A wave is a perturbation of matter, which, propagating in space, transfers energy without transferring matter itself. Each wave has certain characteristics. One of the important characteristics of perturbation processes is the wavelength, the formula for the calculation of which is given in the article.
Types of waves
All waves are classified by their physical nature, by the type of motion of particles of matter, by their periodicity and by the method of propagation in space.
According to the type of motion of particles of matter during the propagation of waves in it, the following types are distinguished:
- Transverse waves are a type of disturbance in which particles of matter oscillate in a direction that is perpendicular to the direction of wave propagation. An example of a shear wave is light.
- Longitudinal waves are waves in which particles of matter oscillate in the direction of wave propagation. Sound is a good example of a longitudinal wave.
According to the physical nature, the following types of waves are distinguished:
- Mechanical. This type of wave requires matter to arise, that is, a solid, liquid, or gaseous medium. An example of mechanical waves are waves at sea.
- Electromagnetic This type of wave does not need matter for its propagation, but can propagate in a vacuum. A striking example of electromagnetic waves are radio waves.
- Gravity. These waves lead to a perturbation of space-time. Large space objects, such as a binary star, which rotates around a common center of gravity, generate such waves.
In accordance with the dimension of the wave, they can be:
- One-dimensional, that is, those that propagate in one dimension, for example, vibration of a rope.
- Two-dimensional or superficial. These waves propagate in two dimensions, for example, waves on the surface of the water.
- Three-dimensional or spherical. These waves propagate in three dimensions, for example, light or sound.
In accordance with the frequency of the wave, we can say that there are:
- Periodic disturbances that differ in strictly repeating characteristics after a certain period of time, for example, sound waves.
- Not periodic, such waves do not repeat their characteristics, at certain intervals of time, for example, waves of an electrocardiogram.
Physical characteristics of the wave
The wave is characterized by 6 parameters, of which only 3 are independent, the rest are derived from these three according to the corresponding formulas:
- The wavelength L is the distance between two wave maximums.
- Height H is the vertical distance between the maximum and minimum of the wave.
- Amplitude - a value equal to half the height.
- Period T is the time during which two maximums or two minimums of the wave pass through the same point in space.
- Frequency - the reciprocal of the period of the wave, that is, it describes the number of maxima or minima that pass through a specific point in space per unit time.
- Speed - a value that characterizes the propagation of a wave. It is calculated by the formula: divide the wavelength by a period, that is, v = L / T.
Independent characteristics are, for example, wavelength, period and its amplitude.
Wavelength
This characteristic contains information about the wave, which largely describes its properties. In physics, the wavelength is defined as the distance between its two maxima (minima), or in a more general case, as the distance between two points that oscillate in one phase. The phase of the wave is understood as the instantaneous state of each point of the wave. The concept of "phase" makes sense only for periodic wave processes. The wavelength is usually indicated by the Greek letter λ (lambda).
In physics, the formula for the wavelength depends on the initial information that is available about this vibration. For example, in the case of electromagnetic waves, you can know the frequency and speed of wave propagation, and then use the usual calculation formula to calculate the wavelength, or you can know the energy of an individual photon, then a specific formula should be applied specifically for energy.
Sine waves
According to the Fourier theorem, any periodic wave can be represented by the sum of sine waves of different lengths. This theorem allows us to study every periodic wave thanks to the study of its sinusoidal components.
For a sine wave with a frequency f, period T, and propagation velocity v, the wavelength formula has the form: λ = v / f = v * T.
The wave propagation velocity depends on the type of medium in which the wave process occurs, as well as on the frequency of oscillations. The propagation velocity of an electromagnetic wave in a vacuum is constant and approximately equal to 3 * 10 8 m / s.
Sound waves
This type of mechanical waves is generated due to a local change in pressure in a substance that occurs during vibrational processes. For example, in the air, we are talking about discharged and compressed areas that propagate in the form of a spherical wave from the source that generates them. This type of wave is periodic, therefore, the formula for the length of the sound wave is the same as for the sinusoidal one.
Note that only longitudinal waves can propagate in liquids and gases, since elastic media do not arise in these media when the layers of the material are shifted relative to each other, while transverse waves can exist in a solid in addition to longitudinal waves.
The speed of sound waves in various environments
The propagation velocity of such waves is determined by the characteristics of the oscillatory medium: its pressure, temperature and density of the substance. Since the elementary particles that make up solids are closer to each other than these particles in liquids, such a structure of a solid substance allows you to transfer vibrational energy through it faster than through a liquid, so the wave propagation speed in them is greater. For the same reason, the speed of sound in liquids is higher than in gases.
Sound speed data in some environments:
| Wednesday | air, 20 ºC | water, 22 ºC | wood | aluminum | glass | steel |
| speed, m / s | 343 | 1505 | 3990 | 5090 | 5190 | 6099 |
In the case of air, we note that Newton derived a formula for the speed of sound in this medium depending on the temperature, which was subsequently modified by Laplace. This formula has the form: v = 331 + 0.6 * t ºC.
Thus, the formula for the sound wavelength with a frequency f in air at 25 ºC will take the form: λ = v / f = 346 / f.
Electromagnetic waves
Unlike mechanical waves, the nature of which is the perturbation of the substance in which they propagate, electromagnetic waves do not require matter for their propagation. They arise due to two effects: firstly, an alternating magnetic field creates an electric field, and secondly, an alternating electric field creates a magnetic field. Oscillating magnetic and electric fields are directed perpendicular to each other and perpendicular to the direction of wave motion, therefore, by their nature, electromagnetic waves are transverse.
In vacuum, these waves move at a speed of 3 * 10 8 m / s and can have different frequency values, so the length of the electromagnetic wave is expressed as: λ = v / f = 3 * 10 8 / f, where f is the oscillation frequency.
Spectrum of electromagnetic radiation
The spectrum of electromagnetic radiation is a combination of all the lengths of electromagnetic waves. The following parts of the spectrum are distinguished:
- Radioelectric radiation. The wavelength of the spectrum for this radiation is from a few centimeters to thousands of kilometers. These waves are used in television and various types of communications.
- Infrared radiation. This thermal radiation has wavelengths of the order of several micrometers.
- Visible light. This is the part of the spectrum that the human eye can distinguish. Its wavelength ranges from 400 nm (blue) to 700 nm (red).
- Ultraviolet spectrum. Its wavelengths lie in the range of 15-400 nm.
- X-ray radiation. It is used mainly in medicine. Their wavelength lies in the region of 10 nm - 10 pm. The source of their radiation are vibrations of electrons in atoms.
- Gamma rays. This is the highest frequency part of the spectrum, with a wavelength of less than 10 pc. Gamma rays have enormous penetration through any substance. They are generated as a result of processes occurring in the nucleus of an atom.
Calculation of wavelength through photon energy
Very often in physics problems arise that raise the question of what is the wavelength for a photon having energy E. To solve this kind of problem, use the following formula: E = h * c / λ, where c is the speed of the photon, h is a constant The bar, which is 6.626 * 10 -34 J * s.
From the above formula, we obtain the photon wavelength: λ = h * c / E. For example, let the photon energy E = 2.88 * 10 -19 J, and the photon moves in vacuum, that is, c = 3 * 10 8 m / s. Then we get: λ = h * c / E = 6.626 * 10 -34 * 3 * 10 8 / 2.88 * 10 -19 = 6.90 * 10 -7 m = 690 nm. Thus, this photon has a wavelength that lies near the upper boundary of the visible spectrum, and will be perceived by man as a red ray of light.