by Gary Leo Welz, M.A./M.S. Waves are familiar to us from the
ocean, the study of sound, earthquakes, and other natural
phenomenon. But as any surfer can tell you, ocean waves come in
very different sizes, as can all waves. To fully understand
waves, we need to understand measurements associated with these
waves, such as how often they repeat (their frequency), and how
long they are (their wavelength), and their vertical size
(amplitude). While these measurements help describe waves, they
do not help us make predictions about wave behavior. In order to
do that, we need to look at waves more abstractly, which we can
do using a mathematical formula. It is possible to look at waves
mathematically because a wave's shape repeats itself over a
consistent interval of time and distance. This behavior mirrors
the repetition of the circle. Imagine drawing a circle on a
piece of paper. Now imagine drawing that same shape while your
friend slowly pulled the piece of paper out from under your
pencil – the line you would h