Properties of ultrasonic acoustic resonances for exploitation in comb construction by social hornets and honeybees

Physical and mathematical considerations are presented in support of the suggestion that social hornets and bees, which construct brood combs with large arrays of cells in a honeycomb structure, exploit ultrasonic acoustic resonances in those cells in order to achieve the great accuracy of the hexagonal symmetry exhibited by these honeycomb-structured arrays. We present a numerical calculation of those resonances for the case of a perfect-hexagon duct utilizing a Bloch-Floquet-type theorem. We calculate the rate of energy dissipation in those resonances and use that, along with other considerations, to identify the resonance that is best suited for the suggested use by bees and hornets. Previously recorded ultrasonic data on social hornets and honeybees are cited which agree with some of our predictions and thus provide support for the above-mentioned suggestion.