|Ivars Peterson's MathTrek|
November 26, 2001
This insight comes from a novel mathematical model of sound production in a songbird's vocal organ.
In mathematical terms, "much of the complexity of the song of the canary (Serinus canaria) can be produced from simple time variations in forcing functions," Tim Gardner of Rockefeller University and his collaborators declared in the Nov. 12 Physical Review Letters.
Recent experiments suggest that a canary's syrinx generates sounds via vibrations of its labiaflaps of tissue that sit where a songbird's two bronchial passages meet its windpipe. The labia behave somewhat like a clarinet's reed, oscillating air that rushes past them. Muscles modify the stiffness of the labia and the width of the gap between the folds.
To develop their model of the syrinx, Gardner and his coworkers assumed that the labial folds act like a spring, moving back and forth to alter the size of the air passage. They also assumed that a canary uses just two mechanisms to control its vocalizations: changing the pressure of air from the lungs and modifying the stiffness of the folds. The researchers expressed their model in terms of a differential equation involving damped harmonic oscillators.
Computer simulations showed that by simply varying the air pressure and stiffness, it's possible to recreate much of a canary's rich repertoire. Indeed, some sequences of notes result from little more than a slowly changing phase relationship between oscillations governing air pressure and those controlling labial stiffness. Such behavior is characteristic of a wide variety of coupled oscillators.
"The starts, stops, and pauses between syllables, as well as variation in pitch and timbre, are inherent in the mechanics and can often be expressed through smooth and simple variations in the frequency and relative phase of two driving parameters," the researchers concluded.
In other words, it may not require a lot of brain power on the part of a canary to sing its heart out and attract a mate.
2001. Singing like a canary. Physics News Update. Nov. 14. Available at http://www.aip.org/enews/physnews/2001/split/565-2.html.
Ball, P. 2001. Canaries change their tune. Nature Science Update. Nov. 2. Available at http://www.nature.com/nsu/011108/011108-2.html.
Gardner, T., et al. 2001. Simple motor gestures for birdsongs. Physical Review Letters 87(Nov. 12):208101. Abstract available at http://link.aps.org/abstract/PRL/v87/e208101.
Peterson, I. 2000. Staying in step. MAA Online. Oct. 9.
Withgott, J. 2001. The secret to seducing a canary. Science Now. Nov. 7. See http://sciencenow.sciencemag.org/.
Tim Gardner has a Web page devoted to his model of vocal production in songbirds, available at http://asterion.rockefeller.edu/time/songmodel/index.html.
Information about the symposium "Nature's Music: The Science of Birdsong" is available at http://www.calacademy.org/research/bmammals/baptista_symposium/.
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