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346 CHAPTER 25 1959 Guide Table 7.... Attenuation Data for Typical 1-in. and J^-m. Thick Duct lining Board I-fodt Thkkmtt y^4adt Thkknea Cycks Pur Absorp Second tion Coeffioent a a1,4 Attenuation db Absorp tion Co efficient a ai. Afteauatioo db 128 0.12 0.051 0M`j 0.09 0.034 043 `j 256 P 0.38 0.26 3.21^ 0.25 0.15 1.9! 512 0.70 0.60 0.40 0.28 3.5 1024 0.80 0.73 9.2 lPj 0.72 0.63 7.9! ^ 2048 0.79 0.72 9.1.5 0.78 0.71 8.9! ^ This formula was empirically developed for a set of duct ranging from 9 x 9 in. to 18 x 18 in.; for crocs-sectional dimension ratios of 1:1 to 2:1; for frequencies between 256 nH 2048 cycles; and for absorption coefficients between 0.20 Mwi 030. The duct lining material used was 1-in. rock wool ahp*t. The absorption coefficients of a material of this type in one-half and one-inch thickness are listed in Table 7. It is nion possible to calculate the absorption by a very com plicated rna.thpmnt.ical theory.17* u Such calculations are in substantial agreement with Equation 22. This equation may be in error when applied to other types of duct lining and to duct sizes and shapes greater than those specified. With every application, the use of sound absorptive mate rial should be considered in the dual function of insulation and sound absorption. It haa been shown theoretically that the reduction (in decibels per linear foot) of sound transmitted along a duct linnrf with sound absorbing material is related in a rather complicated manner to the size and shape of the duct, to the frequency of the sound, and to the sound absorbing characteristics of the lining. Experimental evidence likewise indicates that there is no ample formula involving the variables which will apply accurately to all cases. However, it may be stated generally that the attenuation in decibels at a given frequency is directly proportional to the length of lined duct. It decreases as the cross-sectional area increases, and increases as the aspect ratio is increased. Rectangular Cells (Plate or Cell Absorbers) If the available length of duct between the main duct (or the fan) to the grille is shorter than the length of lining indi cated as necessary by Equation 22, the duct may be sub divided into smaller ducts as shown in Fig. 12, or it can also be even more subdivided by an egg-crate construction. In such a construction in which all the subdivided ducts are the samp, size, sound will be equally absorbed down each channel. It is, therefore, only necessary to calculate the sound attenuation of an individual channel. For this. Equation 22 is ade quate, Assuming that tiie thickness of the material is halved if it forms a common splitter between two cells. When the number of splitter plates or cell partitions is large, the percentage free area of the gross duct size may be mate rially reduced. This leads to a further sound attenuation. Values of the attenuation possible, due to this cause, are given in Table 8. Table 8 .... End Reflection of Plate or Cell Absorbers Percentage Free Area of Absofbet so 40 30 25 20 Attenuation db 1 2 456 Plenum Absorption In systems where individual ducts are directed to a number of rooms, and sound treatment is required in every duct, a sound absorption plenum on the fan discharge as shown in Fig. 13 will often prove the most economical arrangement. Based on both experiment and ray acoustics theory, the following approximate expression has been derived for acoustic plenum attenuation.17 db (attenuation) -- 10 log --------------------------0, cos 1 -- a 2nP~+ .. U43J B. Lined dud C. SpCHor pfcrfe type abrorbw O. Cefl-fype absorber Thu opun orua it the tame far uadi caw drown if T in. flock afawptfon noterloJ it assumed. Fig. 12____Acoustic Treatment of Ducts where a = absorption coefficient of the lining (dimensionless). S. -- plenum exit area, square feet. Sm = plenum wall area, square feet. d = distance between entrance and exit, feet. 9 = the angle of incidence at the exit, i.e., the angle which the direction d makes with the normal to the exit opening. For frequencies sufficiently high so that the dimensions of the plenum exceed about one wavelength, Equation 23 will predict the sound attenuation within a few decibels. At low frequencies, somewhat more attenuation is realized than will be computed by Equation 23, due to the existence of a reso nant muffler action in the duct-plenum system. Outlet Sound Absorbers Outlet sound absorbers are rectangular or plate cells in stalled directly behind an outlet or they may be the lining of a pan or plaque outlet. They are particularly effective in the i I i ^ 4 ; Sound Control TAKEorr 347 elimination of high frequency whistles which are generated by air flow in the ducts. They are also employed in large systems with long runs where only a few outlets near the fan require treatment. Frequently outlet cells are the only means of cor recting existing noisy installations, as the duct sections di rectly behind the outlets may be the only sections accessible for treatment. (See Fig. 14.) Package Units Package units for attenuating sound in ducts are coming more and more into common use. These units have the ad vantage of providing, in a short length, a known amount of noise reduction with a minimum opportunity for errors in installation and for erosion of materials. The cost of inspec tion of the completed job is eliminated the outside di mensions of the duct can be reduced as compared to a duct. These units are available in sizes to fit 6 x 12 in. ducts up to 80 x 84 in. ducts. Charts are supplied by the manufacturers giving the attenuations and pressure drops foT different types of units. In Figs. 15 and 16, the noise reductions and static pressure drops for several types of package units are shown. Manu facturers' literature should be consulted for exact values. Selection of the Absorptive Material When a sound wave impinges on the surface of a porous material, a vibrating motion is set up within the Email pores of the material by the alternating sound waves. As the ratio of the cross-sectional area of the pores to their interior surface is small, the resistance to the movement ofair in the pores is large. This viscous resistance within the pores of the material converts a portion of the sound energy into heat. The decimal fraction representing the absorbed portion of the incident sound wave is called the absorption coefficient. Considerable absorption may also result, particularly in the low-frequency range, from the flexural vibrations of the duct. In the selec tion and application of the absorptive material, the following points should be considered: 1. For the absorption of the low-frequencies below 500 cps the material should be 2* to 12-in. thick. Thin materials, par ticularly when mounted on hard solid surfaces, will absorb only the high frequencies. 2. In order to provide as much low-frequency noise absorp tion as possible by means of flexural vibration, it is desirable to fasten the absorptive panels discontinuously. This result may be attained to some extent by spot cementing, but better re sults are obtained when it is possible to fasten the absorptive panels to furring strips, leaving an air space behind. However, the exact resonance characteristics of the panels, and thus their absorption, are so unpredictable that flexural vibration cannot be relied upon for a specific value of attenuation. Requirements for a good sound absorption material are: (1) high absorption at low frequencies,4* (2) adequate strength to avoid breaJcage; (3) fire resistance and compliance with national and local code requirements; (4) low moisture ab sorption; (5) freedom from attack by bacteria and algae; (6) low surface coefficient of friction; (7) particles should not fray off at tiie higher design velocities; and (8) freedom from odor when either dry or wet. DETERMINATION OF ROOM LEVELS In tiie previous sections on fan and grille noise, sound power levels were given in dbe referred to 10-" watt. These quan tities as they appear at the duct termination (grille) must be MUSLIN COVERED ROCK WOOL OR BOARD 8 ttoucrLi INED WITH L^assori j 8MATER SOUND ABSORPTION BOARD I i IB } Fig. 14 .... Outlet Cells for Pan Outlets or Grilles ' SECTION A-A * PLATE ABSORBERS J