Document VJ68okZM1xQmQxbKjmjrEYB9q

358 CHAPTER 25 Table 9 .... Power level Attenuation at Oucf Branches or Outlets Ratio Brandi Duct Area Soar of Brands Area* Aftonuatioo db Ratio Branch Duct Area Sum of Branch Area* Attenuation db 1.0 0.8 0.63 0.5 0.4 0.32 0 0.25 6 1 0.2 7 2 0.18 8 3 0.13 9 4 0.1 10 5 1960 Guide tion. Generally the total area of the branches leaving a junc tion b greater than that of the duct entering a junction; there fore, the area of the branch should not be divided by the area of tile supply duct. In a complicated branched system, errors incurred by such a practice may accumulate to several db. Table 9 gives the db reduction for various ratios of branch duct area to the total branch duct area. 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 elimination of high frequency whistles which are generated by air flow in the ducts. They are also employed in large systemwitb long runs where only a few outlets near the fan require treatment. Frequently outlet cells are the only means of cors recting existing noisy installations, as the duct sections di rectly behind the outlets may be the only sections accessible for treatment. (See Fig. 14.) End Reflection Losses All of the noise power that is produced in a duct by a fan (or by turbulence) does not radiate from the end of a duct into the room. Instead, part of the power is reflected back from tire end toward the fan. The amount of noise power reflected is related to the product of the frequency of the sound and the length of a duct side L, assuming that the duct is square. If the duct b not square, the value of L b taken to be approxi mately equal to \Zh,Lw. The end reflection loss b shown in Fig. 15 for two cases; (1) a duct ending in free space and (2) a duct ending flush with the wall. In Fig. 15 the re-reflection from within the duct is assumed to be negligible. FREOJENCY X LENGTH X IO'S-/T-/tOOO t*. CPS - INCHES Tfe absents equal* fl/JOOO where f i* fee geometric mean frequency of on octave band in cp and l h the duct dimension in inches. Two cater ere shown, with the duct end fenh in the wall and with the duct end projecting into the room. Fig. 15 .... End Reflection losses in Decibels at the Open End of a Square Duct of Area L* DETERMINATION OF ROOM LEVELS In the previous sections on fan and grille noise, sound power levels were given in dbe.referred to 10~u watt. These quan tities as they appear at the duct termination (grille) must be converted to sound pressure leveb in the room, because it b sound pressure to which the ear and the sound level meter respond. The sound pressure level at a distance r from the grille opening and at an angle 0 with respect to an axis per pendicular to its surface b given by the equation0 L,-Lw + 10 .,,*,, ( + |) + "-5 (23) where bw -- sound power level emitted at the duct termination and is the power summation of the attenuated fan noise and the grille noise, decibels. Q -- directivity factor and is a dimensionless function of 9. r = distance from the duct opening, feet. R ** the room constant, square feet. (A increases with the amount of acoustical absorption in the room and generally depends somewhat upon frequency.) Id Fig. 16 four methods are shown for terminating a ven tilating duct in a room. In each of these cases, the noise power Sound Control radiates into the room. Low-frequency sounds radiate equally in all directions. High-frequency sounds tend to beam in the direction the duct opening b facing. The magnitude of thb beaming effect b described mathematically by the directivity factor Q After the sound at any frequency has reflected from a wall, it generally travels around the room many times to produce reverberant sound. Thb fact appears in Equation 23, wherein the first term in the parenthesis described the direct sound (prior to reflection) and the second term described the reverberant sound (the result of many reflections). The directivity factor Q b of importance only when the listener b near the duct termination, i.e., when r is small. At large distances, i.e., when the first term becomes negligible compared to the second, the listener hears only the reverberant sound. For the four duct positions of Fig. 16, approximate values of Q are given in Fig. 17 for 9 =0 deg and for 6 = 45 degThe abscissa b the product of frequency times L assuming that the duct b approximately square with an area of L* sq in. If the duct b rectangular, the value of Q should be com puted for L equal to the smaller dimension. The room constant R b defined by the equation where R - <15/(1 - -s) (24) s = average sound absorption coefficient (dimensionless) for the room at the mid-frequency of the band of noise being considered. 5 -- total area of the boundary surfaces of the room, sq ft. Where a room contains several surfaces, each with different absorption coefficients, the average absorption coefficient may be determined by the equation Sioa + Sta + * *" Si + St+--- _ (25) 359 A. The value of Q ii giveo for 8 " 0; te., drredfy b front of fee dad opening 0. Same at for (A) except fee *ahe of O it given for 5 45 deg. The frequency of f a b cp* and fee dud is auomed to be tqware wife an area L* b square ktdtot. Rg. 17 .... Directivity Factor Q for the Four Duct Configurations of Rg. 16 5, , Sx * the areas of eaeh type of absorbing material, ai , ax etc., *= the absorption coefficients of each type of material at the mid-frequency of the band of noise being considered. (Valuesof a for many materials are published by the Acoustical Materi&b Association.1*) The room constant R may also be determined by calcuia- WOOL OB BOARD Fig; 14 .... Outlet Cells for Pan Outlets or Grilles 1 mm 1 SECTION A-A PLATE ABSORBERS C. Oucf ui flit cantor of one edge D. Dud b fee comer The Bttener l if at distant* r and angle 9 from fee duct opening. Rg. 16 .... Four Typical Means for Terminating a Ventilating Duct in a Room Tfiete proportion* give S = 6.25V***, Tha parameter it A* overage cound-absorptiaa coefficient for fee roam. Tfie (abjective rotiogs dead, live, efo, are fee author**** and are not aecemarify a standard toe. From Reference 22. Uted by penmetion. Rg. 18 .... Value of (he Room Constant R as o Function of Room Volume for Rooms with Proportions of About 1:1.5*2