Gabriel Weinreich - weinreich@miphys.physics.lsa.umich.edu
Department of Physics
University of Michigan
Ann Arbor, MI 48109-1120
Popular version of paper 3aAA5
Presented Wednesday morning, 15 May 1996
Acoustical Society of America, Indianapolis, Indiana
Embargoed until 15 May 1996
If you have ever wondered, while listening to a violin concerto, how it is that the sound of a single solo instrument can stand out so clearly from its orchestral accompaniment (which generally includes two dozen or so other violins playing at comparable levels of loudness), this paper may provide some of the answers.
As everyone knows, sound from a violin is radiated into the surrounding air primarily by the flexural vibrations of its wooden shell. Except at rather low frequencies, these vibrations form a complex pattern, with various sections of the wood moving in opposition to each other; what's more, this pattern is itself very sensitive to frequency, often changing radically when the pitch varies by as little as a semitone. Thus the wood acts as an intricate "antenna array."
As a consequence, the sound itself acquires a complicated directional dependence, as though the violin consisted of a large number of sharp lighthouse beacons whose directions shift around rapidly from one note to the next. A listener in an enclosed concert space, who receives not only the direct sound but also its reflections from the various walls, will then experience the illusion that each of the violin's notes is coming from a different direction. We call this effect "directional tone color." It endows the sound of a solo violin with a special flashing brilliance which is, incidentally, enhanced by the use of vibrato, because a fluctuating frequency causes the directions of all the "beacons" to waver in synchronism.
Since the exact details of these directional patterns vary from instrument to instrument, they tend to become averaged out when a whole violin section is playing together. We suggest that this is the main reason why a solo violin stands out so clearly. This suggestions is further supported by the well- known fact that it is much easier to distinguish the soloist in a concert performance than in recorded music, where directional tone color is lost through the totally different radiation properties of a loudspeaker.
In our presentation, we show computer-acquired data from a number of different violins to support the statement that, above a frequency of approximately 1 kHz, the sound radiation pattern does, indeed, become very direction-dependent, to the point where the power radiated in one direction relative to that radiated in another direction may vary from +25 dB to -25 dB. Above approximately 2 kHz, the frequency difference between such maxima and minima is one semitone or less. These numbers are explained by considering the vibration of shells and the radiation of sound theoretically.
Finally, we present data to indicate that this rapid variation of sound radiation as a function of angle and of frequency tends to abate above about 4 kHz. We suggest that this change may be due to the rising importance of vibration modes of the air enclosed inside the violin shell, and support this suggestion with a tentative theoretical discussion.