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

14.13 Gas Jet Noise Control 397Figure 14.17. A cutaway view of an in-line silencer used to reduce aerodynamic noise inpipes. (Reproduced with permission of Fisher Controls International, Inc.).been achieved. A disadvantage of this setup that a back pressure may be induced,which has the effect of impeding flows. The use of diffusers is another approach,in which the flow is diffused into smaller interacting jets.In-line silencers, one of which is shown in Figure 14.17, basically consist offlow through ducts surrounded by absorptive materials separated from the flow byperforated metal sheets. A diffusive inlet may precede the tubular portion of theabsorptive liner. The absorption materials typically consist of fiberglass or metalwool.Finally, in the third approach, that of increasing the transmission loss in pipewalls, two methods can be used. One is to increase the pipe wall thickness and theother is to swath the pipe in acoustical absorption materials. However, no simpleprocedure exists for estimating the transmission loss through pipe walls. Pipingstandards are promulgated by mechanical engineering societies, which specify wallthicknesses for high-pressure, high-velocity flow installations. These thicknessesare specified with the principal aim of preventing ruptures and other failures ofthe pipes that are subject to high pressures. For larger pipes, the standard wallthickness is approximately 3/8 inch. A wall thickness greater than that requiredto meet stress requirements can be selected so that more sound attenuation can beachieved from the presence of the thicker walls, in the range of 2–20 dB additionaltransmission loss.However, a resonance-like condition can occur at the ring frequency, at whichvalue the transmission loss virtually disappears. This is somewhat analogous tothe coincidence frequency effect associated with barriers. This dip in transmissionloss occurs in a pipe when a single wavelength of sound becomes equal to thenominal circumference of the pipe wall, a situation the ring frequency f r can bemathematically expressed asf r =π D pwhere c w is the longitudinal speed of sound in the pipe wall material in m/s; andD p the nominal diameter of the pipe (which can be considered the average of theinside and outside diameters of the pipe) in meters. For example, a 25-cm steelpipe would have a ring frequency of 6598 Hz (since c w = 5182 m/s for steel). Itwould then be expected that the peaks noise levels radiated from this pipe wouldc w