A Short Note On The Number Of Dimensions A Wave Propagates

In the usual manner, the motion of a wave does not consider a permanent displacement of the medium’s particles but allows the energy transference from one point to another. Focusing on this particular phenomenon, the current study will include a discussion based on energy in waves. The wave velocity will be discussed in the study in a brief manner along with discussion regarding one, two and three-dimensional waves as well. 

Energy in Waves

It has been seen that the large amplitudes have been considered the source of the larger vibrations. It has been discovered that the energy of wave propagation can depend on two aspects that are the frequency and amplitude of the wave. For instance, if the energy propagated by every wavelength can be considered as a discrete packet of energy, the wave that has a high frequency has the ability to deliver more energy packets per unit. In contradiction, the rate of energy that is transferred in electromagnetic waves is independent of the frequency but is proportional to the square of the amplitude. 

Wave Velocity 

The propagation velocity or the probation speed of the wave refers to the disturbance that has been propagated from one location of the wave to another one. In order to concern the energy propagation depending on the phase and speed, the velocity of speed is represented as vp= ω/ k. In this formula, the term, vp is represented as the phase velocity. The angular frequency has been represented by the term ω. The wavenumber is represented as k. In the dispersion relationship, the formula has been represented as ω = Ω(k). In some cases when the c is constant, the waves have been recognised as the non-dispersive and the formula has changed into Ω(k) = ck. 

One Dimensional Wave: Overview

A dimensional wave has been prescribed to a particular dimension of space that is time. Here the component-time has been represented with the letter t. In the one dimensional wave, the presence of one independent variable can be found, that is time. In one dimensional wave, a single disturbance has been known as a pulse; on the other hand, the periodic wave refers to the repetitive disturbances.  The equation of the one-dimensional wave is 

△F=△m dvx/dt. 

Explanation of Two-Dimensional Wave 

Waves can travel on rough surfaces where two dimensions exist, including the instances of the layer of cloud or the surface of the water. It has been seen that the one-dimensional waves are easier for being analysed or understood in comparison to the two-dimensional wave. The main reason is that the two dimensional waves are easy to animate and see rather than being analysed like a one-dimensional wave. Following the variables such as the height of the surface that exists above the height of the equilibrium helps to determine the two-dimensional waves. Based on these variables, the surface has been described with the coordinates that are y and x. 

Three-Dimensional Waves: Overview 

The waves of sound, radio and light have been considered the three-dimensional waves that are used widely. The three-dimensional waves have been able to propagate in all directions in space. However, the same intensity of the wavelength has been identified in all the directions in the space where the three-dimensional waves can be propagated. On the other hand, if any kind of disturbance has occurred in a specific point of space, as a result, the wave propagates in three spatial directions. The type of wave surface can be elliptical, spherical and many more. 

Reflection of Plane Waves in A Half-Space

Popular examples of the reflection and the propagation of the plane waves include Shear waves and Pressure waves. The analytic solution to these two phenomena is well known in classical seismology.

• The analytical solution of the SV wave propagation refers to that a plane SV wave has the ability to reflect back to the domain as a shear wave and a pressure wave. 
• In a similar manner to the shear wave, the pressure waves possess the ability to be reflected as a pressure and SV wave. 

Conclusion 

In this study, it has been found that the wave and the vibration are considerably important phenomena in the terminology of physics. The description of a wave shares a close relation to each instance of a wave process. On the other hand, it has been seen that the amount of energy a wave transfers shares a relation with the frequency and the amplitude of the wave. Based on this the study has discussed the reflection of plane waves in a half-space.