What is the meaning of wavelength?

The wavelength of a wave, usually denoted by the Greek letter `lambda` ("lambda"), is a quantity that describes the spatial periodicity of the wave.

"Periodicity" means that the disturbance that creates a wave has a repeating pattern. If at time t the disturbance (however it is measured) has a value y, then after time T, called the period, has elapsed, the disturbance will return to the value y. If the wave is traveling with the velocity v, during the time T it will have traveled the distance equal to the wavelength: `lambda= vT` . Alternatively,

`lambda = v/f` , where f is the frequency of the wave.

Waves are typically described by periodic functions such as `y(x, t) = cos(kx - omegat)` . Here, k is the wave number and `omega` is the angular frequency of the wave. Both of this properties of the wave are related to the wavelength. The period of cosine is `2pi` , so the spatial periodicity of the wave is determined by `kx = 2pi` . Since the wave returns to its original form after it travels the distance equal to the wavelength, when `x = lambda` , `klambda = 2pi` . From here, `k = (2pi)/lambda` . Similarly, `omegat = 2pi` when t = T, so `omegaT = 2pi` and

`omega = (2pi)/T` .

The values of wavelength of the waves occurring in nature vary greatly. For electromagnetic waves, the radio waves can have the wavelength of several kilometers. Visible light has the wavelength in the range of 400 to 700 nanometers (`10^(-9) meters.)`  X-rays have wavelength less than `10^(-10)` meters, comparable to the size of atoms. Sound, which is a mechanical wave, can be audible to humans when its wavelength is in the range between several millimeters to several meters.