Questions tagged [dispersion]

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

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Difference between second and zeroth sound?

As I understand it, be it liquid helium or phonons in a solid, one can define the second sound and zeroth sound as quantum mechanical effects where heat propagates as a wave. These effects are ...
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Free acoustic phonon propagator

For fun I am trying to find the propagator of a free acoustic longitudinal phonon, using the vectorial displacement field. The Hamiltonian for our system is $$ H_0 = \sum_{\vec{q}} \omega_{\vec{q}} ( ...
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Group index derivation issue [closed]

How do I derive the expression for the group index $N_g$ as below $$N_g=n-\lambda\frac{dn}{d\lambda}$$ using the Cauchy dispersion relation below? $$n=n_{-2}(hf)^{-2}+n_0+n_2(hf)^2+n_4(hf)^4$$
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Complex $\Phi$ to prove the group velocity of a wavepacket

I am reading a lecture note (author: Pr. Barton Zwiebach from the physics department of M.I.T., Course: 8.04 'Quantum Physics I', title: de Broglie Wavelength and Galilean Transformations, Phase ...
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Dispersive wave and wavelength

Suppose that we have a dispersive medium, for which it is established that $$\frac{\omega}{k\sqrt{1+a^2k^2}}=v.$$ That tells us that if $a>1$ then as the frequency of the wave gets higher and ...
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Dispersion of $E$ and $p$

Is the dispersion of $E = c$. dispersion of $p$? Following that: $\begin{aligned}E^{2}=c^{2}p^{2}+m_{0}^{2}c^{4}\\ \Delta E^{2}=\Delta c^{2}p^{2}\\ 2\Delta E=2\Delta c^{2}p\\ \Delta E=c^{2}\Delta p.\...
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Paradox of light passing through prism and glass slab

When white light passes through a glass slab, Newton's assumption is that a slab is made of 2 glass prisms placed in opposite direction, such that dispersion of both is cancelled out and a white light ...
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Can X-rays travel quicker than visible light in a medium?

I have seen while reading a few books that the refractive index depends on lambda as follows by the Cauchy equation. $${\displaystyle \eta(\lambda )=A+{\frac {B}{\lambda ^{2}}}}$$ From this, the book ...
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Why is the first tsunami not always the largest?

Why is it that very often, the first wave in a tsunami is not the largest? Since the period of tsunamigrnic events are usually shorter than the period of s tsunami wave, it would seem more logical ...
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How does a rainbow show all of its colours?

My question is tied closely to this one, asked a while back on the website. As far as my understanding goes, a rainbow is formed by sunlight undergoing two refractions and a reflection inside ...
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From discrete to continuous superposition of waves, what happens to omega?

The Wikipedia page on group velocity uses the superposition of two cosines (of slightly different wavenumbers and angular frequencies) to show that group velocity $v_g = \frac{d\omega}{dk}.$ The sum ...
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Why is the refractive index of blue light larger than red light in water while the refractive index of radiowaves is larger than both?

So I thought the reason why radio waves have a relatively high refractive index in water is because they have a low frequency which increases the permittivity, but blue light that has a higher ...
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Some confusion on group and phase velocity of a general wave group

While discussing a wave group, it has always been turned up as taking only two waves of different $k$ values, the resultant being a composition of a wave of larger $k$ modulated by an envelope of ...
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Is frequency inversely proportional to wavelength Squared?

In our QM intro class our professor was introducing us to concepts of energy, momentum, frequency, wavelength etc of photons an electrons, On one side of the board he had the various expressions for ...
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Why exactly do higher frequency (>240 Hz) sounds on Mars travel ~4% faster than lower frequencies? What's the physics and are there optical analogies?

SciTech Daily's April 1, 2022 Variable Speed of Sound on Mars: What Sounds Captured by NASA’s Perseverance Rover Reveal About the Red Planet says The result of the recordings: a new understanding of ...
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Issue with $2\pi$ in exchange-dominated dispersion relation

Suppose I have a dispersion formula given by: $\omega = \frac{2\gamma A k^2}{M_s}$, where $\gamma$ is the gyromagnetic ratio, $A$ is the exchange stiffness, $k$ is the wavevector, and $M_s$ is the ...
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On slip factor and the like in particle accelerators

Citing Wikipedia: The momentum compaction or momentum compaction factor is a measure for the momentum dependence of the recirculation path length for an object that is bound in cyclic motion (closed ...
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Why does not the speed of sound in air depend on frequency and wavelength? [duplicate]

I have read that speed of longitudinal waves depends upon the frequency and wavelength and, but why it doesn't happen with sound waves in air? And if velocity of sound doesn't depend upon the ...
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Dispersion laws

I am studying the dispersion law of the pressure $p(t)$ in order to obtain the wavenumber from the frequency. In particular I am studying a discrete signal $p(t_{j})$. Once I have done the spectra $p(...
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Difference between wavelengths relation to frequency and period relation to frequency

I know that: $\frac{1}{T} = f$ For some oscillation or sinusoidal wave. For instance, a period of 2 has a frequency of 1/2 And, in the physics I have taken the formula would be like the one given ...
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How to build numerically a dispersion relation of a finite phononic system?

I have doubts about how to build the plot of dispersion relation for a general finite phononic system, in particular spring-mass systems. Eqs of any of these systems can be written in matrix form as $$...
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How to calculate group and particle velocity given wave function?

Suppose you are given a wave function $\psi(x, t) = C\exp(i(kx - \omega t))$; how can you calculate the group and particle velocity? My intuition was to use group velocity: $v_g = \frac{\partial w}{\...
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$E$-$k$ diagram of valence band

Why is that the E-K diagram of the valence band is bending downward? Namely, why is that the E (energy) of valence band is Ev '-' kinetic energy while the E (energy) of conduction band is Ec '+' ...
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Why is the relation between voltage ratio and frequency a linear one in a lumped transition line?

In an experiment the cutoff frequency of a lumped transmission line is determined by measursing the ratio of the output/input voltages. The lumped transmission line is a ladder network of 40 ...
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Why is a cavity's free spectral range determined by the group refractive index?

Many sources including Wikipedia and others give the free spectral range of a resonator as a function of the group refractive index $n_g$ by $$ \Delta \nu_{FSR} = \frac{c}{2 n_g L}. $$ I have a hard ...
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Is low frequency sound slower (in air)?

Does sound in air experience dispersion? In other words, is the group velocity of sound higher for higher frequencies or the other way round? Is this difference substantial enough to be noticed/heard? ...
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Two waves having same wavelength

Is it possible for two wave to have same wavelength but different speed and frequency? According to $C=λ×f$, if wavelength is constant, then frequency must be proportional to speed. My explanation is :...
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Is the phase velocity infinite for a matter wave with group velocity zero?

The Wikipedia article on matter waves describes the dependency between phase velocity $v_p$ and group velocity $v$ as $$ v_p = \frac{c^2}{v} $$ So for group velocity $v=0$ the phase velocity is ...
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De Broglie relations use which frequency or frequencies of a wave packet?

The Wikipedia article about matter waves lists the De Broglie relation for the frequency $f$ of a matter wave as $$ E = hf = \hbar\omega $$ with Planck constant $h$, total energy $E$ and angular ...
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Peskin and Schroeder, velocity $v=\frac{k}{E}$

On page 105 of Peskin and Schroeder equation 4.77 page 105, Peskin and Schroeder says the velocity $v_A$ is given by $$v_A=\frac{k_A^z}{E_A},$$ can someone please explain to me why this is true? Here $...
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Why does the light passing through a prism get bent in the same direction twice?

Whenever I see a 2D drawing of dispersion occurring when light travels through a solid prism, I see the rays get bent downwards on entry and downwards on exit again. For example here: https://www....
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Non-dispersive magnetic medium

I am aware of how we define a dispersive and a non-dispersive medium. In my script the following is said: "Most media are not magnetically dispersive." What it is meant with that? What does ...
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Dispersion relation for a lattice: Why the optics branch disappear?

I have a linear chain of two atoms type connected by springs and a lattice's constant $a$. Let said that mass is $m_1=m_2=m$ and the spring's constant $C_1$ and $C_2$. I have found the dispersion ...
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Minimal frequency of unspecified drum

I was given the following wave function, related to an unspecified drum: $$\frac{\partial ^2Ψ}{\partial t^2}=c^2 \left ( \frac{\partial ^2Ψ}{\partial x^2} + \frac{\partial ^2Ψ}{\partial y^2} \right )-\...
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de Broglie wavelength ignores rest mass?

The de Broglie wavelength for matter is mimicking how light is treated i.e. $$E=hf=\frac{hc}{\lambda}$$ and $$E^2=m_0^2c^4+p^2c^2\rightarrow E=pc$$ give $$\lambda=\frac{h}{p}.$$ The matter wave ...
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Question regarding the intution behind Group and Phase velocity

I can't understand the proper idea behind Group and Phase Velocity. I don't get it as clearly as I would like. I want the intuition behind it. Phase velocity $v_p$ is given by $\frac{ω}{k}$, This ...
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Understanding radiation pressure

I've been told that the radiation pressure of light can be understood(?) by considering a charged particle as a damped driven harmonic oscillator where the forcing term is the electromagnetic field, ...
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What do you mean by non-radiative surface plasmons?

I would like to know if anyone can tell me what we meant by non-radiative Surface plasmons, when we look at the dispersion relations?
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What are s-bands and d-bands in band structures?

Given a band structure diagrams I can understand whether there are band gaps and what the bands are but what are s-bands and d-bands and how do I tell them apart in these diagrams? Example: I ...
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How to compare effective masses in band structures?

As far as I know the effective mass in Solid State Physics is determined by inverse of the slope of dispersion relations (in band structure diagrams). \begin{equation} m^*=\frac{\hbar}{\frac{d^2\...
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Can "bare" TO phonons in polar materials exist by themselves, or are they always phonon-polaritons?

We know that transverse optical (TO) phonons in polar crystals couple to light strongly and can form hybrid light-matter quasi-particles called phonon-polaritons (solid lines in the figure below). My ...
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QUESTION: why the the refractive indices of dispersed phase and dispersion medium differ greatly in magnitude for colloids (in Tyndall effect)?

I am JEE student in India and while I'm reading my chemistry book (NCERT class12), there mentioned a point that "the refractive indices of the dispersed phase and dispersion medium differ greatly ...
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Dispersive media, imaginary velocity

In a dispersive medium we ave usually 2 dispersion laws: One that relates frequencies and Real Wavenumbers; One that relates frequencies and Imaginary Wavenumbers; With 1. I can find group and phase ...
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Is photon quantum linear polarization dispersive in media-free space propagation?

Identical photons having an ideal single frequency and phase are passed through a real physical / non ideal linear vertical polarizer. Let the photon quantum polarization state, ψ(φ), at the output of ...
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Why glass slab don't show dispersion as prism does?

Why glass slab don't show dispersion as prism does? I have got two answers and I am confused The dispersion that occur at first interface with some angles , that hot reversed at second interface and ...
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Dispersion of finite 2D lattice

Following problem: I have the coupling matrix for an $N$-by-$N$ finite lattice of coupled masses (only nearest-neighbour coupling, periodic until terminated). I would like to numerically calculate its ...
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Does Lens disperse light along with refracting? Why doesn't it depict in diagrams? [duplicate]

Why we depicts every diagram studying in ray optics lenses as 'a ray that is passed after retracting from lenses'? I mean to say , lens is made of glass with non parallel faces so it should disperse ...
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Going from 2D dispersion relation to density of states

If one was to have a 2D dispersion say: $$\varepsilon(k)=k_x^2-k_y^2$$ We know the dispersion relation generally can be written as:$$ D(\varepsilon)=\sum_{k_x}\sum_{k_y}\delta(E-\varepsilon(k_x,k_y)$$ ...
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Why we don't see a spectrum of colours above water?

Why we don't see a spectrum of colours above water? When a light ray enters the water it will become dispersed, and after reflecting from an object in the water, say a pencil, or just the bottom of ...
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Why do wave equations produce single- or few- valued dispersion relations? Why no continuum of possible $\omega$ for one $|\boldsymbol{k}|$?

This question is pretty much the same as What ties high frequency electromagnetic waves to short wavelength and converse? but much more technical, and seeking a more technical answer than any provided....
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