Waves: the frequency of the wave through the length and other formulas

The wavelength is an important physical parameter,necessary for solving many problems of acoustics and radio electronics. It can be calculated in several ways, depending on which 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 the frequency is given below:

l = v / u

Here l is the wavelength in meters, v is its propagation velocity in m / s, and u is the linear frequency in hertz.

Since the frequency is related to the period by the inverse relation, the previous expression can be written differently:

l = vT

T is the period of oscillations in seconds.

It is possible to express this parameter through the cyclic frequency and the phase velocity:

l = 2pi * 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 preceding expression, is as follows:

u = v / l

Consider an electromagnetic wave propagating in a substance with a refractive index n. Then the frequency of the wave through the length is expressed by the following ratio:

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 frequency of the wave through the length is expressed using the constant c = the velocity of light in a vacuum, c = 300,000 km / s.

Waves of de Broglie

For these waves, the formulas will have a slightly differentview. They determine the probability density and are used in quantum mechanics to find the parameters of the particle under consideration. The length and frequency are defined as follows:

l = h / p

u = E / h

h is the Planck constant, p is the particle momentum, and E is the particle energy.

Application

The above formulas can be used forfinding parameters of both electromagnetic and waves of another nature, in a vacuum, air or other medium. To determine how the frequency of a wave is expressed in terms of length or vice versa, one must know the speed of its propagation and the properties of the medium. Electromagnetic will most likely move in vacuum or air, due to low electrical and magnetic permeability, since its velocity 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 / c), gold, silver, platinum. The speed of sound in solid and liquid media is determined by rather complicated dependences, taking into account the density of the medium and the Young's modulus.