Tag Info

Hot answers tagged

14

According to this link sound (especially high frequency sound) is more attenuated in fog, because it is dispersed by the (billions of) air-water interfaces of all the droplets. This is one reason why a fog horn is a very low sound - low frequencies travel further, especially in fog. For echolocation you want to use high frequencies, and fog is more ...


8

As you say, a changing magnetic field is always associated with a changing electric field, and in fact in relativity they are finally revealed to be the same field. So at this level it cannot be said that the one field generates the other, as they are merely two aspects of the same object. But maybe you still want to look at it from the perspective of ...


6

Lets suppose the amplitude of each wave is $A$ and thus intensity will be $I_0 =A^2$. After superposition amplitude of the resultant wave becomes $2A$. but intensity becomes $I=(2A)^2$ Implies $I=4A^2 =4I_0$


6

This plane polarized wave from wikipedia may help Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, ...


4

This depends on the so called dispersion relation of the wave. Even then the answer is complicated, as you can define several velocities (the most commonly used ones are phase, group and signal velocity). I assume you know the relation $c = \lambda \cdot f$. This is written more conveniently (for working with complex exponentials) as $\omega = c k$ in ...


4

Actually, the light beam does not follow the shortest path, but rather the faster path. Else the light would not bend but go straight there. This is Fermat’s principle. what point is the photon trying to reach? Good question. This point you are talking about, is in fact your eye. A straw in a glass of water visually bends at the interface. Look at ...


4

The cochlea has a complex physical structure, with multiple membranes and fluid-filled chambers. Therefore to explain the separation of frequencies along the basilar membrane of the cochlea is complex to. Sure, there are a lot of very general descriptions (even the answer of theblackcat) and a lot never go into the actual physics of the system. This ...


3

Classically (since rob has done a thorough job on the quantum picture), the amplitude of a light wave is not related to any physical extent. It is not the size of the wave in space, it is the strength of the fields (electric and magnetic). We often draw wavy lines, but if you look closely the transverse axes will be label differently for, say, waves on a ...


3

Every function of the form: $$\psi(x, t) = A\cos[k(x\pm ct) + \phi]$$ is a solution of the wave equation $$\frac{\partial^2\psi}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2\psi}{\partial t^2}$$ The equation is linear, and this means that the general solution is in fact, any linear combination of the possible solutions, something that we can express as ...


3

"a changing magnetic field is not generated by a changing electric field, but instead just happens to always be present perpendicular to a changing electric field due to the laws of electromagnetism." So ... it is due to but not caused by. What is the difference? Short answer: it is not only "a thing" it is a correct thing. This is much more clearly ...


3

There is a technique called flageolet where you damp the string with a finger laid lightly onto the site at the node of a higher harmonic. You do not press the string to the fretboard but just damp the string at a position, where there is a node of the specific harmonic. When you now pluck the string all harmonics, which do not have a node at the specified ...


2

If you twisted my arm and forced me to assign an amplitude to a single photon, I'd do it this way: The energy density of a classical electromagnetic field is \begin{align} U &= \frac12 \left( \epsilon_0 E^2 + \frac1{\mu_0} B^2 \right) \\ &= \epsilon_0 E^2 &\text{(only for light in a vacuum)} \end{align} where $E,B$ are the amplitudes of the ...


2

In very general terms, we can analyze this problem via a sort of normal mode analysis. We're going to gloss over a whole mess of details here, such as the precise vibrational modes in which the spheres are oscillating and how efficiently these vibrations are transmitted to & from the surrounding medium. Rather, we can assume that the potential energy ...


2

Maxwell's equations in vacuum are: $$\nabla\cdot\mathbf{E} = 0$$ $$\nabla\cdot\mathbf{B} = 0$$ $$\nabla\times\mathbf{E} = -\frac{\partial\mathbf{B}}{\partial t}$$ $$\nabla\times\mathbf{B} = \frac{1}{c^2}\frac{\partial\mathbf{E}}{\partial t}$$ It's the last two of these that give rise to the interpretation that a changing magnetic field generates an electric ...


2

For the modeling of surface wave motion there are only two restoring forces to consider: surface tension and gravity. Compared to gravity, surface tension forces are very weak and therefore have a greater influence on the regime of the smaller, capillary waves. Waves in deep water carry away the energy dissipated by shear wind forces - perhaps from a storm ...


2

I think that your teacher (?) asked you about thermal de Broglie wavelength, where $$\lambda_T \propto\frac{1}{\sqrt{T}}.$$ You get this expression when you express the momentum in $\lambda=h/p$ in in terms of kinetic energy and the kinetic energy itself in terms of the energy due to temperature. (The derivation is also in the wikipedia article...) Indeed, ...


2

You're not wrong, exactly. When a wave pulse travels from one place to another, it does transfer energy, and therefore mass. However, there's a useful distinction between the mass that is transferred by the wave, and the mass of the medium the wave travels through (e.g. the slinky for a slinky wave, or air for a sound wave, or water for a water wave). It ...


2

Note that $e^{jx} - e^{-jx} = 2j \sin(x)$ So what you have written is not an electromagnetic wave at all. It is an electric field with a fixed direction and an amplitude that varies sinusoidally along the z-axis. Of course if you multiply this by $e^{j\omega t}$, then you do have a wave. Given the wording I suspect you are meant to assume this (though I ...


2

$E = mc^2$ is a special case of the full equation $$E^2 = m^2 c^4 + p^2 c^2$$ It only becomes $E = mc^2$ when applied to objects at rest, i.e. with zero momentum. A wave that is transferring energy through space is not at rest, has a nonzero momentum, and is thus not subject to $E = mc^2$. So no, wave propagation does not violate the equation.


2

The relationship is true by dint of the trigonometric identity $\cos(u+v)+cos(u-v)=2\,\cos u\,\cos v$. A compelling experiment is to listen to two tones a few hertz apart (the LHS of the identity) and hear the throbbing beats (the AM wave on the RHS). A pitch fork and a guitar / violin string (the latter readily tunable) is a good way to do this; Given the ...


2

Let one end of a very long string is being oscillated transversely so as to generate a sinusoidal wave traveling out along the string. In order to set up a wave on a stretched string, the driving force at the end of the string provides energy. This energy is not retained at the source; it flows along the string at the wave speed. The string transports ...


1

Protons and electrons both obey the de Broglie hypothesis: wavelength = Planck constant / momentum. But protons do not act within the atom the same as electrons - they move in a tighter radius at higher speed. They have to be accelerated to reveal their wave nature, and as the momentum of a proton would be much greater than that of an electron at typical ...


1

Assume plane waves. The tangential boundary conditions show that the transverse electric and magnetic field vectors must stay in the same direction on transmission or reflexion from the interfaces, assumed aligned with the wavefronts. Since we know the direction of the waves, let's say the $\vec{E}$ fields are all in the $\hat{X}$ direction, the magnetic ...


1

I believe you are forgetting the dispersion relation i.e. that $\omega$ is a function of $k$ when you work out $\dot{u}(x,0)$ as well as a sign. I make the calculation to be as follows. Since: $$\begin{array}{lcl}u(x,t)&=&\int_0^\infty \,\mathrm{d} k\, e^{i\,k\,x}\left(A(k)e^{i\omega_+t}+B(k)e^{i\omega_-t}\right)\\&=&\int_0^\infty ...


1

If the light was emitted after the recombination, it can't have traveled over 13.7 billion years. The EGS-zs8-1 galaxy is located 13.1 billion light years away , which is close to the maximum for a plausible picture. More details on the wiki http://en.wikipedia.org/wiki/EGS-zs8-1 . If the light is not absorbed by an obstacle, it will probably travel to the ...


1

No. Energy conservation always applies. The elastic potential energy will be maximum at a wavetop, since here the rope is stretched the most, $U=½kx^2$. The transverse velocity and thus the kinetic energy is zero at this point $K=½mv^2$ since this part of the rope stops and starts moving back again. $$E_{before}=E_{after} \implies K_1+U_1=K_2+U_2$$ Energy ...


1

The phase of a wave varies by $2\pi$ over the distance of one wavelength, $\lambda$. So suppose you have some distance $d$, then the number of wavelengths in this distance is $d/\lambda$, and therefore the phase shift over the distance is: $$ \varphi = 2\pi\frac{d}{\lambda} $$ But if the wave is passing through a material with refractive index $n$ this ...


1

For macroscopic systems some physical means must be present for energy to flow between potential and kinetic states, or magnetic and electrical fields. The flow must also not be subject to energy loss. Apples do not have the properties that allow such a flow of energy. Apples do not 'ring' when they are subjected to an impulse of energy. Almost all the ...


1

Electric and magnetic fields themselves are totally uncharged. They are always described as totally uncharged things. They can either be described as two uncharged fields (when treated in the more traditional formulation) or as aspects of a unified electromagnetic field. In both descriptions the field(s) interact with charged things without being charged ...


1

This is a plane wave. Its an idealization of a wave that doesn't exist. Waves that actually exist are spherical waves. A sinusoidal train of spherical wave are represented as following: $$ \psi(r, t) = \frac{A}{r}\cos(kr - \omega t) $$ However, the solution of a general wave for spherical coordinates can be expressed as: $$ \psi(r, t) = \frac{1}{r}F(r - vt) ...



Only top voted, non community-wiki answers of a minimum length are eligible