Questions tagged [plane-wave]
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66
questions
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11 views
A parallel between eddy current and Beer-Lambert law
For AC current flowing in wire eddy currents are the reason for current density decay as we move towards the center.
Similarly, in Beer-Lambert law, for electromagnetic plane wave impinging on ...
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0answers
30 views
Acoustic Plane Wave
Consider an ideal fluid which we have a spherical object on it and a progressive plane wave is heading the object. I have a simple question and it is:
If we assume the amplitude of the incident ...
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0answers
12 views
Compute SH and SV component in shear wave (accoustics wave propagation)
I'm reading this guy right now. Basically I need to add to a ray tracing simulation components for shear waves propagation (in the acoustic/VHF range). Essentially this is related to section 1.2 of ...
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0answers
45 views
Rigorous plane wave expansion in QFT
I work with quantum field theory in curved spacetimes, so I'm not fully aware of the notation used in standard QFT. However, I'll try to make myself clear. In standard QFT, the one-particle Hilbert ...
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1answer
33 views
Behaviour at an interface plane wave
I have this example diagram that was given in one of my lectures and I am just going through what the equation given actually mean and calculating some results from the equation. Which are the angle ...
0
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1answer
44 views
Why is the electric field phase shifted in this circular plane wave?
The $x$-component of a circular polarized plane wave is
$$ E_x(\vec r,t)=E_0\cos\left(\frac{w}{c}(0.6y-0.8z)-wt\right) $$
With only this given, we can devise the total electric field as
$$ \vec E(\...
1
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1answer
46 views
Acoustics: Construction of the pressure field with transmitted and reflected plane waves
So I have been reading one of the papers about wave manipulation, which takes advantage of the phase shifted reflection by tailoring the design of the system. The design has two domains: air and foam (...
0
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1answer
41 views
Glint effect in electromagnetic waves [closed]
Two plane waves having the same frequency and different intensities:
$$E_0=Ae^{i(\omega t-kr_0)}$$ and
$$E_1=Be^{i(\omega t-kr_1)}$$
arrive at point $P=(x,y)$ from two point sources located at a ...
1
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2answers
39 views
Turning angles in Radio and Telephone [closed]
Radio waves and microwaves are usually plane polarised. This is why you can sometimes get a better signal if you turn a radio or telephone through different angles.Okay what happens when we turn a ...
3
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2answers
181 views
What does the spherical-harmonic notation $Y^{m}_l(\hat{\textbf{r}})$ mean, and how does it relate to the usual $Y^m_l(\theta, \varphi)$?
By using the plane wave expansion, the decomposition of stationary harmonic plane wave into partial waves can be given by
$$
e^{i\textbf{k}\cdot\textbf{r}} = e^{ikz} = e^{ikr\cos\theta} = \sum^{\infty}...
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0answers
22 views
Conservation law charge in plane-wave
When considering a charged particle in a plane-wave field, it is possible to show that the 2 following quantities are conserved
$\boldsymbol{p}_{\perp} - e\boldsymbol{A}_{\perp}$
and
$p_z - \gamma$
...
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3answers
162 views
Plane wave and polarisation
I am trying to understand the concept of a polarisation of a plane wave. Generally, the plane wave can be seen as a sum of two orthogonal linearly polarized waves. according to Wikipedia.
So I have ...
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0answers
26 views
What is the load reflection coefficient for a uniform plane wave travelling at the boundary between a dielectric and a perfect conductor?
Suppose you have a uniform plane wave travelling from a dielectric medium towards a perfect conductor (suppose the interface is planar as well).
From my understading of the theory behind EM waves and ...
1
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1answer
41 views
Plane wave propagation constants being equal across all components
Starting from the wave equation for electric field in free-space,
$$ \nabla^{2}\boldsymbol{E}+k^{2}_{0}\boldsymbol{E}=0, $$
where $k_{0}$ is the free-space wavenumber, we usually proceed in deriving ...
2
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2answers
50 views
Oscillations of plane waves
I am reading this notes on electromagnetism.
On page 25 it reads the following, about planes waves:
A plane wave propagating in the direction of z has no oscillations in
the transverse plane $(...
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1answer
91 views
Function expansion in terms of plane waves
I would like to expand a function $f(r)$ in terms of plane waves of the form $e^{ikr}$. With expansion coefficients $f_k$, one can write
$$ f(r) = \sum_kf_k e^{ikr}. $$
Now I need the coefficients $...
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1answer
253 views
The curl of phasor of electric field
Let the phasor electric field of a uniform plane wave be
$\vec{E_{0}}e^{-i\vec{k} .\vec{r}}$
where $\vec{k}$ is the wavenumber vector and $\vec{r}$ the position vector.
why is then,
$\frac{1}{-i\...
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1answer
812 views
What is the Fourier transform of an infinite integral of plane waves?
I'm trying to evaluate this double-integral in the context of Quantum Mechanics. Consider $f(x)$ as
$$ f(x) = \int_{-\infty}^{\infty} \mathrm{exp} \left( \frac{-ipx}{\hbar} \right) dp $$
So $\hat f(...
0
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1answer
456 views
What is the logic behind box normalization and periodic boundary condition?
Free particle energy eigenfunctions are $A\exp{[i(Et-\textbf{p}\cdot\textbf{r})/\hbar]}$ are non-normalizable. To normalize them one introduces a procedure called 'box normalization' where one imposes ...
2
votes
2answers
232 views
Proof of non-orthogonality E and H fields of an electromagnetic wave in certain materials?
I understand that electromagnetic waves must have orthogonal E and H fields in free space from Maxwell's third equation. However, I saw on a Quora post that these fields do not necessarily have to be ...
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1answer
529 views
Is a plane wave necessarily monochromatic?
Is the expression $$\psi(x,t)=A\exp{i(kx-\omega t)}, \hspace{0.3cm}A=\rm constant$$ the most general form of the plane wave?
If yes, does it mean that a plane wave is necessarily monochromatic?
If ...
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1answer
84 views
What are plane waves in Bethe ansatz
I study Bethe ansatz, although my background is mathematics not physics. Can somebody explain to me what is plane waves? I have seen in many papers this expression that "The idea of the Bethe ansatz ...
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0answers
365 views
Wave packets and the uncertainty principle
In my lecture course, I am told that a wave packet $\varphi$ is a superposition of plane waves such that $$\varphi = \int a(k) e^{ik-iw(k)t} dk$$ The function $a(k)$ is then linked to probability and ...
0
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1answer
79 views
Magnetic field of a plane wave hitting a conducting surface
If the $E$ component of a plane monochromatic wave does not penetrate the conducting surface, what happens to the $B$ component? The $E$ field gets reflected back because we are talking about a ...
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0answers
90 views
Null reflection coefficient in oblique incidence
A plane wave traveling in free space has an electric field phasor of
$$
\textbf{E}(x,y,z) = E_{0}^{+}( \textbf{u}_{x} - \textbf{u}_{y} + \textbf{u}_{z})\cdot e^{-jk_{0}(x\sin \theta + z \cos \theta)}
...
16
votes
3answers
924 views
What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?
I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form
$$f(x) ...
4
votes
3answers
11k views
Sinusoidal to complex form of wave equation
I know that a sinusoidal plane wave can be represented by the wave equation
$$ \psi (x,t)=A\, \cos(kx-\omega t) $$
I have also seen that a plane wave can be represented in complex exponential form as
$...
6
votes
2answers
342 views
Understanding the wave equation in 3dimensions
I am learning about waves and the wave equation in lectures, and there was something interesting my lecturer said which I have not been able to find about online or in a book.
With regards to the ...
0
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2answers
172 views
Wave packet expression
Speaking in general about plane waves propagating along $z$ (electro-magnetic waves, for example; not necessarily particles represented as waves), a wave packet can be defined as
$$A(z,t) = \int_{\...
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1answer
91 views
Solution of Dirac equation: arbitrary polarizations
In my lecture notes (signature $-+++$) we find the free Dirac equation solutions. We proceed in this way:
Dirac equation:
$$
(i\,\displaystyle{\not} p +m)\psi(x) = 0
$$
We make the following ansatz:...
-1
votes
2answers
31 views
What is the simplest way to see that this abstract plane wave is “traveling” at the speed of light?
In EMFT notation,
$$
{\bf E} = E_0 \sin(\omega (t - \sqrt{\epsilon_0 \mu_0} z)) \hat{{\bf a}}_x \\
{\bf H} = H_0 \sin(\omega (t - \sqrt{\epsilon_0 \mu_0} z)) \hat{{\bf a}}_y
$$
I am having trouble ...
0
votes
2answers
214 views
Electromagnetic fields in a cubical cavity
I'm trying to solve the standing electromagnetic modes in a cubical cavity problem without using separation of variables. The cube is a perfect conductor, and hence the boundary conditions are $E_{\...
1
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1answer
161 views
Non-plane wave solutions to Dirac equation?
Solutions to Dirac equation
$$(-i\gamma^\mu\partial_\mu+m)\psi=0$$
are usually obtained by acting from the left with complex conjugate Dirac operator
$$(i\gamma^\mu\partial_\mu+m)(-i\gamma^\mu\...
-1
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1answer
451 views
Polarization vectors
There is the known relation between circular and linear polarization bases:
$e_x = \{ 1,0,0\}$, $e_y = \{0,1,0\}$, $e_z = \{0,0,1\}$ and $e_{\pm} = \frac{1}{\sqrt{2}}(e_x \pm ie_y) = \frac{1}{\sqrt{2}...
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3answers
244 views
Describing travelling waves carrying energy from one point to another
A simple harmonic wave in one-dimension (for simplicity) $y(x,t)=A\sin(\omega t-kx)$ in a medium is often presented as an example of a travelling wave. But such a plane wave is infinitely extended ...
2
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0answers
409 views
Can d'Alembert's Formula for the Wave Equation in one dimension (1+1D) be used in three dimensions (3+1D)?
The 3+1D wave equation for spherically symmetric waves is
$$\frac{\partial^2 u}{\partial t^2} = c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right) $$...
2
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1answer
542 views
Physical intuition on the integral contained in D'Alembert's Formula for the wave equation
If $\phi(t,x)$ is a solution to the one dimensional wave equation and if the initial conditions $\phi(0,x)$ and $\phi_t(0,x)$ are given, then D'Alembert's Formula gives
$$\phi(t,x)= \frac 12[ \phi(...
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0answers
159 views
Normalize plane wave on an infinite domain.
I need to make an exercise related to quantum mechanics. (Specifically I need to apply Fermi's golden rule where the initial and final states are both plane waves).
The system is 1 dimensional, ...
2
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2answers
235 views
A general complex electric field
When dealing with a plane wave solution to the electric field such as
$$\vec{E}(r,t)=E_{0}\cos(kz-\omega t+\phi)$$
we usually introduce a complex electric field $\tilde{E}(r,t)$ such that $\vec{E}(r,t)...
0
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1answer
289 views
What happens when two polarized lights of the same wavelength interfere at 90 degrees with each other?
am I right in assuming that if I cross two polarized lights of the same wavelength the result would be destructive interference?
I don't mean 90 degrees as in 'orthogonal polarization', but the two ...
1
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1answer
127 views
Why doesn't the expectation of position for a plane wave obey kinematics?
Consider the plane wave:
$$\Psi = Ne^{i(\vec{p}\cdot\vec{r} - Et)/\hbar}$$
with N is the normalisation factor.
The expectation value of momentum for this wave is:
$$\begin{align}
\langle\vec{p}\...
1
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1answer
89 views
Uniform Plane Question [closed]
Question:
Communicating with submarines is very challenging due to the fact that seawater is a conductor (conductivity of roughly 5 S/m). This conductivity indicates that electromagnetic waves do not ...
0
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1answer
176 views
Pulsed plane wave
My question is specifically concerned with ultrashort pulses: can a plane wave (one with infinite spatial extension) have a finite duration in time? Is there some physical principle that is violated ...
2
votes
3answers
716 views
How can pressure and velocity fluctuations in acoustic plane waves be in phase and still hold to the B.C. that velocity must be zero at a solid wall?
In linear plane-wave acoustics (no mean flow, small perturbations, etc.), it is often derived that the phase of a traveling pressure fluctuation wave and a fluctuation velocity wave are the same. For ...
1
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1answer
193 views
Poyting theorem for a plane wave
I would like to apply and verify the Poynting theorem for a uniform plane wave but there is obviously something wrong in my demonstration.
The Poynting theorem expresses the conservation of energy: ...
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0answers
74 views
Electric field operator in 2D geomatry
In the free field (3D), transverse electric field operator is given by the below expression;
$$e^{\bot}(\textbf{R}) =i \sum_{\textbf{p},\lambda}\Big( \frac{\hbar cp}{2V\epsilon_{0}}\Big)^{1/2} \{e^{(\...
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0answers
57 views
Plane wave conditions
Which conditions have to be fulfilled in order to approximate a light beam by a plane
wave (i.e. $\phi(x)\approx \phi(0)e^{ikx}$)?
I am looking for both mathematical and experimental conditions. At ...
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1answer
1k views
Understanding wave packets, in particular matter waves, dispersion and point particles
Here is what I have gathered so far:
Particles like an electron (i.e. with rest mass) can be represented as matter waves (deBroglie).
The matter wave of a particle can be modelled a wave packet.
A ...
7
votes
3answers
859 views
The ubiquitous Planewave Ansatz
In physics, the planewave ansatz (meaning: an educated solution guess) is very ubiquitously used, when solving differential equations, in different domains of physics. E.g. to solve the dispersion ...
1
vote
2answers
133 views
Importance of the $\exp (i \bar{k} \cdot \bar{r})$ part of the plane wave equation
I am having trouble grasping how the equation
$\bar{E} \left( \bar{r}, t \right) = \bar{E}_{0} \exp \left[ i \left( \bar{k} \cdot \bar{r} - \omega t \right) \right]$
fully describes a plane wave.
...
