Transmission line modelling of acoustical systems with vibrating wallsWilfried Kausel; Daniel W. Zietlow; Thomas R. Moore
The effect of vibrating walls on the radiated sound of wind instruments has often been claimed to be audible by musicians and instrument makers. Many scientists resisted such ideas because comprehensible explanations have been missing. Elliptic oscillation modes which are the most obvious vibration states of tube-like structures could be excluded as a reason for audible timbre differences except in certain cases where structural resonances and air column resonances coincide or where the perfect axial symmetry is broken. Direct radiation cannot explain all the observed effects either, although it is likely that it contributes to a certain extent.
In this paper a theory based on breathing modes is presented which predicts changes in input impedance and transfer function which are qualitatively comparable and in the same order of magnitude as those having been observed in experiments. Sound pressure induced breathing modes are modelled by a local loss of flow into the wall, a loss of energy dissipated by the wall material and additional pressure fluctuations due to the oscillating volume. These influences have been added to a typical transmission line model propagating complex pairs of sound pressure and flow through a sequence of cylindrical elements represented by their transmission matrices.