A stuty on sound production acoustics in the black cieada (C. Atrata Fabricius.)

The long rib of the sounding membrane in the black cicada is an analog to a beam clamped at one end. The fundamental frequency of the activated sound is between 3900-5500 Hz, basically consistent with the possible renge of the main peak frequency (MPF) of the song in the black cicada. The operculum (Op), tymbal cover (TC) and joint membrane (JM) are respectively analogous to a uniform square plate clamped at one edge and free at the others, to another plate clanped at two opposite sides and free at the other two, and to a rectangular membrane clamped at four sides. The fundamental frequencies of activated vibration (f_Op¹=940Hz, f_TC¹=1200Hz, and f_JM¹=810Hz) and f_OP^{3,4.5,5,5.5,6},f_TC^2,2.5,3,3.5 and f_JM^{45,65,66,76,77} ara basically consistent with the MPFs and main high frequency components of vibrations of the Op, TC and JM, respectively.
The resonant cavity and spiracles on both sides are analogous to a resonace circuit with a resistor connected in parallel at the output terminall, and the resonant frequency and quality factor of the circuit are in good agreement with the MPF and its tuning sharpness of the song in the black cicada.