Frequency, wavelength, period and velocity

As shown in the animation the periodic up-and-down motion of the medium in the simplest type of transverse wave is sinusoidal.

The two graphs below show the periodic motion for the same wave using data plotted

in the graph at the left as displacement against the distance that the wave has travelled
in the graph at the right as displacement against time.

Note the mirror image relationship between the graphs.

The wavelength (λ) is the distance between adjacent identical parts of the wave.

For a sinusoidal wave this is the distance between troughs (crests).
In a plot of displacement against distance this can be read directly from the graph.
Wavelength has a unit of distance (m, nm, km....)

The period (T) is the time taken for one complete up and down motion.

In a plot of displacement against time this can be read as shown in the diagram.
Period has a unit of time (s, h....).

The amplitude (X) is the maximum displacement from the equilibrium position.

The frequency (f) is the number of wavelengths per unit time.

Frequency has the unit of inverse time (for example s^–1).
Frequency may also be in hertz (Hz) where 1 Hz is equal to 1 s^–1.

f =	1
	T

unit of result
time^–1

The angular frequency (ω) is the number of rotations through 2π per unit time.

ω = 2πf

ω =	2π
	T

unit of result
rad time^–1

The velocity (v) of a wave is the distance per unit time that it travels.

The velocity of wave has a sign and a number associated with it.
If the wave is travelling to the right the velocity is positive.
The unit of velocity is distance time^–1.
Thus velocity, wavelength, period and frequency are related as shown.

v = λf

v =	λ
	T

unit of result
distance time^–1