Torsional Waves in a Bowed String
Bowing a string with a non-zero radius exerts a torque, which excites torsional waves. In general, torsional standing waves have higher fundamental frequencies than do transverse standing waves, and there is generally no harmonic relationship between them. Although torsional waves have little direct acoustic effect, the motion of the bow-string contact depends on the sum of the transverse speed v of the string plus the radius times the angular velocity (r). Consequently, in some bowing regimes, torsional waves could introduce non-periodicity or jitter to the transverse wave. The ear is sensitive to jitter so, while quite small amounts of jitter are important in the sounds of (real) bowed strings, modest amounts of jitter can be perceived as unpleasant or unmusical. It follows that, for a well bowed string, aperiodicities produced in the transverse motion by torsional waves (and other effects) must be small. Is this because the torsional waves are of small amplitude or because of strong coupling between the torsional and transverse waves? We measure the torsional and transverse motion for a string bowed by an experienced player over a range of tunings. The torsional wave spectrum shows a series of harmonics of the translational fundamental, with strong formants near the natural frequencies for torsion. The peaks in r, which occur near the start and end of the 'stick' phase in which the bow and string move together, are only several times smaller than v during this phase. We present sound files of the transverse velocity and the rotational velocity due to the torsional wave. Because the torsional waves occur at exact harmonics of the translational fundamental and because of similarities in the temporal envelope, the sound of the torsional signal alone clearly suggests the sound of a bowed string with the pitch of the translational fundamental. However, the harmonics that fall near the torsional resonances are so strong that they may be heard as distinct notes.
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Document Type: Research Article
Publication date: 01 March 2005
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- Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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