Bird song—A quantitative acoustic model

Abstract

A detailed quantitative physical model is developed which gives a successful quantitative account of the “voiced” song of birds such as ravens. Using available anatomical and physiological data, the model allows calculation of syringeal membrane motion, volume flow waveform, tracheal pressure waveform, radiated acoustic power, and acoustic energy spectrum. Computed results for radiated acoustic power as a function of air-sac pressure and volume flow are in good agreement with measured values in the literature. The radiated power spectrum consists of exactly harmonic components at multiples of the vibration frequency of the syringeal membrane, the inharmonic modes of which are locked into frequency and phase coherence by the non-linearity of the driving force when the membrane strikes against the cartilage of the opposing air-passage wall. The spectral envelope has formant bands at the “closed-pipe” resonance frequencies of the trachea, supplemented by formant bands at slightly below the “open-pipe” resonance frequencies. The strengths and origins of these bands are made clear by the model. The computed power spectrum is in excellent agreement with the Sonagraph spectrum of Corvus mellori when anatomical parameters for this bird are used. While the model is also able to produce inharmonic “screeched” song, attempts to produce a nearly pure-tone output by restricting the motion of the membrane so that it does not strike against the opposing cartilage have proved unsuccessful, the acoustic output being low in intensity and still exhibiting many overtones of the membrane frequency. This failure suggests that “whistled” song is produced in an entirely different manner from voiced song.