The transit time of sound in a phononic crystal

Electron material waves cannot permeate a periodic atomic lattice at each energy or frequency. There exists a forbidden gap due to the periodicity of the atoms. In analogy, acoustic waves cannot penetrate a phononic or sonic crystal at each frequency. A two-dimensional sonic crystal consists of a periodic lattice of cylinders. The periodicity is adjusted according to the wavelength of sound. Depending on the frequency, there exist “allowed” bands with a propagation of the waves as well as a “forbidden” band without propagation corresponding to the bandgap in a semiconductor. The mathematical description of the phenomena in the sonic crystal and in the atomic crystal is technically similar. Here, we investigate experimentally the velocity of sound in a sonic crystal by measurement of the wave’s transit time through the crystal. The velocity in the crystal depends on the frequency and is smaller than the velocity in air

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This work was supported by grants from the NIH (DP2DK105570-01 and 2P30DK046200 to MLA, DK21397 to HJG, K01DK098319 to KMH, K01MH091222 to LH, DK093848 to RJS, R01DK082590 to LS, R01DK097550 to JT, RO1 DK 076037 to MOT, R01DA024680 and R01MH085298 to JMZ, R01AG019230 and R01AG029740 to RGS) The Wellcome Trust (MK), Science Foundation Ireland (12/YI/B2480 to CWL), the Alexander von Humboldt Foundation (MHT), the Deutsches Zentrum für Diabetesforschung (MHT), the Helmholtz Alliance ICEMED e Imaging and Curing Environmental Metabolic Diseases, through the Initiative and Networking Fund of the Helmholtz Association (MHT), and the Helmholtz cross-program topic “Metabolic Dysfunction” (MHT). Allan Geliebter was sponsored by NIH grants R01DK80153; R01DK074046; R03DK068603; P30DK26687