dB pressure levels respectively (Table 9.16) at the same space point. The composed sound at said point will have a total pressure level of 72.1 dB, calculated by adding 2.9 dB to 69,2 dB. In a similar way, at 250 hertz, for example, if each of the sources has a pres­sure level of 60 dB, the total level will be 63 dB (sum of 3 dB and 60 dB).

Difference in dB between two pressure levels

Term to add at the 3 higher level

TABLE 9.16 Composition Of Pressure Levels

 Frequency (Hz) 63 125 250 500 1000 2000 4000 8000 Total Level (dB) 60 62 60 65 60 55 54 48 69.2 Lj (dB) 60 62 60 60 60 55 60 60 69.0 I. total (dB) 63 65 63 66.2 63 58 61 60 72.1

To determine the levels of each frequency for the same source, it is advis­able to proceed considering two levels at a time, starting from the lower levels. In this way, for example, by determining the pressure levels of source 1, the to­tal level is 69.2 dB. Thus, the same result can be achieved by applying Eq. (9.138) or the method revealed in Table 9.15.

Example 2

In a work area, a machine has a power level of 50 dB. A second machine in the same room has a power level of 50 dB. Determine the final combined power level.

The total power level will be 53 dB.

In work areas, the noise is usually generated by different sources, such as air-handling units, refrigerating plants, etc. (especially extract and sup­ply air fans).

It is important to quantify the sound pressure levels in dB generated by each source and for each frequency (31.5-8000 Hz) in order to establish which noise will be masked or prevalent. It must be noted that when the pres­sure levels of two noises differ by more than 10 dB, the resulting level is equal to that of the higher-level source; in other words, the noise at the higher level masks the noise at the lower level, which will not be perceptible to the listener (or the phonometer). In this case it is useless to reduce the latter noise, as the composed noise will remain the same, being influenced by the higher-level noise only.

It is important to remember that the response by a human ear to sound is different from that detected by scientific instruments, as the human ear is more sensitive in the middle frequency range than at the low and high fre­quencies at the same level.

Therefore, acoustic science has introduced different kinds of weight­ing curves in order to correlate as accurately as possible the sound level with the level really perceived by a generic listener. In practice, A-weight — ing correction is used. It consists of a series of coefficients, shown in Ta­ble 9.17. These are added to sound levels expressed in dB for each frequency.

The results are expressed in dB(A). The suffix (A) means that the new level has been calculated referring to the A-weighting correction. Phonometers have a special filter called the A-filter, which automatically introduces this cor­rection at measured values, allowing the reading of pressure level in dB(A) di­rectly.

 Frequency (Hz) 25 31.5 40 50 63 80 100 125 160 A-wt. correction (dB) -44.7 -39.4 -34.6 -30.2 -26.2 -22.5 -19.1 -16.1 -[.3.4 Frequency (Hz) 200 250 315 400 500 630 800 1000 1250 A-wt. correction (dB) -10.9 -8.6 -6.6 -4.8 -3.2 -1.9 -0.8 0 0.6 Frequency (Hz) 1600 2000 2500 3150 4000 5000 6300 8000 10000 A-wt. correction (dB) 1 1.2 1.3 1.2 1 0.5 -0.1 -1.1 -2.5

Example 3

Referring to example 1, the pressure level of the A-weighted combined noise is 68.8 dB(A). Therefore, the acoustic perception of a listener will be 68.8 dB(A), not 72.1 dB (Table 9.18).