The above equation is called the wave equation. It indicates the mathematical relationship between the velocity (v) of a wave and its wavelength (λ) and frequency (f). With the symbols v, λ and f, the equation can be rewritten as follows: The diagrams on the right show several “snapshots” of the generation of a wave in a string. The movement of the disturbance along the middle after each quarter of a period is shown. Note that in the time it takes from the first snapshot to the last, the hand has made a complete back and forth movement. The deadline has passed. Note that during the same time, the leading edge of the interference moved a distance equal to a full wavelength. In a period of a period, the wave moved a distance of one wavelength. If you combine this information with the velocity equation (speed = distance/time), you can say that the speed of a wave is also the wavelength/period. Waves are generally defined in media that allow most or all of the energy of a wave to propagate without loss.
However, materials can be called “lossy” when they extract energy from a wave and usually convert it into heat. This is called “absorption.” A material that absorbs the energy of a wave by transmission or reflection is characterized by a complex refractive index. The amount of absorption usually depends on the frequency (wavelength) of the wave, which explains, for example, why objects may appear colored. Mathematically, the most elementary wave is the one-dimensional (spatial) sine wave (also called harmonic or sinusoid wave) of amplitude u {displaystyle u}, which is described by the equation: Tags: Law of wave propagation Longitudinal wavesPeriodic wave timeSoundTransverse wavewavesamplitude wavefrequency waves of motion waveswave speed In other words, the frequency and period of a wave are reciprocal. Refraction is the phenomenon of a wave changing speed. Mathematically, this means that the amplitude of the phase velocity changes. Typically, refraction occurs when a wave passes from one medium to another. The amount by which a wave is broken by a material is given by the refractive index of the material. According to Snell`s law, the directions of incidence and refraction are related to the refractive indices of the two materials. For example, a Gaussian wave function could ψ take the form:[33] For example, the sound pressure in a recorder playing a “pure” note is typically a standing wave, which can be written as follows: The first law of motion states that a body remains at rest or continuous at a constant speed unless a force is applied. Essentially, the speed in this law is always constant. In standby mode, the speed remains zero.
During movement, the speed remains the same until a force is applied. At rest, the acceleration of a particle or body (a) is zero and the velocity (v) is zero. The following figure describes a particle with a particle nucleus consisting of one or more wave centers, a standing wave structure extending to the radius of the particle, and spherical and longitudinal waves moving beyond that radius. Standing waves are created by In waves, which are reflected to become Out waves. At rest, the wavelength of standing waves (λlead) coincides with the wavelength of waves (λl). There is no difference in wavelength/frequency between the particle and its environment. The particle is at rest and remains at rest. An electromagnetic wave consists of two waves, which are oscillations of electric and magnetic fields. An electromagnetic wave travels in a direction perpendicular to the direction of oscillation of the two fields. In the 19th century, James Clerk Maxwell showed that in a vacuum, electric and magnetic fields satisfy the wave equation at a speed equal to the speed of light. This gave rise to the idea that light is an electromagnetic wave.
Electromagnetic waves can have different frequencies (and therefore wavelengths), resulting in different types of radiation such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The wave frequency is the number of waves produced by the source in one second, the unit of frequency measurement is “hertz”, and the periodic wave time is the time of a wave. Whenever the medium is the same, the speed of the wave is the same. However, when the medium changes, the speed changes. The speed of these waves depended on the properties of the medium. A wave center moves to reduce the amplitude of the wave, favoring the position of the node on a standing wave or the point of minimum amplitude for a moving wave. This leads to all movements and forces on objects, including the formation of particles. There are two types of waves: longitudinal and transverse and the position of the minimum amplitude is different for these waveforms. This approach is extremely important in physics because stresses are usually a consequence of the physical processes that cause the wave to evolve. For example, if F ( x , t ) {displaystyle F(x,t)} is the temperature in a block of a homogeneous and isotropic solid material, its evolution is constrained by the partial differential equation There are two components of the ether needed for the entire theory of energy waves. The first is the fabric of space, which is the etheric medium. These are called ether granules, which transmit energy in the direction of motion.
one. the properties of the medium through which the wave moves A wave can be described as a field, namely as a function F ( x , t ) {displaystyle F(x,t)} where x {displaystyle x} is a position and t {displaystyle t} is a time. At a given starting time t = 0, where the central wavelength is related to the central wavelength k0 as λ0 = 2π / k0. From the theory of Fourier analysis[34] or Heisenberg`s uncertainty principle (in the case of quantum mechanics), it is known that a narrow wavelength range is required to produce a localized wavepacket, and the more localized the envelope, the greater the scattering in the required wavelengths. The Fourier transform of a Gauss is itself a Gauss. [35] Given the Gaussian principle: when a wave is confined in an enclosed space, it undergoes both reflection and interference. Consider, for example, a tube of length l. A disturbance somewhere in the air in the tube is reflected from both ends and usually creates a series of waves that travel along the tube in both directions.
According to the geometry of the situation and the finite constant value of the speed of sound, these must be periodic waves whose frequencies are determined by the boundary conditions at the end of the tube. The permissible frequencies of the waves in the tube meet sin kl = 0; That is, the permissible frequencies are ν = nV/2L, where n is any integer and V is the speed of sound in the tube. These are the frequencies of harmonic waves that can exist in the tube and that still meet the boundary conditions at the ends. They are called characteristic frequencies or normal modes of oscillation of the air column. The fundamental frequency (n = 1) is ν = v/2l. Consider a source that emits a wave such as light or sound of frequency ν, which moves away from an observer at speed v. The successive combs of light waves reach the observer at longer intervals than if the observer were at rest, and the calculation shows that the observer receives them at a frequency ν(1−V/c), where c is the speed of the wave. The frequency of the wave appears to the observer a little weaker than if the source was at rest.
As the source approaches, the frequency is higher. A plane wave is a type of wave whose value varies only in one spatial direction. That is, its value is constant on a plane perpendicular to this direction. Planar waves can be specified by a vector of unit length n ^ {displaystyle {hat {n}}}, which indicates the direction in which the wave varies, and a waveprofile describing how the wave changes as a function of displacement along this direction ( n ^ ⋅ x → {displaystyle {hat {n}}cdot {vec {x}}} ) and time ( t {displaystyle t} ). Because the waveprofile depends only on the position x → {displaystyle {vec {x}}} in the combination n ^ ⋅ x → {displaystyle {hat {n}}cdot {vec {x}}}, any movement in directions perpendicular to n^ {displaystyle {hat {n}}} cannot affect the value of the field.
