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