Chapter 4. Underpinnings II: making waves


This chapter is the second of the “Underpinnings” series. It deals with sound waves and acoustics, in a similar way that Chapter 2 dealt with mechanical vibration. Key concepts are introduced and illustrated, to prepare the ground for discussing question like how sound is radiated from a vibrating violin body, and what determines how loud the instrument seems to a listener out in the concert hall.

Section 4.1 introduces the basic ideas of sound waves: how sound can be generated by a vibrating body, how the waves then spread out in space, and how waves from different sources can interfere to cause complicated patterns in space.

Section 4.2 deals with acoustic resonators of various kinds. All the musical wind instruments involve resonances of sound inside tubes of various shapes. The frequencies and mode shapes of these resonances determine how each instrument behaves: what notes it can play, how it will “overblow” when played outside the lowest pitch range, and how the tuning of these resonant frequencies is governed by the shape of the tube bore. But tubes are not the only type of acoustic resonator relevant to music. The simplest of all resonators, the Helmholtz resonator, is responsible for the popping noise when a cork is pulled from a bottle, and also governs the sound of a violin or guitar in its lowest register. Finally, rooms have acoustic resonances, and these influence the sound and reverberation behaviour of different kinds of performance space.

Section 4.3 looks at the spatial patterns of sound radiation from different kinds of vibrating structure. Most sound sources, whether loudspeakers, violins or trumpets, tend to radiate sound rather uniformly in all directions at low frequency, but they all become increasingly directional as frequency rises.