Anatomy of a Wave

A sinusoidial wave confined to travel along the x-axis, as illustrated below,

...is defined by the function

`y(x,t)=Acos(kx-omegat+phi)`

Equation 1

Where its properties incldue amplitude, `A`, wavelength, `lambda`, period, `T`, its frequency, `f=1/T`, wave-number, `k=(2pi)/lambda`, angular frequency, `omega=2pif`, speed, `v=omega/k` and phase-constant, `phi`.

Amplitude, `A`	The maximum height of the wave measured from y=0
Wavelength, `lambda`	The distance between any two similar points, ie., between crests
Period, `T`	The time it takes for the wave to do one complete cycle
Frequency, `f`	How many cycles the wave performs per unit time
wave-number, `k`	How many cycles the wave perform per unit distance
Angular frequency, `omega`	How many degrees the wave cycles per unit time, ie., in radians per second
Phase-constant, `phi`	A shift of the wave along the axis, providing the phase as `x=0, t=0`
Speed, `v`	The rate at which the crests propagate along the direction of travel

It is possible, using the above definitions, to express the wave-function in an alternate form, although one which is less commonly used,

`y(x,t)=Acos(2pi(x/lambda)-2pit/T)`

We will next see an application to more realistic wavefunctions, those we deal with more commonly in quantum mechanics.

Next: Electron waves