Abstract
We propose that social hornets and bees, who construct large arrays (known as combs) of cells for hatching and brooding their offspring, exploit ultrasonic acoustic resonances in those cells in order to implement the accurate honeycomb structure exhibited by those arrays. This idea is supported by a number of theoretical considerations, including a detailed analysis of the spectrum of lateral acoustic resonances in a cell with circular cross section, considered as an approximation to the actual perfect hexagon shape. It is also supported by the results of some previous measurements of the acoustic spectrum in a nest of Oriental hornets.
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References
Duncan, C.D., 1939. A Contribution to the Biology of North American Vespine Wasps. Stanford University Press. Palo Alto, CA.
Hales, T.C., 2001. The honeycomb conjecture. Discrete Comput. Geom. 25, 1–22.
Hexagonal Lattice. In: Wikipedia, the Free Encyclopedia, available at: http://en.wikipedia.org/wiki/Hexagonal_lattice.
Ishay, J., 1975. Frequencies of the sounds produced by the Oriental hornet, Vespa orientalis. J. Insect Physiol. 21, 1737–1740.
Ishay, J.S., 1976. Comb building by the Oriental hornet Vespa orientalis. Anim. Behav. 24, 72–83.
Ishay, J.S., Abes, A.H., Chernobrov, H.L., Barenholz-Paniry, V., Parmet, Y., Fuchs, C., 1995. Building activity and longevity of queenless groups of the Oriental hornet Vespa orientalis. Bull. Math. Biol. 57, 441–460.
Ishay, J.S., Bytinski-Salz, H., Shulov, A., 1967. Contributions to the bionomics of the Oriental hornet Vespa orientalis. Isr. J. Entomol. II 45–106.
Ishay, J.S., Ganor, E., 1990. Comb cells and puparial silk in the Oriental hornet nest: Structure and function. J. Morphol. 203, 11–19.
Ishay, J.S., Levanon, D., Avidor, N., Shechter, D.S., 1983. Photoperiodicity stimulates all size and caste determination in the Oriental hornet Vespa orientalis Linne 1975. Insectes Soc., Paris 30, 332–346.
Ishay, J.S., Rosenzweig, E., Paniry, V.A., 1982. The genesis of hexagonal cells and the frugality in comb and cell building by social Vespinae (Hymenoptera). Insectes Soc., Paris 29, 34–43.
Ishay, J.S., Sadeh, D., 1975. Direction finding of hornets under gravitational and centrifugal forces. Science 190, 802–804.
Kisliuk, M., Ishay, J.S., 1977. Influence of an additional magnetic field on hornet nest architecture. Experimentia 33, 885–887.
Landau, L.D., Lifshitz, E.M., 1977. In: Sykes, J.B., Bell, J.S. (trans.) Quantum Mechanics—Non-Relativistic Theory, 3rd edition, revised and enlarged. (original work in Russian). Pergamon Press, Elsevier, Amsterdam, Chap. 12.
Matsuura, M., Yamane, S., 1990. Biology of the Vespine Wasps. Springer-Verlag, Berlin.
Morse, P.M., Ingard, K.U., 1968. Theoretical Acoustics. McGraw-Hill, New York, 503 pp.
Peterson, I., 1999. The honeycomb conjecture. In: Science News Online, available at: http://www.sciencenews.org/pages/sn_arc99/7_24_99/bob2.htm, 24 July.
Pierce, A.D., 1991. Acoustics 2nd Printing. Acoustical Society of America, New York.
Pirk, C.W.W., Hepburn, H.R., Radloff, S.E., Tautz, J., 2004. Honeybee combs: Construction through a liquid equilibration process? Naturwissenschaften 91, 350–353.
Roy, R.R., Robert, D., 1996. Tympanal hearing in insects. Annu. Rev. Entomol. 41, 433–450.
Spangler, H.G., 1986. High-frequency sound production by honeybees. J. Apic. Res. 25, 213–219.
Spradbery, J.P., 1973. Wasps. Sidgwick and Jackson, London.
Thompson, D.W., 1942. On Growth and Form. Cambridge University Press, Cambridge, UK.
von Frisch, K., 1975. In: Gombrich, L. (trans.) Animal Architecture (originally in German). Hutchinson, London.
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Bergman, D.J., Ishay, J.S. Do Bees and Hornets Use Acoustic Resonance in Order to Monitor and Coordinate Comb Construction?. Bull. Math. Biol. 69, 1777–1790 (2007). https://doi.org/10.1007/s11538-006-9190-9
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DOI: https://doi.org/10.1007/s11538-006-9190-9