# Tagged Questions

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

6k views

### 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 ...
4k views

### 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 ...
8k 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 ...
3k views

### 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?...
658 views

### 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 ...
148 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,...
678 views

### 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? ...
122 views

### 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 ...
3k 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?
312 views

190 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 ...
76 views

### Rayleigh length determination for Laguerre-Gaussian Modes

Recently I have measured the Rayleigh length of a Gaussian electron beam probe in a scanning electron microscope, using the function: $$w(z) = w_0 \times \sqrt{1 + (z/z_r)^2}$$ Where $w$ is beam ...
562 views

### How to calculate the dispersion relation for a wave equation with non-constant speed of wave propagation?

Specifically, it is a one-dimensional wave equation for waves on a string with a non-constant cross-section, i. e. $$S(x)=S_1+S_2 \cos{2x}; \qquad c(x)=\sqrt{F/\rho\, S(x)}.$$ Separating the variables ...
81 views

### What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
187 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 ...
3k views

### 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 ...
179 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 ...
58 views

### Why is it possible to choose an arbitrary zero energy level when dealing with frequencies of a wave function?

This is a followup of my previous Why don't the De Broglie dispersion relation contain a constant term? question. Answerers pointed out that only differences in energy matter I can understand ...
673 views

### 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=...
46 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 ...
150 views

### The lineshape of a 2D photonic crystal dispersion diagram

Using simulation software (CST Studio), I calculated the dispersion of the eigenmodes of a photonic crystal, that is frequency vs wavenumber for the desired propagation direction. I wonder what kind ...
Suppose we have an operator $Q$ with eigenvalue $q$. Expectation value is $\langle Q \rangle$ and dispersion $D(Q) = \sqrt{\langle \left( Q - \langle Q \rangle \right)^2 \rangle}$. I want to find ...