A literature review:
The acoustics of the violin
Lei Fu April, 2015 Instructor: Prof. Gary P. Scavone
Final project of Seminar MUMT 618 Schulich School of Music, McGill University
1 Introduction
A violin is a wooden box that serves as a mechanical amplifer to convert some of the evergy from vibrating strings into radiated sound. But how does it work? What distinguishes a good one from a bad one?
Figure 1 shows reprensentative frequency responses of two violins. Details will be explained later. The two curves look very similar in general terms, but the market values of these two violins differ by about four orders of magnitude ( a few hundred to a few million dollars). One general reader can not distinguish which of the two is the classic Cremonese Guarneri 'del Gesu'.
Of course not all violins are quite this similar in frequency response. Nevertheless the comparison suggests immediately that the preferences of violinists, and the pricing policy of dealers, may turn on physical differences that are quite subtle. This in turn challenges the physicist: many of the things that matter most to a violinist turn out to involve fine details.
The acoustics of musical instruments is a subject fascinates both scientists and the general public, which taps into contemporary science in several disciplines. Musical instruments raise a variety of problems of classical physics, material science and engineering, and offer applications of many theoretical and experimental techniques, but the distinctive flavour of the subject comes from the fact that the key questions are posed by subjective judgements: what is 'good sound'? This survey of violin physics involve an excursion into perception and psychophysics. the science of giving quantitative form to subjective judgements.
This literature review will follow the main stages of making sound on a violin. First, the string is set into stick-slip frictional oscillation by the bow. This will reveal a problem in nonlinear dynamics. The vibrating string then excites the violin body. The vibration amplitudes are small enough to apply linear theory. Then gives the questions about the vibration modes and sound radiation efficiency and patterns, also the questions how these factors can be controlled by the violin maker by choice of materials and details of construction. Once the sound has been produced, radiated into the air, enters the ears of listeners or players, the question of percepthion and psychophysics immediately come into play: what constitutes 'good' violin sound? But sound is not the whole story, an experienced player may be able to make most violins sound 'good', meanwhile, he or she will find that some instruments make that job easier than others. All the threads come together in the idea of 'playability'. This question involves an interplay between the bowed string and the vibration of the instrument body. One important statement must be made at the outset: these theories involves in this review can be applied not only violin, but all bowed-string instruments.This includes the viola, cello and double bass, viol family, and Chinese erhu.