Now we have enough background material on vibration and acoustics, we use it in this chapter to start looking at stringed instruments. As explained back in Chapter 2, we want to stick as long as we can with problems that can be tackled using linear theory. That means we won’t be looking yet at what happens when a string is bowed, but we already know enough to look at plucked strings. In any case, the body vibration of all stringed instruments is generally small enough that linear theory works well, so although the chapter is mainly focussed on plucked strings, we can say some useful things already about the body vibration of a violin or cello.
Section 5.1 gives a general overview of how stringed instruments work. The behaviour of an instrument body is most easily captured by measuring a frequency response function. Since the vibrating strings mainly drive the body at the bridge, this also makes the best place to apply forcing in order to do laboratory measurements. Throughout this chapter, examples of the resulting bridge admittance functions from a guitar, a violin and a banjo will be used to highlight the similarities and differences between these instruments, to give a sense of the wide range of stringed instruments.
Section 5.2 will look at the question of what determines how loud a stringed instrument can be. For many instruments, increasing loudness seems to have formed part of the motivation for changing designs over the years: a clear example is the modern piano, compared to its predecessors the harpsichord and fortepiano. It also may have been true of the violin: we will look at a number of design features of the violin, and suggest that these may have been motivated, at least in part, by a desire to make a loud instrument.
Section 5.3 gives a systematic comparison between the guitar, violin and banjo. This section will emphasise the importance of two aspects of design. All these instruments have signature modes at low frequency, which can be manipulated individually by the instrument maker, and these account for some aspects of the sound quality of the instruments. But there is a second, and less obvious aspect of the vibration behaviour which an instrument maker can manipulate. Many instruments, although apparently not the guitar, show formants in their frequency response. These are bands of frequency where all the modes show enhanced amplitude. The violin, cello and banjo all exhibit such formants, and understanding them can explain many things about “tonal adjustment” of instruments.
Section 5.4 explores how we can put together things we have already met, in order to build computer models for plucked-string instruments. These models can be used to synthesise sounds. That in turn can allow “virtual adjustments” to be carried out in the computer, to explore the effect on sound of changes to the body vibration behaviour, or to things the player can control (such as the plucking point along the string).
Finally, section 5.5 gives an extended case study of the banjo. The banjo, with its drum-like stretched membrane instead of a wooden soundboard, represents an extreme case among plucked-string instruments. In this section we explore whether the models we have developed are good enough to capture the key differences, and thus to “sound like a banjo”. An extensive set of virtual adjustments are illustrated.