Wave per unit distance (typically per meter), can be associated with the wavelength by the relation The period formula_33 is the time for one complete cycle of an oscillation of a wave. The frequency formula_34 is the number of periods per unit time (per second) and is typically measured in hertz denoted as Hz. These are related by: In other words, the frequency and period of a wave are reciprocals. The angular frequency formula_28 represents the frequency in radians per second. It is related to the frequency or period by The wavelength formula_30 of a sinusoidal waveform traveling at constant speed
Wave shoaling the product of the wave energy density with the group velocity, between two wave rays is a conserved quantity (i.e. a constant when following the energy of a wave packet from one location to another). Under stationary conditions the total energy transport must be constant along the wave ray – as first shown by William Burnside in 1915. For waves affected by refraction and shoaling (i.e. within the geometric optics approximation), the rate of change of the wave energy transport is: where formula_13 is the co-ordinate along the wave ray and formula_14 is the energy flux per unit crest length.