Physics Behind Music An Introduction

Sound in one-dimensional systems, pipes, is considered in the context of modeling of the physics of wind instruments. Acoustic impedances are defined, which are used to characterize a system’s response to a force. The convenience of using complex numbers, which have real and imaginary parts, to describe impedance for waves, which have an amplitude and phase, is presented. Reflection and transmission of sound at points where a pipe’s impedance changes are considered, along with how these lead to resonances. The differences between sound propagation in cylindrical, conical, and Bessel horn-shaped pipes are presented. A model pipe with periodic holes is used to model the finger holes found in woodwinds. Such a pipe exhibits a critical frequency below which the impedance is imaginary, resulting in reflection, and above which is real-valued, allowing sound to propagate. An explicit example is shown using simple calculations for a fife, illustrating that the critical frequency becomes important for the upper range of woodwinds. A solution method for more advanced pipe models is presented. One more advanced model is that used for the human vocal tract, which can be modeled with pipes and acts as a time-dependent filter.