What is the scientific definition of amplitude?

In scientific terms, amplitude describes a change of magnitude in an oscillating or wave-like system. When used without specifications, the term refers to the distance between a line drawn through the middle of the system at the point of equilibrium to the wave peak farthest from that line.

The technical term for the measurement between the point of equilibrium and the wave peak is "semi-amplitude," because it is actually a measurement of one-half of the wave. Peak-to-peak amplitude refers to the measurement between the lowest and the highest wave values. Because waves are caused by energy, and more energy creates larger waves, amplitude is also used to talk about the amount of energy in the system.