IV. THEORETICAL DISCUSSION 



The theory of an acoustically resonant chamber is 

 examined here, to develop pertinent relations for the natu- 

 ral frequencies and the particular attenuation factors which 

 are related to the chamber geometry and the contained 

 fluid. For a chamber which contains an ideal, inviscid 

 pure fluid, free of any trapped gas phase, the primary loss 

 of acoustic energy occurs at the walls and free surface by 

 radiation to the environment. The amount of such loss 

 depends upon the configuration of the chamber, the flex- 

 ural properties of the walls, and the acoustic impedance 

 of the environment compared with that of the fluid. 



For a chamber containing a complex fluid mixture 

 like sea water, the additional attenuation which occurs is 

 closely related to the irreversible processes associated 

 with viscosity, heat conduction, and diffusion. In the 

 present analysis only the viscous loss is considered. 

 However, from a phenomenological point of view, all 

 internal losses can be expressed in terms of an equivalent 

 viscosity effect. For sea water the effective viscosity can 

 be several orders of magnitude greater than the actual 

 viscosity. 



The notation in the ensuing discussion is patterned 

 after that of A. Sommerfield. 39 The development starts 

 with the formulation of the wave equation for acoustical 

 disturbances in a viscous fluid. Vortex motion and gravity 

 wave modes are excluded at the outset by adopting the 

 conventional approximations of acoustic theory. 



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