Questions tagged [dispersion]

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

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270
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23k views

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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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 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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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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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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5answers
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Do colors differ in terms of speed? [duplicate]

Here is a very simple question about light. As far as I remember from the school program, each color is merely one of the frequencies of light. I also remember that each color's wave length is ...
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3answers
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Does a man on the moon experience day?

Does a man on the moon (or any other similar body) experience daytime like we do? By daytime I mean looking upward and seeing a bright "sky," not dark space. If not, then what is the reason behind it?...
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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 ...
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1answer
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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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1answer
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Dispersion of ferromagnetic ($E\propto k^2$) and antiferromagnetic ($E\propto k$) spin wave

The dispersion of ferromagnetic spin wave at low energy is $E\propto k^2$, while $E\propto k$ for antiferromagnetic case. Is there a simple/physical argument (such as symmetry) for these results? ...
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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
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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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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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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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396 views

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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What is energy in $z \neq 1 $ theories?

In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
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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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979 views

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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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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Is it possible to implement the reversed dispersion of a white light beam and how?

The dispersion of white light beam while passing through a triangular prism is well known. Considering the reversibility of optical path, it should be possible to reverse the experiment. How can one ...
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1answer
197 views

Can I make a rainbow in shower?

As droplets of shower acts like rain, and say a light bulb will take place of sun. In this scenery, is it possible to make a rainbow?
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Why does Snell's law not factor in wavelength?

If dispersion is caused due to different wavelengths bending with different angles, how is Snell's law right in generalizing it as $\sin(i) / \sin(r)$? Or am I missing something?
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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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What really is the speed of light in a medium/vacuum, group or phase velocity?

While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser ...
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2answers
14k views

Why do all electromagnetic waves travel at the same speed when travelling through vacuum?

What does my teacher mean when he says that all electromagnetic waves travel at the same speed when travelling through a vacuum? If you may, please answer as simple as possible.
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1answer
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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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5answers
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Light beam vs sound beam

Why is it that it's very common to have beams of light but not beams of sound? Laser beams are widely available, and I am aware that it is also possible to direct sound, however, we rarely see ...
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3answers
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Which electromagnetic radiation is faster in water, microwaves or light?

Well I've been asked this question, but I haven't been able to come with an answer yet using books and some web searches. The point is as the title says, to answer the question with the whole ...
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1answer
101 views

Physical meaning of third derivative with respect to position

I currently on a numerical solver for the KdV equation which reads $$ u_t + uu_x = u_{xxx} $$ I was wondering the physical sense of this third derivative with respect to $x$. I know that the $uu_x$ ...
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2answers
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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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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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1answer
536 views

Fermat principle: which index of refraction?

I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of ...
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1answer
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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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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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2answers
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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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1answer
385 views

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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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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2answers
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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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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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2answers
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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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4answers
284 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
831 views

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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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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2answers
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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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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
272 views

Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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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 ...
3
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2answers
184 views

Why we do not use $v=f \lambda$ for the waves associated with particles?

As the waves travel with velocity $$v= f \lambda,$$ where $v$ is velocity, $f$ is frequency and $\lambda$ is wavelength. Here we can see that velocity of wave is directly proportional to wavelength. ...
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3answers
610 views

Order of colors after reflection in a raindrop

I studied two figures of sunlight reflecting in a raindrop: In the first image, red is shown above violet, but in the second image, red is below violet. Are both cases possible?
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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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