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
Doppler effect emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is then increased, so the waves "spread out". For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which