Wavelength is an important physical parameter needed to solve many problems of acoustics and electronics. It can be calculated in several ways, depending on what parameters are set. It is most convenient to do this, knowing the frequency or period and speed of propagation.
Formulas
The basic formula that answers the question of how to find the wavelength through frequency is presented below:
l = v / u
Here l is the wavelength in meters, v is the speed of its propagation in m / s, u is the linear frequency in hertz.
Since the frequency is inversely related to the period, the previous expression can be written differently:
l = vT
T is the oscillation period in seconds.
This parameter can be expressed in terms of cyclic frequency and phase velocity:
l = 2 pi * v / w
In this expression, w is the cyclic frequency expressed in radians per second.
The frequency of the wave through the length, as can be seen from the previous expression, is as follows:
u = v / l
Consider an electromagnetic wave that propagates in a substance with a refractive index n. Then the wave frequency through the length is expressed by the following relation:
u = c / (l * n)
If it propagates in a vacuum, then n = 1, and the expression takes the following form:
u = c / l
In the last formula, the wave frequency through the length is expressed using the constant c - the speed of light in vacuum, s = 300000 km / s.
De Broglie Waves
For these waves, the formulas will have a slightly different form. They determine the probability density and are used in quantum mechanics to find the parameters of the particle in question. Length and frequency are defined as follows:
l = h / p
u = E / h
h - Planck's constant, p - particle momentum, E - particle energy.
Application
The above formulas can be used to find the parameters of both electromagnetic and waves of a different nature, in vacuum, air or other medium. To determine how the wave frequency is expressed in terms of length or vice versa, you need to know the speed of its propagation and the properties of the medium. Electromagnetic will move most quickly in a vacuum or air, due to low electrical and magnetic permeability, since its speed is inversely proportional to the root of the product of these parameters.
With a sound wave there will be another situation. The speed of sound in solids and liquids is greater than in air. The highest speed will be in iron and lithium (about 6000 m / s), glass - 4800 (m / s), gold, silver, platinum. The speed of sound in solid and liquid media is determined using fairly complex dependencies, taking into account the density of the medium and Young's modulus.