In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities, sometimes as described by a wave equation. In physical waves, at least two field quantities in the wave medium are involved. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.
The types of waves most commonly studied in classical physics are mechanical and electromagnetic. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium. Other examples of mechanical waves are seismic waves, gravity waves, surface waves, string vibrations (standing waves), and vortices. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields which sustains propagation of a wave involving these fields according to Maxwell's equations. Electromagnetic waves can travel through a vacuum and through some dielectric media (at wavelengths where they are considered transparent). Electromagnetic waves, according to their frequencies (or wavelengths) have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.
Other types of waves include gravitational waves, which are disturbances in spacetime that propagate according to general relativity; heat diffusion waves; plasma waves that combine mechanical deformations and electromagnetic fields; reaction-diffusion waves, such as in the Belousov–Zhabotinsky reaction; and many more.
Mechanical and electromagnetic waves transfer energy, momentum, and information, but they do not transfer particles in the medium. In mathematics and electronics waves are studied as signals. On the other hand, some waves have envelopes which do not move at all such as standing waves (which are fundamental to music) and hydraulic jumps. Some, like the probability waves of quantum mechanics, may be completely static.
A physical wave is almost always confined to some finite region of space, called its domain. For example, the seismic waves generated by earthquakes are significant only in the interior and surface of the planet, so they can be ignored outside it. However, waves with infinite domain, that extend over the whole space, are commonly studied in mathematics, and are very valuable tools for understanding physical waves in finite domains.
A plane wave is an important mathematical idealization where the disturbance is identical along any (infinite) plane normal to a specific direction of travel. Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic motion at one frequency. In linear media, complicated waves can generally be decomposed as the sum of many sinusoidal plane waves having different directions of propagation and/or different frequencies. A plane wave is classified as a transverse wave if the field disturbance at each point is described by a vector perpendicular to the direction of propagation (also the direction of energy transfer); or longitudinal if those vectors are exactly in the propagation direction. Mechanical waves include both transverse and longitudinal waves; on the other hand electromagnetic plane waves are strictly transverse while sound waves in fluids (such as air) can only be longitudinal. That physical direction of an oscillating field relative to the propagation direction is also referred to as the wave's polarization which can be an important attribute for waves having more than one single possible polarization.
Hello! I have been recently studying Quantum mechanics alone and I've just got this question.
If the potential function V(x) is an even function, then the time-independent wave function can always be taken to be either even or odd. However, I found one case that this theorem is not applied...
I've marked the right answers.
They mainly indicate at power carried by the particles being zero, and here is my doubt- why should it be zero? Shouldn't it have some definite value?
I do understand that the kinetic energy is max at the y=0 and potential energy is max at y=A, but I don't know...
To begin with, I am trying to understand how does ##E^2 (x,t)## transform to ##A_y^2 + A_z^2##. And, noting that the already established equation of ##E^2 = E_y^2 + E_z^2##, I would assume that ##E^2 (x,t)## somehow ends up to being ##A_y^2 + A_z^2##. However, noting that ##E^2 = (A_y...
This is not a homework question, it is for my understanding so please do not answer this question with a question.
I have found this great animated gif but it appears to be for a fixed end (notice wave inversions at the end). Has anyone seen a similar one for a free end?
Many Thanks
Summary:: A plane wave incident upon a planar surface - determining polarization, angle of incidence etc.
𝐄̃i = 𝐲̂20𝑒−𝑗(3𝑥+4𝑧) [V. m−1 ]
is incident upon the planar surface of a dielectric material, with εr = 4, occupying the halfspace z ≥ 0.
a) What is the polarisation of the incident wave...
The problem I am having is "What can you conclude about wave prorogation in SR given the results?". The best I can come up with is that the number of wave planes N crossing a section of spacetime in either frame is the same. The section may be bigger or smaller depending on which frame you're in...
I am solving the wave equation in z,t with separation of variables. As I understand it, Z(z) = acos(kz) + bsin(kz) is a complete solution for the z part. Likewise T(t) = ccos(ω t) + dsin(ωt) forms a complete solution for the t part. So what exactly is ZT = [acos(kz) + bsin(kz)][ccos(ωt) +...
Hello everybody,
I have to find the amplitudes of a wave that goes through 4 different mediums in terms of ##E_0##, suffering reflection in the first three but not the last one. I calculated the corresponding reflection indexes of the three mediums (all of them real).
Following calculations, I...
I want to split a fat laser beam and interfere it with itself, kind of like this:
The very obvious problem is that the wave peaks shown as black lines would be a whole lot closer together, so the interference fringes would be sub-microscopic. If a couple of glass wedges - oddly-shaped prisms...
Does each point in a stationary wave change its displacement and hence it's amplitude? If yes, why is this so? However, why does the amplitude at the node and antinode remains zero and maximum respectively? Does the above have to do with the fact that all the formation of a stationary wave is...
To begin with, I can first let ##T(x,y) = X(x) Y(y)## to be the given solution. With this, I can then continue by writing:
$$Y \frac{\partial^2 X}{\partial x^2} + X \frac{\partial^2 Y}{\partial y^2} = 0$$
$$\Longrightarrow \frac{1}{X} \frac{\partial ^2 X}{\partial x^2} + \frac{1}{Y}...
hello , hope all of you are doing well ,
i have question about the unit of the function of waves of string fixed in both boundary , the function of waves is function of two variables x and t , so it's function describe the displacement in function of place and time ,
Ψ(x,t)=φ(x)*sin(ωt+α)...
Hello all, I am a newcomer here. Not a physicist, just an enthusiast. ;)
I was thinking whether it is possible to separate a one-particle wave function into two, "completely disjoint" parts. The following thought experiment explains better what I am thinking about.
Let us suppose, that there...
Hi there! This is my first post here - glad to be involved with what seems like a great community!
I'm trying to understand the acoustics of a finite plane-wave tube terminated by arbitrary impedances at both ends. So far all of the treatments I've managed seem only to address a different...
The book's procedure for the "shooting method"
The point of this program is to compute a wave function and to try and home in on the ground eigenvalue energy, which i should expect pi^2 / 8 = 1.2337...
This is my program (written in python)
import matplotlib.pyplot as plt
import numpy as...
How do I get the wave dispersion for a 2D continuum unit cell subjected to a periodic boundary which is excited longitudinally? I'll be applying forces in ABAQUS with varying frequencies. I have come across Blochs theorem but I can't find any application of it in continuous systems. Every...
Applying the time reversal operator to the plane wave equation: Ψ = exp [i (kx - Et)]
T[Ψ ] = T{exp [i (kx - Et)]} = exp [i (kx + Et)]
This looks straightforward as I have simply applied the 'relevant equation' however my doubt is in relation to the possible action of operator T on the i...
Some questions:
Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well.
Since we have no complex components. I am guessing that the ##\psi *=\psi##.
If...
I was thinking about a problem I had considered a long time ago in some thread, finding an example of a wave function ##\displaystyle \psi (x) =e^{iax}\phi (x)## with ##\displaystyle\phi (x)## being periodic with period ##\displaystyle L## and the corresponding Schrödinger equation...
First, I have a question about supereposition of the plane waves - whether the direction of all such plane wave is same, i.e. ##\vec{n}## is in some direction. If not, I think it would be ##\vec{E}(\vec{x}, t)=\int\mathbf{\mathfrak{E}}(\vec{k}')e^{i\vec{k}'\cdot\vec{x}-i\omega t}d^3k##. Besides...
Hi,
I was trying to get some practice with the wave equation and am struggling to solve the problem below. I am unsure of how to proceed in this situation.
My attempt:
So we are told that the string is held at rest, so we only need to think about the displacement conditions for the wave...
To plot ##u(r)## we need to find the solutions for each region. Which is in the relevant equations part. Now, I have to do this numerically. Using python 3.7 I made an ##u## which is filled with zeros and a for loop with if/elseif statement, basically telling it to plot values for whenever...
Hi,
I just need someone to check over my work. I am having trouble with the next part of this question and I just wanted to check that this part was correct first.
I have two particles in an infinite square well (walls at x=0 and x=L). I need write an expression for the spatial wave...
So to do this problem I need the relevant formula for phase difference which is this:
I first need to find wavelength and this is lambda = velocity/frequency
So lambda = 257/641 = 0.40093603744 m
Hence phase difference (in radians) = 2pi * (2/0.40093603744) = 31.3 rads
My concern is that...
There is a multiple choices question about traveling wave in my book.
Based on the graphic, if T = 2s, the wave equation is ...
My answer :
ω = 2π/T = 2π/2 = π
k = 2π/λ = 2π/4 = 0,5π → in my country, we use comma (,) for point (.)
y = ±A sin (ωt - kx)
y = -0,5 sin (πt - 0,5πx)
y = -0,5 sin...
Hi all. I just watched a great video on gravity wave 'telescopes'. So i have been wondering if any of my intuitive hunches are right about gravity waves.
Accelerated masses generate gravity waves that dissipate energy..
So let's say i turn my rocket ship engine on while sitting in deep...
Hi,
So the main question is: How to deal with power loss in E-M waves numerically when we are given power loss in dB's?
The context is that we are dealing with the damped wave equation: \nabla ^ 2 \vec E = \mu \sigma \frac{\partial \vec E}{\partial t} + \mu \epsilon \frac{\partial ^ 2 \vec...
Since the membrane doesn't break, the wave is continuous at ##x=0## such that
##\psi_{-}(0,y,t) = \psi_{+}(0,y,t)##
##A e^{i(k \cos(\theta)x + k \sin(\theta)y - \omega t)} = A e^{i(k' \sin(\theta ') y- \omega t)}##
Which is only true when ## k' \sin(\theta ') = k \sin(\theta) ##.
From the...
I've searched threads and can't find easy explanation - sorry if I'm missing something basic / have a basic understanding error!
In the classic picture of an EM wave with the Electric and Magnetic components oscillating at 90 degrees to each other, both components cross the middle axis at the...
I am not sure what is meant by "equation of propagation of crest" but this is my attempt:
First, I find the velocity of wave:
v = ω / k = 0.5 / 0.25 = 2 m/s
Then I calculate wavelength:
k = 2π / λ
λ = 4 m
I imagine the crests will move to the right along with the wave so I try to use equation...
By reversibility, if we turn the direction of the light propagation by 180 degrees, then the new propagation path follows the old propagation path. I suspect that when there is diffraction, the light propagation is not reversible?
Maybe because when you don't observe it, the Schrödinger equation predicts the totality of interactions (paths) of the electron over an infinite time, all the paths it can take ( forming a wave like function ) which is actually all the paths the electron can take overlapped... and when u...
I found this on the internet.
Source
How does the crest reach the end of the medium? As the other end is fixed there is no way the crest can reach the interface. Isn't it?
My book gave an alternative explanation. It stated that as there is no net displacement at the interface, we can use the...
Laplace pointed out that the variation in pressure happens continuously and quickly. As it happens quickly, there is no time for heat exchange. This makes it adiabatic. But Newton believed it to be isothermal.
Why isn't it isothermal but adiabatic? Why is there a change in temperature?
I'm looking for material about the following approach : If one suppose a function over complex numbers ##f(x+iy)## then
##\frac{df}{dz}=\frac{\partial f}{\partial x}\frac{1}{\frac{\partial z}{\partial x}}+\frac{\partial f}{\partial y}\frac{1}{\frac{\partial z}{\partial y}}=\frac{\partial...
When I tried using the equations the only thing I could see is that it is impossible for such point to be an anti-node. In this case, how do I find the frequency? The answer is not even with the form of v*n/2L which is very confusing to me, I thought that the frequency of a standing wave must...
I thought I could start somewhere along the lines of ##\psi(x,t)= \psi(x,0)e^{-iE_nt/\hbar}##, but I'm not sure what ##E_n## would be.
I also thought about doing the steps listed below in the picture, but I'm not sure how to decompose ##\psi(x,0)## like it says to in the first step.
Any help...
I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant.
I recently watched a video by PBS infinite series...
I tried plugging Psi into the right of the Schrodinger equation but can't get anything close to the solution or anything that is usable. How should I solve this?
ANY AND ALL HELP IS GREATLY APPRECIATED :smile:
I have found old posts for this question however after reading through them several times I am having a hard time knowing where to start.
I am happy with the sketch that the function is correctly drawn and is neither odd nor even. It's title is...
For a specific wave vector, ##k##, the group of wave vector is defined as all the space group operations that leave ##k## invariant or turn it into ##k+K_m## where ##K_m## is a reciprocal vector. How the translation parts of the space group, ##\tau##, can act on wave vector? Better to say, the...
The solution for the wave equation with initial conditions $$u(x,0)=f(x)$$ and $$u_t(x,0)=g(x)$$
Is given for example on wikipedia : $$u(x,t)=(f(x+ct)+f(x-ct)+1/c*\int_{x-ct}^{x+ct}g(s)ds)/2$$
So a vibrating string, since there is no conditions on ##g## (like ##\sqrt{1-g(x)^2/c^2}##), could...
I was planning to find the value of N by taking the integral of φ*(x)φ(x)dx from -∞ to ∞ = 1. However, this wave function doesn't have a complex number so I'm not sure what φ*(x) is. I was thinking φ*(x) is exactly the same φ(x), but with x+x0 instead of x-x0.
Thank you
A composite object made of many atoms has a large mass hence a small de Broglie wavethength...and we know that recent experiments succeeded to obtain interference patterns even for such objects (for instance the C60 molecule). Did theoretician understood how a wavefunction with such a small...
Considering Bell’s theorem and the expected correlations between entangled particles or photons.
In a measurement setup e.g. Like Alain Aspect‘s with 2 entangled photons.
If we could make a setup that guarantees that the measurement on both photons is done at exactly the same moment, what...
By the time the gravity wave reaches us it is very small in energy, I assume. We do not know how to make gravity waves in a laboratory but we have a place where we have a very sensitive gravity wave detector. If we had a lab set up a few blocks away we might be able to do various experiments...
image due to graph, I tried to duplicate this sin wave on desmos but was not able to.
so with sin and cos it just switches to back and forth for the derivatives so thot a this could be done just by observation but doesn't the graph move by the transformations
well anyway?