# [Answer] The amplitude of a wave is the height of a wave as measured from the highest point on the wave________ to the lowest point on the wave ________.

Depending on context wave height may be defined in different ways: • For a sine wave the wave height H is twice the amplitude: $H=2a.\$ • For a periodic wave it is simply the difference between the maximum and minimum of the surface elevation z = η(x – cp t): $H=\max \left\{\eta (x\ -\ c_{p}\ t)\right\}-\min \left\{\eta (x-c_{p}\ t)\right\} \$
Depending on context wave height may be defined in different ways: • For a sine wave the wave height H is twice the amplitude: $H=2a.\$ • For a periodic wave it is simply the difference between the maximum and minimum of the surface elevation z = η(x – cp t): $H=\max \left\{\eta (x\ -\ c_{p}\ t)\right\}-\min \left\{\eta (x-c_{p}\ t)\right\} \$ with cp the phase speed (or propagation speed) of the wave. The sine wave is a specific case of a periodic wave. • In random waves at sea when the surface elevations are measured with a wave buoy the individual wave height Hm of each individual wave—with an integer label m running from 1 to N to denote its position in a sequence of N waves—is the difference in elevation between a wave crest and trough in that wave. For this to be possible it is necessary to first split the measured time series of the surface elevation into individual waves. Commonly an individual wave is denoted as the time interval between two successive downward-crossings through the average surface elevation (upward crossings might also be used). Then the individual wave height of each wave is again the difference between maximum and minimum elevation in the time interval of the wave under consideration. • Significant wave height H1/3 or Hs or Hsig as determined directly from the time series of the surface elevation is defined as the average height of that one-third of the N measured waves having the greatest heights: $H_{1/3}={\frac {1}{{\frac {1}{3}}\ N}}\ \sum _{m=1}^{{\frac {1}{3}}\ N}\ H_{m}$