Questions tagged [dispersion]

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

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43
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4answers
22k views

Why do prisms work (why is refraction frequency dependent)?

It is well known that a prism can "split light" by separating different frequencies of light: Many sources state that the reason this happens is that the index of refraction is different for ...
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1answer
2k views

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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1answer
21k views

Why does the refractive index depend on wavelength? [duplicate]

Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the ...
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3answers
908 views

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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2answers
897 views

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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4answers
12k views

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?
4
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1answer
750 views

Why don't the De Broglie dispersion relation contain a constant term?

Wikipedia says that the dispersion relation for a non-relativistic particle is: $$ \omega = \frac{\hbar k^2}{2m}. $$ But when I tried to calculate it myself, I seem to get a constant term in that ...
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1answer
205 views

More extensions of the wave equation for dispersion

The Phys.SE question Minimal Extension of Wave Equation to Include Dispersion extended the wave equation for only a very simple form of dispersion. However, what about more complex dispersion ...
270
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2answers
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What is Chirped Pulse Amplification, and why is it important enough to warrant a Nobel Prize?

The 2018 Nobel Prize in Physics was awarded recently, with half going to Arthur Ashkin for his work on optical tweezers and half going to Gérard Mourou and Donna Strickland for developing a technique ...
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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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2answers
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Understanding dispersion relation

I am trying to understand the physical meaning of the dispersion relation. Is it how inhomogeneous a media is ? Or how much the electromagnetic fields spread in the media? Or ?
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1answer
58 views

Is difference in wave number always small?

Over the last few days I have been looking at a derivation of group velocity. The derivation is the one shown in this question Deriving group velocity. I have seen this derivation in many places, and ...
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1answer
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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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4answers
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Why is the speed of oceanic waves not a constant like sound?

I cant understand this, according to what I read here. The speed of a wave depends on its wavelength and its depth, through the relation $$ v=\sqrt{\frac{g\lambda}{2\pi}\tanh\left(2\pi \frac d\lambda\...
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2answers
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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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4answers
5k views

Do we say that phonon has effective mass through its dispersion relation?

The effective mass is proportional to the second derivative of the dispersion relation $d^2k/dE^2$. Do we say that phonon have effective mass through it? Spin wave have.
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2answers
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Why do convex lenses not disperse light like prisms, given that entry and exit points aren't parallel?

I understand that light entering a parallel block of glass at a non-90 degree angle will cause dispersion of colours within the block but that these will be refracted by the same degree upon exit so ...
4
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4answers
285 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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1answer
489 views

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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1answer
561 views

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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1answer
173 views

Minimal Extension of Wave Equation to Include Dispersion

Let's say you are modeling some process with the wave equation $\frac{1}{c^{2}}\frac{\partial^{2}\psi}{\partial t^{2}} = \nabla^{2}\psi$. You wish to improve your model by including dispersive effects,...
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2answers
207 views

Light dispersion in gravitational theories

GR predicts no Ricci curvature in vacuum (or at least when we can ignore the cosmological constant). Would theories that violate this lead to observable light dispersion in solar system tests of ...
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1answer
681 views

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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3answers
2k views

Frequency dependence of the speed of light in air

According to this link, the speed of light of different colors in a medium should be different. But if the refractive index of light in air is 1 then this means that the speed of light in air and ...
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5answers
3k views

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
196 views

Speed of different em radiation in a medium [duplicate]

Does all frequency of light travel with the same speed in a particular material like glass? Since by cauchy's relation refractive index change with wavelength which implies the speed also changes. ...
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2answers
259 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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1answer
509 views

Group velocity with gaussian pulse

A gaussian pulse wave propagating in a non-dispersive medium with velocity $v$ can be expressed as $$h(z,t) = e^{-a(t - z / v)^2}$$ as suggested in this answer. In the case of a dispersive medium ...
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2answers
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Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
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1answer
390 views

If the speed of a light wave decreases, doesn't the frequency decrease as well?

The dispersion of white light is due to the fact that violet light slows down more when entering a denser medium, compared to red light. However, doesn't the violet light disperse more because it's ...
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1answer
244 views

Is quantum velocity generally equal to group velocity?

It is often said that the velocity operator in quantum mechanics identifies the group velocity. Here's the argument: for the free particle, we have $\omega = \hbar k^2/2m$ and the (quantum) velocity ...
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3answers
175 views

A question regarding the speed of light in a vacuum, specifically putting a 'color' in

I know that red and blue etc. lights are produced when 'white' light is put through mediums. I have learned that all light in a vacuum, all electromagnetic waves, travel at the same speed in a ...
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1answer
89 views

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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1answer
488 views

Interpreting group velocity of free particle wave packet

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