Thomas D. Rossing - firstname.lastname@example.org, Uwe J. Hansen
Physics Department, Northern Illinois University
DeKalb, IL 60115
Popular version of paper 3aMU8
Presented Wednesday morning, March 17, 1999
ASA/EAA/DAGA '99 Meeting, Berlin, Germany
It is well known that the tone quality and the playability of a violin are largely determined by the normal modes of vibration of the violin body. The great Italian violin makers were skilled at laboriously tuning these modes of vibration by ear. However, we now have the means for studying the normal modes of vibration with precision in the laboratory, and guiding the construction of violins through the various stages.
Frequency response curves showing the sound radiation from high quality violins are generally characterized by peaks around 275 Hz, 450 Hz and 550 Hz, a prominent broad peak around 2500 Hz, and a collection of less prominent peaks around 1000 Hz. Considerable effort has been made to relate these sound radiation peaks to normal modes of vibration of the violin body.
Two commonly used techniques for studying normal modes in violins are holographic interferometry and experimental modal testing. The results obtained using these two techniques are generally in agreement, although some differences have been reported. This paper reports on a further analysis and comparison of the normal modes obtained by these two methods.
Holographic interferometry offers by far the best spatial resolution of operating deflection shapes (and hence of normal modes), since it looks at almost an infinite number of points. Recording holograms on photographic film tends to be rather time consuming, but electronic TV holography makes it possible to observe structural motion in real time and to record operating deflection shapes and determine the normal modes.
Experimental modal testing was done by tapping the violin at 300 selected points and noting the response with an accelerometer fixed to another point, generally near the bass bridge foot. Determination of modal parameters was done with the Star Modal program on a digital computer. The violin used in these studies, SUS 295 by Carleen Hutchins, has been used in several investigations.
The lowest mode that radiates appreciably is the Ao or f-hole mode. The top plate moves more than the back plate, and a fairly large volume of air is pumped in and out of the f-holes. If the soundpost is removed, the asymmetrical motion of the top plate gives way to a symmetrical motion.
Two beam-like bending modes occur at 175 Hz and 288 Hz. The first, which has two transverse nodes, is often designated as the C1. In the second one, designated as the Bo mode, the free end of the fingerboard moves (with large amplitude) in the same direction as the tailpiece. This mode generally has a frequency close to that of the Ao mode, and some players prefer instruments in which these two modes are closely matched in frequency.
The C2 (corpus) mode, observed at 398 Hz when the violin is mounted on rubber bands and 405 Hz when it is supported by the neck and button, is characterized by torsional or twisting motion of the body. It radiates sound very weakly. The T1 mode at 450 Hz is especially prominent in the top plate.
The most prominent mode in the low-frequency range is the C3 corpus mode. It occurs as a doublet at 530 and 550 Hz due to a torsional resonance of the fingerboard (the fingerboard rotates Other modes in our "top ten" are the C4 at 665 Hz, the A2 at 827 Hz, and the C5 corpus mode at 892 Hz. All of these modes have been observed using both holographic interferometry and experimental modal testing methods. The modal frequencies obtained by the two methods are compared in the table below.
|C-1||B-1|| ||175Hz||175 Hz|
|Bo||fingerboard|| ||not observed||286Hz|
|C2|| || ||398/405||400 Hz|
|A2|| || ||827Hz||not observed|
|C5|| || ||892Hz||897Hz|
|A3|| || ||1087Hz||1080Hz|