The Scaling of Song Frequency in Cicadas

In male cicadas, sound is generated by a pair of tymbals on the abdomen (Pringle, 1954). The tymbals buckle inwards causing pressure changes in the abdominal cavity, from which sound is radiated through the tympana (Young, 1990). A recent model of sound production in cicadas suggests that the abdominal cavity and tympana act as the components of a Helmholtz resonator that is excited by the drive from the tymbals (Bennet-Clark and Young, 1992). A Helmholtz resonator consists of a cavity open to the outside via a hole which has a real or notional neck, and the resonant frequency fo is given by the general equation: where c is the speed of sound in the fluid, taken as 340 m s-1 for air, A is the area of the neck, L is the length of the neck and V is the volume of the cavity. Where the resonator has two holes, these terms should be somewhat modified: A is the combined area of the two holes, L is 16/3pi r (~1.7r) for a simple hole in a thin-walled vessel and r is the radius of one hole (Seto, 1971). These modifications to equation 1, which include corrections for the acoustic end-effect at either side of a simple hole in the wall of a vessel, are applicable to a model of the male cicada, in which there are two tympana close to the ventral surface of the abdomen.