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874 CHAPTER 40 1951 Guide* Table 5. Attenuation op Elbows* Elbow Size, iN.b 3 to 15 15 to 36 36 plus Attenuation per Elbow, db 3 2 1.5 1 *The attenuation in vaned elbows should be considered the same as in elbows having the same dimen sions as the radius of curvature of the vanes. If the vanes are lined for the purpose of damping any vibra tions in them, one third may be added to the attenuation values listed. bThese attenuation values are based on elbows having a center Une radius 1.5 to 2 times the diameter or width of the duct. The attenuation will b% greater if the ratio is less than 1.5 and less when the ratio is greater than 2. This attenuation is a function of the total grille area (supply and return) and the total sound absorption of the room in sabins. (The sound absorp tion of a room in sabins is the summation of the products of each surface of the room measured in square feet multiplied by its corresponding absorption coefficient. The sabin is a unit of, sound absorption equivalent to theabsorption of one square foot of a totally sound-absorbent.surface). The attenuation is given in Equation 5 as: Attenuation between\ . Total Room Absorption in Sabina . . \ grilles and room ) ~ 10 l0gl" Total Grille Area : Values in Table 7 approximate the attenuation for various rates of air change, and general types of room surfaces. DUCT SOUND ABSORBERS The difference between the required sound attenuation and the natural attenuation must be supplied by the proper sound treatment of the ducts. 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 small 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 of air 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 qf 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 selection and application of the absorptive material, the following points should- be considered: Table 6. Attenuation at Duct Branches ob Outlets Ratio Branch Duct 4- Oun.gr Area or Sum op Branch Areas Supply Duct Area Supply Duct Area 1.00 1.20 1.35 Attenuation per Transformation, db 0,0 0.8 1.3 Sound Control 875 1. For the absorption'of the low frequencies below 500 cycles per second the material should be at least 1 to 2 in. tnick. Thin materials, particularly, when mounted on hard solid surfaces, will absorb the high frequencies and reflect the low. 2. In order to provide as much low frequency noise absorption.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 results 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;5 (2) adequate strength to avoid breakage; (3) fire resistance and compliance with national and local code require ments; (4) low moisture absorption; (5) freedom from attack by bacteria Table 7. Approximate. Attenuation Between Grilles and Room Outlet Velocity FPU - 600 760 1000 1250 Air Change i Min. 5 10 15 20 -5 10 15 20 5 10 15 20 5 10 15 20 Live Room1* 00 cr o.05 db ii 14 16 17 13 16 18 19 14 17 19 20 J.5 18 20 21 Medium Rooms o = 0.15 db 16 19 21 22 18 21 23 24 19 22 24 25 20 , 23 25 26 Dead Room* a *= 0.25 db 18 21 23 24 20 23 25 26 21 24 26 28 22. 25 27 28 Average absorption coefficient for the room. t>Live room-average absorption coefficient 6.05. Bare wood or concrete floor--hard plaster walla and ceiling--minimum of furniture. Medium room-average absorption coefficient 0.15. Carpeted floor, upholstered furniture, hard plaster walls and ceiling or bare room with acoustically treated ceiling, dOead room-average absorption coefficient 0.25. Heavy carpeted floor. Walls and ceiling acoustically treated. - Upholstered furniture. and algae; (6) low surface coefficient of friction; (7) particles should not fray off at the higher design velocities; and (8) freedom from.odor when either dry or wet. With every application, the use of sound absorptive material should be considered in the dual function of insulation and sound absorption. It has been shown theoretically6 that'the reduction (in-decibels per linear foot) of sound transmitted through a duct lined 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 char acteristics of the lining. Experimental evidence likewise indicates that there is no simple formula.involving the.variables which will apply, accu rately to all cases. However, it.may be stated generally, that the attenuaT tion in decibels at a given-frequency is directly proportional to thelength of