Computer modelling of coupled spaces: variations of eigenmodes frequency due to a change in coupling area

Acoustically coupled spaces have recently been drawing
more and more attention in the architectural acoustics community, thus a
determination of shapes and frequencies of eigenmodes in these room systems from
computer-based models has become increasingly significant. In this
investigation, an eigenvalue problem was solved numerically for a simple room
system consisting of two connected rectangular spaces. In a numerical procedure,
the forced oscillator method with a finite difference algorithm was applied. In
order to determine the influence of irregularity of system shape on eigenmodes
frequency, a modal behaviour in the coupled spaces was studied for several sizes
of coupling area. Calculation results have shown that with the exception of a
fundamental mode, the changes in resonant frequencies were relatively small.
However, an increase in a system irregularity led to a coincidence of
frequencies of neighbouring modes and variations in a sequence of modes on a
frequency axis, which both contributed to a degeneration of eigenmodes.