In regard to boundary conditions, two simple cases 

 will be considered first. These correspond to total reflec- 

 tion of energy at the boundaries of the tank. A more gen- 

 eral boundary condition is considered later. 



Rectangular Cavity with Hard Walls 



If all of the walls are considered absolutely rigid, as 

 a limiting case, then (with I = 1, 2, 3) 



S. = at x. = 0, I. (48) 



where I , ^ s ,l 3 denote the dimensions of the cavity. 

 Relations (45) will satisfy the six boundary conditions 

 stipulated by (48) provided that 



cosh \|j£ = 



and (49) 



cosh (K i l i + ^ i ) = 



The possible roots of these relations yield 



H = ± j(j + m i n ) 



and (50) 



K i l i = ± J n t rr 



45 



