THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

14.14 Mufflers and Silencers 403Let(m − 1 m) 2= Then[ ( ) ]A B 2− BB A A − 1 = 0where from Equation (14.63) = 2(10 TL/10 − 1) 1/2The solution to the quadratic expression inside the bracket isBA = + √ 2 + 42Note the negative root carries no physical significance. For a transmission loss of20, = 19.90 andBA = 19.90 + √ 19.90 2 + 4= 19.952The cross-sectional area A of the inlet pipe and the outlet pipe are each π(60) 2 /4 =2827 mm 2 . The expansion chamber cross-sectional area isB = A × B A= 2827 × 19.95 = 56,399 mm2If the expansion chamber has a cylindrical cross-section, its inside diameter d isfound fromB = π d24Hence√ √4B 4 × 56,399d =π = = 268 mmπArea B represents the minimum cross-sectional area of the expansion chamberthat is required to produce the 20-dB transmission loss.Dissipative Mufflers and SilencersIn the preceding paragraphs, dissipative silencers were discussed. Lining the ductsof HVAC systems with sound absorptive materials generally provides adequatenoise attenuation. However, many industrial applications require a silencer thatcan provide a large amount of noise attenuation or insertion loss in a relativelysmall space. If the noise energy covers a narrow frequency range, reactive silencersconstitute the better solution. Reactive silencers are preferred where the gas flowscontain particles or other components that could contaminate sound absorbing