After the Lips: Acoustic Resonances and Radiation

Abstract

In this chapter describes the resonant properties of the air column contained within a brass instrument and the nature of the sound radiated from it. The wave equation is presented. Lumped and distributed resonators are defined; travelling and standing waves are explained, and the relationship between standing waves and acoustic resonances is discussed. Time domain and frequency domain descriptions of acoustic processes are compared, and the related concepts of impulse response and input impedance are introduced. Experimental techniques for measuring the input impedance of a brass instrument are described, and the technique of pulse reflectometry is outlined. The concepts of equivalent cone length and equivalent fundamental pitch are explained. The different types of bore profile which are found in brass instruments (cylindrical, conical and flaring) are reviewed, and the Bessel horn model of a flaring tube is examined. The ‘horn function’ is defined and its properties discussed. The effects of the mouthpiece and flaring bell on intonation and timbre are outlined, and the modifications introduced by opening toneholes, muting and hand stopping on horns are explained. The nature of sound radiation from brass instruments is reviewed. In a Going Further section, mathematical techniques for calculating input impedance are discussed, including transfer matrix methods taking into account the effects of losses and bends.