Wavefunction Properties
* amplitude (A) - the maximum magnitude of the displacement from equilibrium, in SI units of meters. The amplitude is indicated in blue in the picture.
* period (T) - is the time for one wave cycle (two pulses, or from crest to crest or trough to trough), in SI units of seconds (though it may be referred to as "seconds per cycle").
* frequency (f) - the number of cycles in a unit of time। The SI unit of frequncy is the hertz
(Hz) and
1 Hz = 1 cycle/s = 1 s-1
* angular frequency (omega) - is 2pi times the frequency, in SI units of radians per second.
* wavelength (lambda) - the distance between any two points at corresponding positions on successive repetitions in the wave, so (for example) from one crest or trough to the next, in SI units of meters. The wavelength is indicated in red in the picture.
* wave number (k) - also called the propagation constant, this useful quantity is defined as 2 pi divided by the wavelength, so the SI units are radians per meter.
* pulse - one half-wavelength, from equilibrium back
Some useful equations in defining the above quantities are:
v = lambda / T = lambda f
omega = 2 pi f = 2 pi/T
T = 1 / f = 2 pi/omega
k = 2pi/omega
omega = vk
The vertical position of a point on the wave, y, can be found as a function of the horizontal position, x, and the time, t, when we look at it. We thank the kind mathematicians for doing this work for us, and obtain the following useful equations to describe the wave motion:
y(x, t) = A sin omega(t - x/v) = A sin 2pi f(t - x/v)
y(x, t) = A sin 2pi(t/T - x/v)
y(x, t) = A sin (omega t - kx) uote>