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348 CHAPTER 25 1959 Guide Fig. M____ Approximate Pressure Drop Across Typical Package Units fig. 15 .... Typical Values of Sound Attenuation Through Several Types of Package Units converted to sound pressure levels in the room, because it is 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 angel 6 with respect to an axis per pendicular to its surface is given by the equation*0 L, - PWL + 10 log* + |) + O-5 dbo (24) tchere PWL = sound power level emitted at the duct termination and is the power summation of the attenuated fan noise and the grille noise in dbe (see Example 5). Q -- directivity factor and is a dimensionless function of 8. r -- distance from the duct opening, feet. R = the room constant, square feet. (ft increases with the amount of acoustical absorption in the room and generally depends somewhat upon frequency.) In Fig. 17 four methods are shown for terminating a ven tilating duct in a room. In each of these cases, the noise power radiates into the room. Low-frequency sounds radiate equally in all directions. High-frequency sounds tend to beam in the direction the duct opening is facing. The magnitude of tins hoaming effect is 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. This fact appears in Equation 24, 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 is of importance only when the Ifeteper is nfar 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. 17, approximate values of Q are given in Fig. 18 for 6 -- 0 deg and for 6 = 45 deg. The nhwiaat is the product of frequency times L assuming that the duct is approximately square with an area of L* sq in. If the duct is rectangular, the value of Q should be com puted for L equal to the smaller dimension. The room constant ft is defined by the equation R - &S/(1 - a) (25) s = average sound absorption coefficient (dimensionless) for the room at the mid-frequency of the band of noise being considered. S = 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 Sjai + Sm + a" & + &+ - (26) A. Duet projecting in (be room S. Duct in (he center of and flush with the wa0 C. Duct in the center of one edge 0. Duct in the comer .The listener t is at distance r end engfo 8 front the duet opening. Fig. 17.... Four Typical Means for-Terminating a Ventilating Duct in a Room Sound Control 349 Fig. 18 .... Directivity Factor Q for the Four Duct Configurations of Fig. 17 where Si , St = the areas of each type of absorbing material, at , * etc., -- the absorption coefficients of each type of material at the mid-frequency of the band of noise, being considered. (Valuesof a for manymaterials are published by the Acoustical Materials Association.*') For estimating purposes, approximate values of the room constant R may be obtained from Fig. 19 as a function of room size for five classes of rooms. The value of the second and third terms of Equation 24 (including 0.5 db) is plotted in Fig. 20 with distance r from the source as the abscissa, with the sound pressure level in'decibels, as the ordinate and the room constant ft in sq ft as the param eter. The directivity factor Q is given at the bottom left-hand, side of the graph. The procedure for using the graph is as follows: Determine the room constant ft and the directivity factor Q for the particular direction 8 of interest. Enter Fie. 20 at the bottom at the distance r. Then move diagonally to the left until the value of Q is reached. Then move vertically until the value ft is reached. Then read the relative sound pressure level from the ordinate. An example is shown by. the dotted line in Fig. 20 for r -- 7 ft, Q -- 2, and ft -- 2000 eq ft. The relative sound pressure level is added algebraically to the sound power level to yield the sound pressure level at the distance r and the angle 8 in the room (see Equation 24). It is seen from Fig. 20 that the noise from a.ventilating duct is less at distances far from it than nearby. Moreover, at large distances, the levels produced in the room depend only on the power level of the source and the room constant and not on the directivity factor and the distance r. Example 8: To illustrate the application of the noise criteria and control procedures outlined in this chapter, calculation will be made for the required treatment for the ventilation system supplying the library reading room of Fig. 21. This room has a total volume of 80,000 cu ft and may be considered as an average room for acoustic properties (see Fig. 19). The total air supply to the reading room is 6000 cfm wbicn is equally divided between four 12 x 18 in. supply grilles located along one wall. The supply of outdoor air is from a central fan system which handles a total of 25,000 cfm at 2-in. water static pressure and requires a 15 hp motor. Solution: It is necessary to determine the noise level in the reading room as a result of the ventilating system, both for the position of the nearest listener to a grille, and for a position remote from the suppiy grilles since it is impossible io ieii be forehand which wifi be greater. The required attenuation for acceptable octave band noise levels will then be determined. Analysis of Fan and Duet System The acoustic power level of the fan should be computed from Equation 18 when the specific power level is available. In this example it is assumed that the specific sound power level is not known. Therefore, employ the approximate Equations 19 or 20. From Equation 19: PWLw, ab> *=100+10 log 15 + 10 log 2 - 114.7 dbe or from Equation 20: PWLMm, as; -65 + 10 log 25,000 + 20 log 2 = 115 dbe which agreement is better than the accuracy expected from these equations. Of this total acoustic power generated by the fan the main interest is in the part that reaches the reading room. At each duct branch the power will divide approximately as the ratio of the branch duct area to the total duct area after the branch. Thus at Station B (Fig. 21) the acoustic power delivered to the 18 x 48 in. duct, neglecting any attenuation.in the system, will be PWL>etBC> " PWLldo,, AB) + 10 log (Abrwfc/Afeui) = 115 + 10 log f;--------- ti*_X_48---------- 1 = * |_(24 X 48) + (18 X 48)J At Station C the.power division gives JFWLu^tcn - 111 + 10 log I;--------- 12 * 48---------- 1 B |_(18 X 24) + (12 X 48) = 108 dbe Thus neglecting, at first, the attenuation in the connecting duct These proportions give S " 6^5VUI. The poremeter ii the overage sound-absorption coefficient for (he room. The subjective ratings dead, five, ete* ore fte author's0 and an net necsssarity in standard use. from Reference 20.- Used by permission. Rg. 19 .... Value of the Room Constant R as a Function of Room Volume for Rooms with Proportions of About 1:1.5:2