Janelle Resch , Applied Mathematics, University of Waterloo
A Three-Dimensional Study of Brass Instrument Nonlinear Acoustic Models
Experiments have revealed that loud, high frequency musical notes played in brass instruments produce sounds that have a bright timbre, i.e., quality of sound. This happens when pressure disturbance entering the narrow tubing of the bore are a significant fraction of atmospheric pressure. Such waves are called finite-amplitude sound waves and must be described using nonlinear acoustic theory. Assuming the narrow portion of the tubing is long enough, propagating finite-amplitude waves will distort leading to a transfer of energy to the higher harmonic components of the signal. The corresponding spectral enrichment is often referred to as the 'brassiness' of the instrument.
Although various models have been proposed to describe such sound propagation in brass instruments, there is no complete reliable model that can handle realistic input and output sound measurements. Therefore, there is still much discussion among the acoustic community regarding how models can be simplified without compromising the physics. Until a complete model can be formulated, the acoustic consequences of nonlinear effects in brass instruments cannot be verified or further examined. The purpose of this comprehensive exam presentation is to discuss the goal to establish a qualitatively accurate three-dimensional model that will be able to simulate the evolution of nonlinear wave propagation inside brass instruments.