Cavity Theory - Inviscid Fluid 



The resonators used for the measurements have been 

 discussed in a previous section. For the present develop- 

 ment it will suffice to know that they are made of stainless 

 steel sheets in the shape of a square -cornered tank. In 

 the following computations an orthogonal Cartesian coordi- 

 nate system is employed with the three axes labeled (x 1 , 

 x 3 , x 3 ). The tank is taken in the positive octant with a 

 corner in (0, 0, 0). The three coordinate planes will then 

 coincide with three sides of the tank. The corner diagonally 

 opposite (0, 0, 0) is labeled {\ , l s , l 3 ). 



The wave equation for loss free fluids is given by (15a). 

 A possible solution of this wave equation is given by 



S t = A t cosh (K i x i + ^ i ) sinh (Kjxj + ^j) sinh (KfrXfr + iffr) e (45) 



where the subscripts i, j, h are cyclic. The value of the 

 subscript designates the particular component, in the same 

 sense as the coordinate designation. Each of the quantities 

 As, K^, \|j£ and Q can take on complex values. 



Thus 



(46) 



Q = a.£ - J(d 



etc. The wave equation is satisfied provided that 



3 



Q 2 = o 3 ^K t 3 (47) 



44 



