Dispersion refers to the frequency dependence of the properties of a wave.

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Equations of motion of displacement field

We have an action: $$S[\boldsymbol{u}] = \frac{1}{2} \int dt \int d^3x \left\{ \mu (\frac{\partial u_{i}}{\partial t})^{2} - \nu (u_{ii})^{2} - \rho(u_{ij})^{2}\right\} $$ Where $u_{ij} = (\partial_{...
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Why are the harmonics of a piano tone not multiples of the base frequency?

I was trying to figure out which piano keys were being played in an audio recording using spectral analysis, and I noticed that the harmonics are not integer multiple of the base note. What is the ...
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Why do some types of waves disperse?

We know that some mediums/waves are non-dispersive such as air for sound waves, and waves on a string. But, why do some waves, for example deep water waves, disperse? I am trying to understand the ...
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Is dispersion a property of medium or wave

I got a problem in learning Lewin's 'Vibration and Waves'. He first solve the eigenvalue of 5 beats connecting together and with fixed boundary condition. Then the velocity for different modes are ...
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trouble calculating dispersion curve for TE Mode symmetrical step-index waveguides

I'm trying to work on a problem where I'm needing to show the dispersion curves for a slab waveguide. I'm given the refactive index of the core, $n_1$, the refractive index of the cladding, $n_2$, the ...
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Dispersion relation for lattice vibrations: Why are there two and not four solutions?

A linear chain of diatomic molecules can be modeled by a chain of molecules with different spring constants $C_1$ and $C_2$ (See Figure) The corresponding equations of motion are: $$M\ddot{u}=-c_1[...
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Why can the dispersion relation for a linear chain of atoms (connected by springs) be written as $\omega(k)=c_s \lvert k\rvert$?

On the german wikipedia site (right under "Akustische Moden"), the dispersion relation for a linear chain of atoms (connected by springs): $$\omega(k)=2 \sqrt{\frac{K}{M}} \left \vert \sin{\frac{ka}{...
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Critical Value for Dispersion of light [closed]

If there is a ray of light moving from $n_1$ to $n_2$ you can get dispersion if $n_1$ is a function of wavelength. What angle of incidence ($\theta_1$) will maximise the dispersion? My solution so ...
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Is speed of sound really constant?

Does not speed of sound actually depend on the frequency and/or amplitude of the waves? If so, why it is constant?
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Dispersion Relation for Convective Wave Equation

The convective wave equation governs the propagation of sound in the presence of mean flow: $$ \frac{D^2p'}{Dt^2}-\bar{c}^2\nabla^2p'=0 $$ or, expanded out: $$ \frac{\partial^2p'}{\partial t^2}+2\...
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Interpreting group velocity of free particle wave packet

I am trying to understand the concept of group velocity of a free particle wave packet: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
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Non-linear waves and shock formation

In the cases of non-linear acoustics, why is shock formation unlikely when the dispersion is strong when compared to the non-linearity of the wave?
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Derviation of group velocity

I am working thru a derivation of the group velocity formula and I get to this stage: $$y=2A\cos(x\frac{\Delta K}{2} -t\frac{\Delta \omega}{2})\sin( \bar k x-\bar \omega t)$$ Then all the derivations ...
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What makes a wave dispersive?

Water waves are dispersive ( longer wavelengths travel faster ) but sound waves in air are not, otherwise we would listen first the high frequencies and the low frequencies after. What decides if a ...
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Why do water waves with longer wavelengths travel faster?

When wind blows over the sea, it excites a range of wavelengths. Why do longer wavelengths travel faster?
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Where can i find the complex index of refraction in the radio spectrum for aluminium?

I am looking for the (complex) index of refraction or the dispersion relation of aluminium for frequencies/wavelengths roughly between 30Mhz/10m and 30GHz/1cm. I have found a few sources that give ...
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Why does my wooden door disperse light into a rainbow color spectrum?

On a clear morning, light comes through this window (viewed from the inside) It then hits the door on the opposite side (so viewing from the outside the door straight on the other side) There is ...
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Interpretation of dispersion relation

In my research, I found that my system has the following dispersion relation: $$\omega^2=k^2+k_0^2\ , $$ where $k_0^{-1}$ is an intrinsic lengthscale of the system and the units are chosen so that the ...
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Amplitude-Modulated Wave in a Dispersive Medium

Amplitude-Modulated Wave in a Dispersive Medium. An amplitude-modulated wave with complex wavefunction $a(t)=[1+m\cos(2\pi f_st)\exp(j2\pi\nu_0t)$ at $z=0$, where $f_s\ll\nu_0$, travels a distance $z$ ...
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Dispersion of light through a prism but not through glass or lense

Why does dispersion happen in prisms but not in glasses nor lenses? I need a detailed answer please!
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294 views

Density of states for graphene

I have seen a lot of plots for the density of states for graphene: but have been unable to find the calculation explicetely. I know the dispersion relation for graphene is $E_{\pm} (\textbf{k}) =\...
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Why rainbows form around flashes?

I read that to see a rainbow, your back must be towards the sun, and you have to look at roughly 42 Degrees from the imaginary line to spot the red band. But many times, me and many of my friends see ...
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Third-order dispersion in glass, direction influence

I have learned that the third-order dispersion $\chi$ is a tensor with 81 elements. Nevertheless in glass one only has four elements, which either can be $x$ or $y$ (in this case). Now there exist ...
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Derivation problem of second dispersion constant

According to "Nonlinear fiber optics" from Agrawal the mode propagation constant $\beta = n\cdot\frac{\omega}{c}$ can be taylored into $$\beta = \beta_0+\beta_1(\omega-\omega_0)+\frac{1}{2}\beta_2(\...
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Intuition behind Airy waves dispersion relation

Using Airy wave theory, one can derive the dispersion relation of water waves (under some physical assumptions): $$ \omega^2 = gk\tanh{kh} $$ where $k$ is the wave number, $h$ the distance from the ...
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What's the microscopic and macroscopic effect of wavefunction dispersion?

In Quantum Mechanics (Merzbacher 2nd ed.), problem 2.1 asks us to derive the time evolution of a one-dimensional Gaussian wavefunction (formula given for $t=0$), assuming the velocity is in the $+x$ ...
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What happens to the group and phase velocity of light as it travels through a medium?

We have all been told that when light travels from, say, a vacuum through water it slows down. What I want to know is what happens to its phase velocity and group velocity. Refractive index is $n = \...
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Derivation of group velocity using Fourier transform

The aim is to determine the group velocity of a wave packet with the general form $$\Psi\left(x,t\right)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \phi\left(x\right)e^{i\left(kx-\omega t\right)}dk....
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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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56 views

Dispersion relation from Hamiltonian

Note: This is obviously for homework so I'm not asking for the answer to be spoon fed, I'm just not understanding the steps I have to take. I have a fairly simple Hamiltonian for a ring tight binding ...
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entropy and dispersion

If I know the positions and the speeds of each particle in a box over the time, how can I compute the entropy ? (I`m making a simulation where I want to show that the disperion of the particles over ...
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How do chirped mirrors compensate dispersion?

How do chirped mirrors compensate dispersion? I understand that if you have longer wavelengths penetrating deeper into a chirped Bragg stack, then there will be some anomalous dispersion because the ...
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What experimental evidence shows that sound velocity is the same for all wavelengths?

I'm studying sound waves with Halliday's book, and after reading the whole chapter, one of the questions suggested was: What is the experimental evidence that allows the assumption that the sound ...
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Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
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Density of States in NOT Free Electron Gas

I think that I understand how the density of states works for a free electron gas. It is effectively just a conversion factor between summing over values of k and integrating over values of E. If you ...
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determination of electron dispersion curves

I am somewhat new to quantum physics and I am studying electron dispersion band structures of SiC like the one here I want to know what spectroscopic techniques/methods or if they are spectroscopic ...
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Dispersing ultrasound in a tube - patters

I am looking for patterns (Surface texture, inserted material, grooves, spirals, elasticity of materials etc) to efficiently disperse reflected ultrasound in the range of wavelengths 1mm to 4mm within ...
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Dispersion for a highly energetic electron

The dispersion relation can be expressed as: $$w=\frac{\hbar k^2}{2m}$$ The energy of a free particle is: $$E=\sqrt{p^2c^2+m^2c^4}$$ For a highly energetic electron we have $E\approx pc.$ The ...
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Is $E=\hbar \omega$ correct for massive particles?

From Planck's relation we can say that the energy of a photon is $$E=h\nu=\hbar \omega \, .$$ where $\hbar \equiv h / 2\pi$. On the other hand, the energy of a free particle can be expressed as $$E=...
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Silicon parabolic dispersion for X minima

I am constructing a minimal model of the silicon conduction band minima for a monte-carlo program. Assuming the six equivalent bands are parabolic and spherical, since the conduction band minima lie ...
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Why is rainbow always circular?

From the article that I read on physics classroom website on rainbow, rainbow is formed with red on the top and violet on the bottom because violet refracts more, and has a smaller angle of deviation ...
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Refraction of white light through a glass slab: what does it actually look like?

When a collimated beam of white light enters a rectangular prism, it develops slightly coloured edges due to the dispersive refraction of the glass: each ray in the beam is displaced differently ...
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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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PDE from dispersion relation?

Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, $\omega=i\...
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About light nature [closed]

I have some particular questions about the nature of light...cause all I know from all sources is that it is a wave and a particle and stuffs, but if light "COMES" from all directions, and is in every ...
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Periodically connected QHO's

I've recently been thinking about what happens when you connect quantum harmonic oscillators in a periodic way. I'm actually thinking about when you take a mass-spring system (which can easily be put ...
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Constructing a dispersion relation from the Hamiltonian

I'll begin by saying that I'm not entirely clear on if this is possible. I have a Hamiltonian of the form $$ \left( \begin{array}{cccc} \text{$\omega $1} & \text{J12} & 0 & \text{J14} \\ ...
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Maxwell Equation in dispersive media Griffiths

I am wondering where is the following equation (9.162) of Griffiths Electrodynamics 4e from? $$ \nabla^2\tilde{E} = \tilde{\epsilon}\mu_0{\partial^2\tilde{E}\over\partial t} \tag{9.162}$$ I know ...
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What is the difference between dispersion and diffusion?

What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of ...
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Question about group velocity and travelling waves

I'm trying to learn some basic quantum mechanics and I have a question related to group velocity of a travelling wave. I know there are already a few questions related to group velocity, but I couldn'...