A simple model of sound in enclosures with a low frequency harmonic excitation

In the paper the problem of a room with a sound source inside is investigated. The effect, an acoustic field inside is affected by two factors: the shape and the boundaries of the enclosure. In order to evaluate the acoustic field, modal analysis assumption has been applied to describe the room's pressure distribution. Thus, the sum over a set of the room's eigenfunctions and proper time components represents the values of the acoustic field. Eigenfunctions can be obtained by solving the Helmholtz equation for rigid walls. Time components can be determined applying Green’s theorem. This approach allows boundary conditions to be adjoined to time components and thereafter obtain a set of ordinary differential equations for each specified time component correlated with corresponding eigenfunction. Assuming a harmonic excitation, time components are harmonic as well. Therefore, the values of coefficients of each time component (i.e. the modal amplitudes) are required. Directly, one can evaluate the modal amplitudes by solving simple algebraic equations. As a result of this calculation, the finite set of eigenfunctions of an enclosure and modal amplitudes has been obtained. In this case of an additional assumption of high enough boundary impedance, the modal coupling can be neglected and consecutive formula reduction is possible. Under frequency limitation, the modal approach to a room's acoustic field modelling, involves much less computational effort than the alternative, for instance applying Finite Element Method (FEM) or Boundary Element Method (BEM).