Jim Woodhouse

Accurate simulation of the motion of a bowed violin string requires a reliable tribological model for rosin, with which the bow-hairs are coated. None of the models proposed in the past have given entirely satisfactory results. An enhanced model is proposed here, which combines influences from the contact temperature and the sliding speed. Transient vibration predictions using this model are compared with earlier experimental measurements in the “Guettler diagram”, demonstrating better agreement than with earlier models.

Violin makers and acousticians have long sought correlations between sound qualities, construction parameters and vibroacoustic measurements. This is challenging for three main reasons: it is difficult to build violins reliably enough to ensure that the change in the sound is only a result of the intended change of construction parameters; no clear link has been found so far between measurements and perceived qualities; and when listening to violins being played, differences tend to be smoothed out by the players who adapt very quickly. Therefore, while we have previously preferred using players in our experiments to maximise ecological validity and account for the complexity of the interaction between the player and the instrument, in this study we test whether other methods that reduce the player's influence, though more artificial, may be useful for exploring the impact of certain construction parameters on the sound. In the context of a set of violins built with controlled thickness variations in their plates, we conducted two listening tests, based on real recordings of a player and a bowing machine, along with synthesised sounds created from an excerpt recorded with piezo sensors by convolution with radiation measurements in an anechoic chamber. The hybrid synthesis was found to be the most effective of the three in highlighting instrument differences, capturing properties perceived in the actual instruments, and correlating with radiation measurements.

A number of rectified nylon harp strings, having the same nominal diameter, were subjected to different sequences of applied stress steps. Each string was tested continuously for several weeks to allow sufficient time for the stretching responses to be clearly observed. Qualitatively, much of the observed behaviour was in accordance with established expectations. However, the quantitative data gathered here are believed to be novel, and revealed some surprises. The strings displayed a combination of elastic stretching, fully recoverable viscoelastic stretching, and apparently non-recoverable plastic stretching. The elastic and recoverable viscoelastic stretching behaviour was quite straightforward, but the plastic creep behaviour was more complicated, with a number of the strings displaying an unanticipated phenomenon. When the applied stress was left unchanged, or was stepped down and back up again, it was noticed that, in some cases, the extent of the subsequent plastic stretching, when the applied stress was next increased beyond its previous maximum, was significantly less than might have been expected. The tests revealed that this apparent plastic creep ‘constraint’ mechanism seemed to depend primarily on the length of time between successive overall rises in the applied stress, with a threshold somewhere in the range of 30–40 days. It is suggested that this phenomenon may be due to a gradual increase in the polymer crystallinity during this rest period. Two of the strings, which were tested over a wider range of applied stress levels, revealed another aspect of the creep behaviour. There appeared to be an initial ‘straightening’ phase during which the plastic stretching rose with the applied stress in a diminishing manner to reach a stretching limit. As the applied stress was increased, this initial straightening was overtaken by an unlimited main stretching phase, which rose slowly at first before approaching a linear increase with the applied stress.

This chapter provides an introduction to the scientific study of bowed-string instruments, concentrating on aspects that are of direct relevance to performers. Points of similarity and contrast with plucked-string instruments are discussed. A key similarity is in the question of what governs the loudness of any acoustical string instrument. The key contrast is in the manner in which a bowed string vibrates: this is governed by more complicated physics than the vibration of a plucked string, and this has important implications for “playability” and other aspects of performance such as the wolf note. Because of the nature of the subject matter, the organization of the chapter does not separate the background science from the implications for performance: as each successive topic is discussed, implications for performers and teachers are discussed in an integrated way.

Measurements of vibrational response of an American 5-string banjo and of the sounds of played notes on the instrument are presented, and contrasted with corresponding results for a steel-string guitar. A synthesis model, fine-tuned using information from the measurements, has been used to investigate what acoustical features are necessary to produce recognisable banjo-like sound, and to explore the perceptual salience of a wide range of design modifications. Recognisable banjo sound seems to depend on the pattern of decay rates of “string modes”, the loudness magnitude and profile, and a transient contribution to each played note from the “body modes”. A formant-like feature, peaking around 500–800 Hz on the banjo tested, is found to play a key role. At higher frequencies the dynamic behaviour of the bridge produces additional formant-like features, reminiscent of the “bridge hill” of the violin, and these also produce clear perceptual effects.

A previous paper [Woodhouse et al., Acta Acustica 5, 15 (2021) https://doi.org/10.1051/aacus/2021009] showed acoustical measurements of an American 5-string banjo alongside similar measurements on a guitar, revealing a strong contrast in bridge admittance. Theoretical and numerical modelling is now presented to probe the physics behind this contrast. Without the bridge and strings, the banjo membrane has a rising trend of admittance associated with its modal density, and it has a distinctive pattern of sound radiation because an ideal membrane has no critical frequency. When the bridge and strings are added to the banjo, three formants shape the amplitude envelope of the admittance. One is associated with local effects of mass and stiffness near the bridge, and is sensitive to bridge mass and the break angle of the strings over the bridge. The other two formants are associated with dynamical behaviour of the bridge, analogous to the “bridge hill” in the violin.

The long-term mechanical behaviour of a number of fluorocarbon and gut harp strings has been examined, and the results compared with a previous study of rectified nylon strings. The stretching behaviour of the three materials was studied via different measures of the Young’s modulus; with test time scales on the order of weeks, minutes, and milliseconds. The strings were subjected to cyclic variations in temperature, enabling various aspects of their thermal behaviour to be investigated. The effects of humidity changes on gut strings were also examined. The behaviour of the fluorocarbon strings was found to be similar in many ways to that of the nylon strings, despite their different chemical formulation and significantly higher density. In particular, the faster measures of Young’s modulus were found to show an almost identical strong variation with the applied stress; while the thermal behaviour of both materials was largely determined by the balance between opposing effects associated with thermal contraction and thermal variations in the Young’s modulus. The gut strings showed some similarities of behaviour to the synthetic materials, but also major differences. All three measures of the Young’s modulus remained constant as the applied stress was increased. The gut strings were far more sensitive to changes in humidity than the synthetic materials, although some of the results, especially the thermal tuning sensitivity of the strings when held at constant length, displayed remarkable stability under changing humidity. The observed behaviour suggests very strongly that there is significant coupling between humidity-related changes in the linear density of a gut string and complementary changes in its tension.