The principle of wave superposition is one of the basic principles of physics. When several waves exist in the medium at the same time, each wave can maintain its own propagation law without interfering with each other. The physical quantity of vibration at each point in the overlapping area of ??waves is equal to the vector sum of the physical quantities caused by each series of waves at that point. In the area where two waves overlap, any particle participates in two vibrations at the same time, and its vibration displacement is equal to the vector sum of the displacements caused by the two waves. When the vibration directions of the two waves are on the same straight line, the two displacements The vector sum of can be simplified to an algebraic sum after selecting the positive direction.

The principle of wave superposition is one of the basic principles of physics. When several waves exist in the medium at the same time, each wave can maintain its own propagation law without interfering with each other. The physical quantity of vibration at each point in the overlapping area of ??waves is equal to the vector sum of the physical quantities caused by each series of waves at that point. In the area where two waves overlap, any particle participates in two vibrations at the same time, and its vibration displacement is equal to the vector sum of the displacements caused by the two waves. When the vibration directions of the two waves are on the same straight line, the two displacements The vector sum of can be simplified to an algebraic sum after selecting the positive direction.

Note: The principle of superposition of waves is generally true only when the intensity of the wave is small and the wave equation is transformed into a linear equation.

Wave refers to the propagation of vibrations. The propagation of electromagnetic vibrations is electromagnetic waves. For the sake of intuition, take the simplest example of rope shaking. There is a vibration source vibrating up and down at one end of the rope, and the vibration propagates forward along the rope. Looking at the whole, the wave crests and troughs are constantly moving forward, while the particle of the rope only moves up and down and does not move forward.

Waveulation is an important form of material movement and widely exists in nature. There are many forms of physical quantity disturbance or vibration being transmitted. The transmission of mechanical vibration constitutes mechanical waves, the transmission of electromagnetic field vibration constitutes electromagnetic waves (including light waves), the transmission of temperature changes constitutes temperature waves (see liquid helium), and the transmission of crystal lattice vibration constitutes Lattice waves (see lattice dynamics), spin waves are formed when the perturbation of the spin magnetic moment propagates in the ferromagnetic body (see solid state physics). In fact, the perturbation of any macroscopic or microscopic physical quantity is transmitted in space. Waves can be formed at any time. The most common mechanical wave is the propagation process in space of the mechanical movement of the particles constituting the medium (causing changes in physical quantities such as displacement, density, pressure, etc.), such as waves in strings, water surface waves, sound waves in air or solids, etc. The prerequisite for generating these waves is the interaction of elastic or quasi-elastic forces between adjacent particles in the medium. It is with the help of this interaction that the vibration of a certain point is transmitted to adjacent particles, so these waves are also called elastic waves. . The physical quantity of vibration can be a scalar quantity, and the corresponding wave is called a scalar wave (such as a sound wave in the air), or it can be a vector, and the corresponding wave is called a vector wave (such as an electromagnetic wave). If the vibration direction is consistent with the propagation direction of the wave, it is called a longitudinal wave, and if it is perpendicular to the direction of the wave propagation, it is called a transverse wave.

The common characteristic of various forms of waves is that they are periodic. The disturbed physical quantity has time periodicity when it changes, that is, the physical quantity at the same point completely returns to its original value after a cycle; it also has space periodicity when it is transmitted in space, that is, it will change after passing a certain spatial distance along the propagation direction of the wave. The same vibrational state occurs (such as the displacement and velocity of the particle). Therefore, the disturbed physical quantity u is a periodic function of both time t and spatial position r. The function u(t, r) is called a wave function or wave expression, which is a mathematical expression that quantitatively describes the wave process. Broadly speaking, any function that describes the state of motion with time periodicity and space periodicity can be called a wave, such as gravitational waves, probability waves of microscopic particles (see wave-particle duality), etc.

The unique characteristics of various waves include: ① Reflection and refraction can occur at the interface of different media. For the interface of isotropic media, the law of reflection and the law of refraction are observed (see the law of reflection) , the law of refraction); ② When superimposing linear waves, the principle of wave superposition is observed (the principle of independent propagation of light); ③ Two or more waves can produce interference phenomena when they are superimposed under certain conditions (the principle of independent propagation of light). ); ④ When waves encounter obstacles on the propagation path, they can produce diffraction phenomena (see light diffraction); ⑤ Transverse waves can produce polarization phenomena (see optical polarization phenomena).

Wave forms are diverse.

The space in which it propagates can be filled with matter or empty (for electromagnetic waves). Some forms of waves can be felt by human senses, while others cannot. The most familiar ones are surface waves, of which there are several types. For example, on the surface of deep water, there are surface waves that mainly use gravity as the restoring force, with typical wavelengths from 1m to 100m; there are ripples that mainly use surface tension as the restoring force, with wavelengths shorter than 0.07m. These two waves often have sinusoidal shapes. Within deep water, there are internal gravity waves, which occur in areas with density stratification within the ocean. Internal gravity waves can also appear not only in the ocean, but also in the atmosphere. What is more widely encountered in the air is, of course, sound waves. What propagates in sound waves is the disturbance of physical quantities such as pressure and density in the air. The disturbance refers to the deviation from the original value when there are no sound waves.

Ripples are constantly occurring in solids. From the perspective of large objects, such as seismic waves that often appear on the earth; from the perspective of small objects, such as the lattice waves that are transmitted between the atomic lattices of crystals all the time. For solid materials with special physical properties, some special waves can also be excited: for example, there can be electroacoustic surface waves in piezoelectric materials; in ferromagnetic materials, there can be spin waves, magneto-elastic waves, etc. Some different types of waves can also be excited in plasma. In the Earth's ionosphere, because the magnetic field lines moving with the fluid exert magnetic pressure on the fluid, and because the fluid pressure can automatically adjust to balance the changing magnetic pressure, a magneto-acoustic wave that propagates along the magnetic field lines can be excited. . This is just one of many types of waves that can be produced within a plasma.