Waves are disturbances that propagate through space and time. Classically, they travelled through a medium, disturbing the particles but not changing their mean position. Electromagnetic waves/particle-waves need no medium; they are disturbances in their respective fields.

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Physical intuition for the solutions of the wave equation

I have been studying the wave equation in $\mathbb{R}^n$ for the cases $n=1,2$ and $3$. In the three cases, working all over $\mathbb{R}^n$. That is: $u_{tt}(x,t)=c^2 \Delta_{x} u(x,t)$ for $x \in ...
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192 views

Numerical Solution of the Propagation-Dispersion equation

I have asked this question on Computational Science and also on Mathoverflow, but no satisfactory answers so far. I thought maybe the physics community could shed some insight on the issue. I am ...
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76 views

How to calculate dispersion relation from a Finite Difference (FD) wave simulation

I have a python code that calculates the solution of the inhomogeneous acoustic wave equation for a 2D medium with any velocity and source configuration. It was implemented using Finite Differences ...
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144 views

The logarithmic decay of WIFI

I have been told that Wi-Fi, LTE etc signal strength fall of as $$\propto \frac1{\log(r)}$$ where $r$ is the distance. I am wondering why this is. I better explain what I mean with this question. ...
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93 views

What's the difference between exchange spin wave and magnetostatic spin wave?

So far I've heard of three kinds of spin waves Magnetostatic spin waves (MSW) Dipole-exchange spin waves (DESW) Exchange spin waves (ESW) What's the difference?
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45 views

Proof that fixed points of a null field are zero

Suppose we have a scalar field $V$ (which can be acoustic pressure, or a scalar electric potential) that is a solution of the wave equation $$\Box V(x,y,z,t) = 0$$ I am wondering if a fixed (non-...
3
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68 views

Linear KDV eq. asymptotics

The question arises from the book Solitons by P. G. Drazin about the linearized KDV eq. $$ u_t+u_{xxx}=0 $$ My first step was to take a Fourier transform of the equation, find that the dispersion ...
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47 views

Boundary conditions for enthalpy waves inside a pipe

So I'm trying to solve a form of the wave equation for sound produced by a vortex distribution $\vec{\omega}$ convecting at velocity $\vec{v}$ . $$\left(\frac{1}{c_0^2} \frac{\partial^2}{\partial t^...
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52 views

Mechanical waves edge between material and vacuum

I have been thinking about the propagation of EM waves vs. mechanical waves and some of their odd cases. One such case that I haven't been able to puzzle out is what happens when a mechanical wave ...
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75 views

What happens to Newton's Third Law during the reflection of a pulse from a free end?

Well, it is known that a pulse gets inverted when it gets reflected from a fixed support while the polarity of the pulse remains same when the incident pulse gets reflected from a free end. However, ...
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44 views

Distinguishing transverse and longitudinal from wave equation

Can we distinguish if a general wave or disturbance $f$ (not necessarily electromagnetic) which satisfies the wave equation \begin{equation} \frac{1}{v^2}\frac{\partial^2 f}{\partial t^2} = \frac{\...
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37 views

How efficient is the forward transfer of energy in gravity (surface) waves?

Ocean waves (properly categorized as gravity waves since gravity provides the restoring force within the medium they travel) propagate the major part of the energy derived from winds along the air-...
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87 views

What criterion did Abbe use?

For a microscope (correct me if I am wrong) the Rayleigh Criterion gives us: $$ R=\frac{1.22 \lambda}{NA_{condenser}+NA_{objective}}$$ But with the Abbe diffraction limit: $$ R=\frac{\lambda}{NA_{...
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102 views

Diffraction grating from first principles

I have realised that a lot of books and online resources fail to give a detailed treatment of the derivation of the diffraction grating interference pattern. Normally only the result is stated. I was ...
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44 views

Ray tracing a three-way intersection

I've been studying ray tracing in media with linear velocity-depth functions. One of the key concepts I've come across is the ray parameter, and in particular the idea that the ray parameter is ...
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141 views

Direction of particle's vibration.

I have seen a question related to the the direction of the vibration when a wave moves. I see there two opposite picture that represents contradictory notion of getting the accurate direction of the ...
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564 views

How to calculate the dispersion relation for a wave equation with non-constant speed of wave propagation?

Specifically, it is a one-dimensional wave equation for waves on a string with a non-constant cross-section, i. e. $$S(x)=S_1+S_2 \cos{2x}; \qquad c(x)=\sqrt{F/\rho\, S(x)}.$$ Separating the variables ...
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44 views

Normal modes of two wires fastened together

The problem is to find the normal frequencies of the system formed by two fastened wires of length L, and different mass per unit length. I already wrote the boundary conditions, but I need to know ...
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70 views

What is the longest distance over which echolocation is effective?

Some animals, most notably bats, use echolocation in order to navigate and detect the location and size of objects and prey. This usually takes place over short distances. What are the theoretical ...
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224 views

Constructive and destructive interference in De Broglie matter waves

I'm a little confused about matter waves and especially interference. $\lambda = h/p$ The denominator is momentum and is thus reliant on mass. If we assume that the property holds for particles ...
2
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103 views

What could be the distribution of an explosion energy of a mining-grade and seismic exploration explosives?

Seismic exploration involves the excitation of seismic waves using the industrially made explosive charges. What could be the distribution of explosion energy of such a charges? My guess is that it ...
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1k views

Chladni Plate Mathematics

I am a high school student doing an IB Extended Essay investigation concerning the resonant frequencies of Chladni plates of differing materials and sizes. Would someone please explain the definition ...
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1k views

The physical meaning of electromagnetic wave

What, fundamentally, is an electromagnetic wave? As far as I know, all wave phenomena are derivations of an oscillating processes, e.g. particles vibrating in a medium. I can't imagine a wave process ...
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154 views

Classical wave equation from fermions

Every time there is a classical wave equation, the underlying system is bosonic. For example, em waves are made from photons, sound from phonons (technically quasi-particles), etc. What would be the ...
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58 views

Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly ...
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234 views

Fourier Transform of ribbon's beam Electric Field

I have a monochromatic ribbon beam with $E(x)e^{i(kz-\omega t)}$ being the electric field's amplitude. I want to show that the lowest order approximation in terms of plane waves is $\mathbf{E}(x,z,t)=...
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174 views

Physical difference between two different attenuation coefficient functions

The attenuation of a wave through a medium can be modeled by the Beer-Lambert Law using an attenuation coefficient. If $I$ is the intensity, and $I_r$ is a reference intensity, then what is the ...
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106 views

Can we compute the magnitude of the stress caused by sound waves on a wall?

As a follow up to this question, Could we really compute the magnitude of the stress caused by sound waves on a wall? If so, How do we do that?
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98 views

After quantization of electron vibrations, do we need electrons anyway?

The title question is not ment in a general context, but one in which goes to the plasmon theory. In that case, how is are the statistics (boson vs. fermions) of plasmons determined? And is there an ...
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106 views

Can D'Alembert's Formula for the Wave Equation be used in Three Dimensions?

PART A) The 3D 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} \...
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34 views

Why does the amplitude of the pulse never return to its original value when the number of waves used to construct it tends to infinity?

I was reading Constructing a pulse of Modulations, Pulses, and Wave Packets from Waves by Frank S. Crawford Jr. ; here, in the following concerned excerpt, the author is describing of constructing a ...
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39 views

Nonlinear Saturated Schrodinger Equation in 1D- Physical Models

I'm studying the Nonlinear 1d Schrodinger equation $$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$ and specifically, its solitary ...
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25 views

Standing waves on compound string

Please help with this question - No data is given as such. The 2 strings have different thickness. Initially, minimum frequency of the thick string is 120 Hz. Then if we push the cart such that only ...
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64 views

Is there any solution manual to A.P. French's 'Vibrations and Waves'?

I'm trying to work through A.P. French's Vibrations and Waves. Unfortunately, I can't check the details of my solutions since the solutions aren't given with the textbook. Does someone know where I ...
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66 views

Meaning of a Dirac delta speed in 1d shallow-water equations

A 1d thin layer of a fluid of constant density in hydrostatic balance can be modeled by shallow-water equations: $$\begin{align*}\partial_tu+\partial_x\left(v+\frac{u^2}{2}\right)&=0,\\ \...
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34 views

How is the Rayleigh criterion connected to the Abbe limit

I am interrested whether one can derive a formula for the point resolution (like Abbe did) of an optical system from the Rayleigh criterion (without the use of small angle approximation i.e. $\rm{sin}(...
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68 views

advantages/disadvantages of a cylindrical microwave oven cavity in comparison to a rectangular cavity

Why are rectangular cavities preferred for standard microwave ovens with a frequency of 2.45 Ghz? What is the reason that you can hardly find a circular cavity? What are the disadvantages of ...
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25 views

How does a linearly polarized spin 1/2 wave look like?

Spin 1 waves are easy to illustrate and a linearly polarized spin 2 wave looks like this, but what is the counterpart for a spin 1/2 wave?
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36 views

Is disturbance propagation velocity equal to wave velocity in a solid body?

How do the disturbance propagation velocity and wave propagation velocity relate to each other? To explain my question in details I will describe the following situation from the theory of acoustic ...
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39 views

Photon transmission

I want to know exactly how light travels. Are each photon in a light beam traveling in a cosine function? I'm confused because only when it goes through polarization that it starts to show this type ...
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43 views

Mechanical energy in an harmonic wave and in normal modes

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while ...
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29 views

What is the highest frequency for ripples on water

I want to transmit sound vibrations as ripples on water, as an experimental audio delay effect. Can I make ripples at audio frequencies, that will travel over about 10cm or more? How about other ...
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18 views

Scale analysis for the vertical component of the Boussinesq equation to obtain a complete hydrostatic relation

This is actually an exam question which i have been trying to solve for my studies. Consider the Boussinesq vertical equation: \begin{align} \frac{\partial \widetilde{w}}{\partial t} = - \frac{1}{\...
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32 views

Standing Waves in a String of two Linear Densities

Given a string with sections of two linear densities like this: Does the point where the two linear densities meet have to be a node if a standing wave is produced? Are there alternatives? Could I ...
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24 views

Standing waves arbitary frequency

Suppose I have a string that is fixed rigidly at one end. Now when I start making wave, it will get reflected and should lead to standing waves (Mathematically and by visualization), but then we have ...
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30 views

1D transmission lines wave equation solution

you may know that the solution of 1D wave equation by d’Alembert is F(x-ct)+F(x+ct) and my question is that like is this F(x-ct) at transmission lines only the equation of one forward going wave that ...
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32 views

Energy and power in a travelling sinusoidal wave

This stuff is driving me crazy. Here: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/AnalyzingWaves.htm I found that the average kinetic energy per unit length is: $$ \frac{1}{4}\mu \omega^...
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37 views

How to arrange a 3d cymatics experiment?

Various researchers have filmed levitating polystyrene using sound waves. If i were to take 3 speakers and attempt to visualize the standing wave fields formed by the three speakers, how would i do ...
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52 views

WHY do waves diffract - what is the mechanism behind the diffraction?

Having recently studied wave diffraction at an introductory level, I don't feel that I understand why waves diffract like they do. What is it about the obstacle or the waves interaction with it which ...
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85 views

Can TE and TM modes propagate together in a waveguide?

I recently came to understand the TE and TM modes. As it is defined that E=0 for transverse electric and vice-versa. I have a few basic questions in mind which I thought to ask in one thread only. Q....