Thomas D. Rossing - Rossing@physics.niu.edu
Mark Roberts, Eric Bynum, and Laura Nickerson
Physics Department
Northern Illinois University
DeKalb, IL 60115
815/753-6493
Popular version of paper 3aMU2
Presented Wednesday morning, June 24, 1998
ICA/ASA '98, Seattle, WA
When a violin or a cello string is bowed, the body of the instrument vibrates in a rather complicated way. Body vibrations largely determine the sound of the instrument, because the string itself radiates only a minuscule amount of sound. Therefore, to determine the quality of the sound, and the quality of the instrument itself, it is necessary to analyze the vibrations of the body.
The vibration of the entire instrument, including the body and strings, can be described in terms of normal modes of vibration. To determine these normal modes takes considerable care, however, since the vibrations are profoundly influenced by the way the instrument is excited, the way it is supported, and the way its motion is sensed. (For hundreds of years, violin makers have held instruments by the neck, tapped its body, and listened, for example.) Modern instrumentation allows modern researchers and violin makers to determine the normal modes of vibration with great accuracy. Some violin makers use these techniques to make "tonal copies" of treasured old Italian violins, for example.
Holographic interferometry offers by far the best spatial resolution of normal modes of vibration. Using holographic techniques, "contour maps" of the vibrating instrument can be recorded on photographic film as it vibrates in each of its normal modes. Optical holography is precise but time-consuming, and we now use electronic or TV holography to make these contour maps on a TV screen by means of a computer.
Another useful method for determining normal modes of vibration is to tap it in carefully selected locations with a hammer that is specially instrumented to measure the exact tapping force while the body motion is observed with a tiny accelerometer. A computer sorts through the electrical signals generated by the accelerometer and the force gauge on the hammer, using them to determine the normal modes of vibration. Careful comparison of the modes determined by these two different techniques further increases the accuracy and reliability of the measurements.
Complicated structures such as violins and cellos have hundreds of normal modes, but the ones of greatest interest are those that radiate the most sound or that contribute dramatically to the "feel" of the instrument. Both the violin and cello have a strong "breathing" mode, characterized by air flow in and out of the f-holes; it occurs around 100 Hz in cellos, and around 280 Hz in violins. Other important modes are the so-called T1 mode, characterized by a motion of the top plot pivoting on the sound post (around 140 Hz in the cello, 450 Hz in the violin) and the C3 mode which involves considerable motion of both the top and back (180 Hz in the cello, 450 Hz in the violin). Ratios between corresponding frequencies in the cello and violin are typically in the range of 0.3 to 0.4, although their body lengths and widths are more nearly in the ratio of 0.5.