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Questions tagged [dispersion]

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

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1answer
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Speed of light in different mediums with different frequencies

As I know the speed of the light doesn't change while it travels through a vacuum. But while it travels through a prism, it shows different deviation angles to different frequencies. So ...
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Light in fibre optic cables

Imagine a fibre optic cable stretching from London to New York (5571 km) carrying a data signal This data signal is split into two parts, red and blue light Both signals start travelling down the ...
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2answers
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How do you pick the wavenumber at which the group velocitiy is evaluated?

The equation for group velocity is $ v_g(k) = \frac{d\omega}{dk}.$ This is obviously a function of $k$ but typically the word is used as if there is a single group velocity and not a whole function. ...
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Index of refraction of a specific wavelength using Abbe number

I am stuck with a problem, maybe my understand of it is not correct. I would like to solve, given an Abbe number and some index of refraction at a known wavelength, the ior of any wavelength λ. From ...
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1answer
27 views

Dispersion relation of a medium

In a dispersive medium I have a wave equation: $$ \frac{\partial^2E}{\partial z^2} + \eta \frac{\partial^4E}{\partial z^4} - \frac{1}{c^2}\frac{\partial^2E}{\partial t^2}=0. $$ How can I find the ...
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310 views

The effect of frequency and amplitude on the speed of sound

I don't do physics, but a sound-related question came up in a project. I've googled extensively but I still can't get a hang of the basics. The following are two related questions. Assume the source ...
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How to derive the group velocity in a dispersive medium and how to interpret it in momentum space? [closed]

I had this homework where I was supposed to derive the group velocity of a given wave packet $$\psi (x,t) = \frac{1}{\sqrt{2\pi}}\int_{-\infty }^{\infty}dk\,g(k)e^{i(\omega t-kx)}$$ where $$g(k)=e^{-\...
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1answer
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Why is the phase velocity of waves on a rope independent of the wave length?

A rope is described by the wave equation $$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$ It is well known that there is no dispersion for resulting wave solutions. This implies that all plane waves ...
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3answers
173 views

Proof that $v=\frac{dE}{dp}$ at relativistic speeds?

This is a formula I have seen stated in two different places in a relativistic context, but I do not know the proof and seem unable to derive it on my own. $E$ is the energy of a free particle, $v$ is ...
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1answer
52 views

Why violet light bends the most? [duplicate]

I have read about refraction through a triangular prism,rainbow formation and other natural phenomena.They all told about the strong bending of violet light . I know that it has a shorter wavelength ...
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4answers
255 views

Why does the phase velocity of a string attached to springs depend on the wave length?

A string can be described by the wave equation $$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$ while a string attached to a spring (i.e. with a harmonic restoring force) at each location is ...
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Understanding group velocity

Group velocity as a concept in Classical Waves confuse me. It's very easy to point out visually, like in this really helpful graphic here. Okay, it's the speed of the moving bulge, which, notably ...
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The effect of velocity on dispersion of light

It is stated that red light bends less than blue light as white light is dispersed through a glass prism. I understand that red light travels faster within the glass because of its higher wavelength, ...
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2answers
54 views

Treatment of electrons and phonons in condensed matter physics

I was watching the lectures by steve simon(oxford) on solid-state physics. In the course, he derived the dispersion relation for phonons(assuming spring between atoms) and dispersion relation for ...
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1answer
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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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Dispersion through Glass Slab

My questions related Dispersion through Glass Slab: Why does a parallel surface makes a difference? Why is that light do get disperse in a prism and a glass slab at surface one but at backs normal ...
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3answers
913 views

What is the significance of dispersion relation i.e. frequency vs. wave vector relation?

There are lots of pages in my textbook dedicated to this sole relation and frequency vs. wave vector graph. I do not understand what are practical significance and uses of the relation and the graph. ...
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Dispersion: any software to work out the dispersed waveforms of EMW signals that propagate via interstellar medium for some distance?

I asked this question in the Astronomy site, but seems few people feel interested in, so I hope to have a try here in the Physics site...... Is there any software (toolbox, code, package, paid or ...
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4answers
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Sound frequencies travel at the same speed?

as the diagram shows sound frequencies travel at the same speed or each frequency has a given speed ?
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1answer
274 views

Time delay of a laser pulse due to 2nd, 3rd and 4th order dispersions

I'll explain my problem : Given a Gaussian pulse with central wavelength 550 nm and a HMFW of 300 nm, and let's assume the pulse is transform-limited. I need to get the pulse through 1mm of quartz. ...
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2answers
55 views

Why is group velocity the important velocity?

It seems that universally in all systems, group velocity is the relevant velocity but why? I read that this is the speed of information transmission but why is that the case? How do you define where ...
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7answers
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Why do wave packets spread out over time?

Why do wave functions spread out over time? Where in the math does quantum mechanics state this? As far as I've seen, the waves are not required to spread, and what does this mean if they do?
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1answer
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What happens to frequency during dispersion?

I'm a bit confused about what happens to frequency during the dispersion of white light passing through a prism. I understand that when a light wave is travelling in one medium, velocity is constant ...
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1answer
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Dispersion under Classical and Quantum regimes

If I understand correctly the literature on dispersion, the atom is modeled as an electron bound to an atom by a spring with the electron behaving as a driven, damped oscillator. The electron ...
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2answers
143 views

If a black colored body absorbs all colors, why does the spectrum of light appear on a black shoe?

Few days back in a 10 grade school practical, we were shown the dispersion of light by a prism to create spectrum. Then we went into the open sun and performed it under a linear building roof and ...
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0answers
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What is a dispersive and reactive medium in mechanical waves?

Would it be possible to have some explanation about the dispersive and reactive medium in the field of mechanical waves. As far as I understand : Let $\omega$ be the excitation frequency and $\...
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0answers
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Wave packet - phase vs group velocity

So, I've been revising QM recently and the concept of group vs phase velocity has me confused. Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
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4answers
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Is light dispersed over distance by flat mirrors?

Hello and thank you for your time: Let's assume I have a 100 squared meter circular flat mirror placed 1 AU from the sun, and let's assume my intention is to shine light on a circular area on another ...
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1answer
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Interpreting phonon dispersion relations

I have been working with phonon dispersion relations for a while now on the topic of metamaterials (phononic band gaps). However, I still do not feel that I have fully grasped how to interpret these ...
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2answers
145 views

Dispersion between analog and digital signal in optical fiber

We know that optical fiber is used to transmit data in digital format.As a result, there is either Intermodal or Intramodal dispersion occurring based on the fiber used for communication. If an ...
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2answers
99 views

Why does violet light bend the most? [duplicate]

When white light passes through a prism, refraction occurs and it splits into its seven constituent colours. If the spectrum is obtained on a screen violet light appears much more bent than red light. ...
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2answers
97 views

Do gravitational waves disperse/refract (like EM waves in a prism)?

I have read this question: What is the relationship between a gravitational wave and a graviton? where kingledion says: Gravitational waves were theorized a century ago and recently ...
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Dispersion, surface acoustic wave devices

I am trying to understand dispersion, and to do it within the context of surface acoustic waves (SAWs). For surface acoustic wave devices the inter-digital transducers (IDTs) produce Rayleigh waves ...
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3answers
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How to describe the unit vector for a complex wave vector?

In optics, we often come across complex wave vectors that describe absorption, dispersion, etc. given as: $\textbf{k} = \textbf{k}_{real} + i\textbf{k}_{imag}$ The electric field in phasor notation ...
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1answer
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Color dispersion at the edge of a slanted mirror

When I look at the edge of a slanted mirror it looks like its affected by color dispersion which you can see by Image 1 but, when it reflects off the flat part of the mirror it looks normal, Image 2. ...
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3answers
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Why doesn’t a normal window produce an apparent rainbow?

When light refracts in a prism it creates a rainbow. My question is, why don’t all windows or transparent objects create this dispersion, i.e. why is the refractive index dependent on frequency in a ...
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Klein-Gordon/Maxwell Equation: dissipative or dispersive?

In Aspects of Symmetry, Coleman says (p. 185) ''Most of the simple field theories with which we are familiar have the property that all of their non-singular solutions of finite total energy are ...
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1answer
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Why does the intensity of the scattered light vary when a monochromatic laser is shined into a transparent object?

When a laser is shined into a glass ball such as this video (link) or a bottle of water (link) the light is refracted through the whole transparent body. However, the intensity of the light scattered ...
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5answers
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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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1answer
116 views

Can dispersion relations be derived using Euler-Lagrange equations?

The question is long because of the demonstrations I give, but the problem is simple, so bear with me for a minute. I am trying to derive the dispersion relation of a semi-infinite system using Euler-...
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0answers
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Physical Interpretation of Energy-wavenumber Graphs

Consider an energy-wavenumber graph, typical in solid state physics, like the one below. I can follow the mathematics in the derivations with a KP model. But I don't understand the physical ...
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2answers
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What does phase velocity physically represent, and why can it be superluminal? [duplicate]

Phase velocity is defined as $v_p=\frac{\omega}{k}$ and is described in various textbooks as being the speed at which the phase of a wave propagates. If you have a wave train that is modulated by an ...
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2answers
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Why don't the oscillator coherent states disperse in time?

A Gaussian wavepacket is made of a continuum of frequencies (or energies) and stretches in time due to the phenomenon of dispersion: the different plane wave components with different frequencies ...
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1answer
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Wave packet in dispersive medium, how will the group velocity be affected? [closed]

A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10^3 m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3%. ...
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Dispersion relations in 2 atom and above

I am having a little trouble understanding this information of dispersion relations show below for a two atom basis. So it states that there should be in total 6 dispersion branches but there only 4. ...
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2answers
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Where does dispersion actually take place?

Out of 1 & 2, which is most accurate? And, out of 3 & 4, which is most accurate? Do they both agree with each other? Please explain?
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Group and phase velocity for a superposition of 2 monochromatic waves

A wave packet in one dimension with a dispersion relation $\omega$ is a function of the form: $$f(x,t):=\sum_{i=1}^n\lambda_i\exp[i(k_i x+\omega[k_i] t)]\hspace{1cm}\forall i\leq n\colon\lambda_i,k_i\...
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0answers
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Using convolution to simulate acoustic dispersion in shallow water

Background I'm a marine biologist who's trying to wrap my head around shallow water propagation. I'm interested in how acoustic dispersion (as described by Pekeris' waveguide) alters how sounds ...
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1answer
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What does the curve branch for $\omega > \omega_p$ mean for surface plasmon dispersion?

Consider a half-infinite metal (the other half is vacuum with $\varepsilon=1$). By solving Maxwell's equations and using boundary conditions at the interface, we get the dispersion: $$ \frac{\...
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2answers
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Time-of-flight spectroscopy and energy-time uncertainty

I am a bit confused about spectral and temporal filtering of light. I consider a single-photon source of a bandwidth of $1\,$nm at $1550$ nm. That means, that the wavelength of the emitted photons ...