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
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