Bloch wave – MoM method the wave numbers in any of the 3 periodic coordinate directions. This can happen for example when the free space wavelength exactly equals the lattice spacing. This is a statistically rare occurrence in computational practice and corresponds to a propagation anomaly similar to a Wood's reflection anomaly for gratings. To compute bands of the crystal (i.e. "k"-"k" diagrams), successive values of frequency ("k") are tried - in conjunction with pre-selected values of propagation constant ("k") and propagation direction (θ & φ) - until a combination is found which drives the determinant of the matrix to zero. Equation (4.2) has been
Acoustic wave equation include acoustic wave equations that incorporate fractional derivative terms, see also the acoustic attenuation article or the survey paper. The wave equation describing sound in one dimension (position formula_3) is where formula_1 is the acoustic pressure (the local deviation from the ambient pressure), and where formula_6 is the speed of sound. Provided that the speed formula_6 is a constant, not dependent on frequency (the dispersionless case), then the most general solution is where formula_9 and formula_10 are any two twice-differentiable functions. This may be pictured as the superposition of two waveforms of arbitrary profile, one (formula_9) travelling up the x-axis