Small-Sized Rectangular Liquid-Filled Acoustical Tank Excitation: A Modal Approach Including Leakage Through the Walls

Small-sized water-filled tanks with thin (compared to the acoustic wavelength) walls that are surrounded on all sides by air, have been used over the past decades for underwater studies. So far, the analytical modelling of the acoustic field inside such an enclosure considers either the eigenvalue problem with pressure release conditions at the walls or imposes empirical impedance boundary conditions, or even proceeds in analogy with the field within a waveguide. At low frequencies, approximations involving an incompressible fluid or the Laplace equation have been used. Those models have limitations that are always caused by simplification of the boundary conditions. This paper deals with both an analytical formulation expressing the acoustic leakage through the walls (lossy and reacting walls) and modal solutions for the acoustic pressure and acoustic velocity fields when a source emits energy and when it is shut off, providing the transient acoustic response of small tanks quantitatively. Several analytical results are compared with experimental observations.