[Virtual Presenter] Hello everyone . I am honored to present to delve into the fascinating realm of plane wave propagation. In the world of physics and engineering, understanding how waves traverse through space is fundamental to our comprehension of various phenomena. Imagine for a moment a ripple moving across a pond after a stone is tossed into its calm waters. Much like this scenario, plane wave propagation involves the transmission of energy through a medium, but on a more and complex scale. Today, we embark on a journey to unravel the intricacies of these waves that play a pivotal role in fields ranging from telecommunications to acoustics and electromagnetic radiation..
[Audio] A plane wave propagation graph typically represents the behavior of a wave, such as an electromagnetic wave or acoustic wave, as it travels through space. Let's break down the key components and concepts associated with a plane wave propagation graph: Waveform Representation: The graph often shows the variation of the wave's amplitude (intensity) with respect to both time and distance. Time is usually represented on the horizontal axis (x-axis), and distance or space is represented on the vertical axis (y-axis). Wave Parameters: Wavelength (λ): The distance between two consecutive points in the wave that are in phase (e.g., two peaks or two troughs). It is often denoted by the symbol λ. Frequency (f): The number of oscillations or cycles of the wave per unit of time. Frequency is inversely proportional to the wavelength and is related by the formula: f=λc, where c is the speed of the wave. Wave Vector (k): A vector that points in the direction of wave propagation and has a magnitude equal to λ2π. It is often denoted by the symbol k. Propagation Direction: The slope of the wave in the graph indicates the direction of wave propagation. In a plane wave, the wavefronts are planar surfaces that extend perpendicular to the direction of propagation. Phase Velocity: The phase velocity of the wave is the speed at which a specific phase of the wave (e.g., a peak or trough) travels through space. It is given by the ratio of the frequency to the wave vector: vp=kf. Group Velocity: The group velocity represents the velocity at which the overall shape or envelope of the wave (the group of frequencies) propagates. It is given by the derivative of the angular frequency with respect to the wave vector: vg=dkdω. Dispersion: Dispersion occurs when different frequencies in a wave travel at different phase velocities. This can lead to the spreading out of the wave components over time. Amplitude: The amplitude of the wave represents the maximum displacement of the wave from its equilibrium position. It is a measure of the wave's intensity..
[Audio] A plane wave is a type of wave whose wavefronts are planar, meaning that the surfaces of constant phase (points that are in phase with each other) are flat and extend infinitely in the direction of propagation. In other words, the wave is uniform and has a constant phase over any plane perpendicular to the direction of propagation..
[Audio] Comparison between plane wave propagation and spherical wave propagation: First we talk about plane wave propagation: plane wave disturbances propagated in single direction like string wave. Transverse electromagnetic waves (TEM waves) are an example of a plane wave. The secondone is spherical wave propagation: while in spherical waves disturbances propagated outward in all directions from the source of wave. .Light waves is an example of spherical wave..
[Audio] Wave propagation refers to the way in which waves travel through a medium or space. Waves are disturbances that transfer energy from one place to another without transferring matter. The study of wave propagation is crucial in various scientific and engineering fields, including physics, acoustics, optics, electromagnetics, and seismology. There are different types of waves, and their propagation characteristics depend on the nature of the wave and the medium through which they travel..
[Audio] Planar Wavefronts: The wavefronts of a plane wave are planar surfaces perpendicular to the direction of propagation. This means that at any given moment, all points on a wavefront are in phase with each other. Uniform Amplitude: Plane waves are assumed to have a constant amplitude throughout space, meaning that the wave does not vary in intensity or magnitude..
[Audio] Direction of Propagation: Plane waves travel in a specific direction, and the wavefronts are perpendicular to that direction. Homogeneity and Isotropy: Plane waves are assumed to be homogeneous (uniform in amplitude) and isotropic (uniform in all directions perpendicular to the propagation direction)..
[Audio] Constant Phase: All points on a wavefront have the same phase at any given instant. The phase is a measure of the position within a wave cycle. The mathematical representation of a one-dimensional plane wave traveling in the x-direction is often given by Acos(kx−ωt+ϕ), where A is the amplitude, k is the wave number, ω is the angular frequency, x is the spatial coordinate, t is time, and ϕ is the phase constant..
When EM waves radiate from a source, such as an antenna, they radiate as spherical waves . As the waves move farther from the source, their energy gets spread out over a bigger spherical surface area. At big distances, which we call the far-field, a spherical wave front can be approximated as a uniform plane waveover a defined area..
[Audio] Skin Depth (δ): The skin depth is a measure of how quickly the amplitude of an electromagnetic wave decreases as it penetrates into a conductor. It is given by the formula: δ=μσω2 where: μ is the permeability of the material, σ is the conductivity of the material, ω is the angular frequency of the wave. Complex Permittivity (ε): The complex permittivity describes how a material responds to an applied electric field. In a good conductor, it has a real part (ε′) and an imaginary part (ε′′). The relationship is often expressed as: ε=ε′−jωσ where: j is the imaginary unit, σ is the conductivity of the material, ω is the angular frequency of the wave. Attenuation Constant (α): The attenuation constant represents the rate at which the wave amplitude decreases as it propagates through the conductor. It is related to the imaginary part of the complex permittivity and is given by: α=cωωε2σ where: c is the speed of light. Phase Velocity (vp): The phase velocity of a wave in a good conductor is affected by the complex permittivity and is given by: vp=1+εωσc where: c is the speed of light..