Longitudinal wave and seismic P-waves (created by earthquakes and explosions). In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave, and waves can be either straight or round. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. In the case of longitudinal harmonic sound waves, the frequency and wavelength can be described by the formula where: The quantity "x"/"c" is the time that the wave takes to travel the distance "x". The ordinary frequency ("f") of the wave is given by The wavelength
Successive over-relaxation methods were designed for computation by human calculators, and they required some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young, Jr. Given a square system of "n" linear equations with unknown x: where: Then "A" can be decomposed into a diagonal component "D", and strictly lower and upper triangular components "L" and "U": where The system of linear equations may be rewritten as: for a constant "ω" > 1, called the "relaxation factor". The method of successive over-relaxation is an iterative