Wave motion

Wave motion . Process by which energy is propagated from one place to another without transfer of matter, by means of mechanical or electromagnetic waves.

Summary

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  • 1 General
  • 2 Types of Waves
    • 1 Longitudinal wave
    • 2 Transverse wave
    • 3 Wavelength
    • 4 Speed ​​of propagation
  • 3 Wave behavior
  • 4 Experimental examples
    • 1 Reflection of wave pulses
    • 2 Interference from point sources
      • 2.1 Constructive interference
      • 2.2 Destructive interference
    • 3 Wave interference
  • 5 See also
  • 6 Sources

Generals

At any point in the propagation path, periodic displacement, or oscillation, occurs around an equilibrium position . Can be a swing of molecules of air , as in the case of the sound that travels through the atmosphere , molecules water (as in the waves formed on the surface of the sea ) or portions of a string or a spring.

In all these cases, the particles oscillate around their equilibrium position and only the energy advances continuously. These waves are called mechanical because the energy is transmitted through a material medium, without any global movement of the medium itself. The only waves that do not require a material medium for their propagation are electromagnetic waves ; in that case the oscillations correspond to variations in the intensity of magnetic and electric fields (see Electronics ).

Wave Types

The waves are classified according to the direction of the movements of the particles in relation to the direction of the movement of the wave itself. If the vibration is parallel to the wave propagation direction, the wave is called longitudinal (see Figure 1.).

Wave motion of water

Longitudinal wave

A longitudinal wave is always mechanical and is due to successive compressions (states of maximum density and pressure ) and rarefying (states of minimum density and pressure) of the medium. The sound waves are a typical example of this form of wave motion.

Cross wave

Another type of wave is the transverse wave, in which the vibrations are perpendicular to the direction of wave propagation. The transverse waves may be mechanical, such as waves propagating along a taut string when a disturbance occurs in one end (see Figure 2), or electromagnetic, as the light , the X – rays or waves radio . In those cases, the directions of the electric and magnetic fields are perpendicular to the direction of propagation.

Some mechanical wave motions, such as the surface waves of liquids , are combinations of longitudinal and transverse movements, making the liquid particles move in a circular fashion.

Wavelength

In a transverse wave , the wavelength is the distance between two successive ridges or valleys. In a longitudinal wave, it corresponds to the distance between two compressions or between two successive strains. The frequency of a wave is the number of vibrations per second.

Propagation speed

The propagation speed of the wave is equal to its wavelength multiplied by its frequency . In the case of a mechanical wave, its amplitude is the maximum displacement of the vibrating particles. In an electromagnetic wave , its amplitude is the maximum intensity of the electric field or the magnetic field .

Wave behavior

The speed of a wave in matter depends on the elasticity and density of the medium. In a transverse wave across a taut chord, for example, velocity depends on the chord tension and its linear density or mass per unit length.

Speed ​​can be doubled by quadrupling the voltage , or halved by quadrupling the linear density. The speed of electromagnetic waves in a vacuum (including light ) is constant and its value is approximately 300,000 km / s. When passing through a material medium, this speed varies without ever exceeding its value in a vacuum.

When two waves meet at a point, the resulting displacement at that point is the sum of the individual displacements produced by each of the waves. If the displacements go in the same direction, both waves are reinforced; if they go in the opposite direction, they weaken each other. This phenomenon is known as interference. (See Diffraction ).

When two waves of equal amplitude, wavelength, and velocity advance in the opposite direction through a medium, standing waves are formed. For example, if the end of a string is tied to a wall and the other end is shaken up and down, the waves reflect off the wall and reverse. If we assume that the reflection is perfectly efficient, the reflected wave will be half a wavelength behind the initial wave. Interference will occur between both waves and the resulting displacement at any point and time will be the sum of the displacements corresponding to the incident wave and the reflected wave. At points where a peak of the incident wave coincides with a valley of the reflected wave, there is no movement; these points are callednodes .

Halfway between two nodes, the two waves are in phase, that is, the ridges coincide with ridges and the valleys with valleys; at these points, the amplitude of the resulting wave is twice that of the incident wave; therefore, the chord is divided by the nodes into sections of one wavelength. Between the nodes (which do not advance through the string), the string vibrates transversely.

Standing waves also appear on the strings of musical instruments. For example, a violin string vibrates as a whole (with nodes at the ends), by halves (with an additional node in the center), by thirds. All of these vibrations occur simultaneously; the vibration of the string as a whole produces the fundamental tone and the remaining vibrations generate the different harmonics.

In mechanical quantum structure the atom is explained by analogy with system of waves stationary. Much of the advancement in modern physics is based on elaborations of wave theory and wave motion. (See also Earthquake .

Experimental examples

Wave pulse reflection

Wave Types

Quickly shaking a rope generates an undulatory pulse that progresses down the rope to the left ( A ).

If the end of the rope can move freely, the pulse returns through the rope on the same side ( C1 ). If the rope is tied to the wall, the pulse returns through the rope on the opposite side ( C2 ). If the end is free, the pulse will be twice the original amplitude at the reflection point ( B1 ); if the end is fixed, the amplitude of the pulse at that point will be zero ( B2 ).

Interference from point sources

This interference pattern was formed by moving two rods rhythmically up and down in a tray of water . Similar effects can be observed by putting two fingers in and out of the water or watching two ducks swimming in a pond close to each other.

Interference from point sources.

Constructive interference

The waves from a point source (the rod, the finger or duck) interfere with those from the other source. If two ridges come together at one point, they overlap to form a very high ridge; if two valleys come together, they overlap to form a very deep valley ( constructive interference ). The bright and dark rings are zones of constructive interference.

Destructive interference

If the crest of one source reaches one point at the same time as the valley of the other, they cancel each other out ( destructive interference ). Radial dark lines are zones of destructive interference.

Wave interference

Wave interference.

When two pulses going down a string meet, their amplitudes add together to form a resulting pulse. If the pulses are identical but advance on opposite sides of the string, the sum of the amplitudes is zero and the string will appear flat for a moment ( A ). This is known as destructive interference. When two identical pulses move on the same side, the sum of amplitudes is twice that of a single pulse ( B ). This is called constructive interference.

 

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