Notes on Acoustics

In Chapter 7, flow interaction with a stationary solid body was considered. As far as sound generation is concerned, however, it is the relative motion of the body and the fluid that matters. In devices such as fans, propellers, pumps, and compressors, it is primarily the solid object (blade) that is moving but in the process it induces motion of the fluid also. This interaction often results in significant sound generation which has become an important engineering (environmental) problem and a field of its own with an extensive literature (refer to Appendix A6 for supplementary notes).
As far as sound generation is concerned, there is essentially no difference between a propeller and a fan except for the translational motion of a propeller and related acoustical effects, such as Doppler shift. A fan often operates in a duct and this introduces the problem of coupling with the acoustic modes in the duct but the flow-induced force distributions on the blades on fans and propellers are essentially the same.
The extensive literature on fans includes empirical relations between the sound power and operating parameters, such as flow rate and pressure change across the fan. We shall consider here merely some of the physics involved in sound generation which forms the basis for analytical studies (refer to Appendix A6 for supplementary notes).
The sound generated by a fan contains a periodic as well as a random part. The former is related to the impulses produced by the...