New answers tagged

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Having worked in an anechoic chamber in a previous lifetime, being inside one is exactly like being in the open air in a completely quiet place- if you are talking about sound frequencies associated with music or human speech. Those frequencies are especially well-absorbed by the walls. But for sound frequencies where the wavelength is similar to the major ...


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There's a number of oscillatory phenomena, with different physical character, that follow this kind of rule. Electric waves (light, radio, X-rays etc.) are capable of interacting with matter in such a way as to downshift the frequency; an X-ray hitting a fluorescent screen is a classic example. This is because the energy per photon of the X-rays can create ...


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Electromagnetic radiation is the emission of photons from excited subatomic particles. The light from a heated wire is an example of the stochastic emission of photons from the excited electrons in the wire. The concept of EM radiation as a stream of quanta was a by-product of Planck's equation for blackbody radiation. He did not initially believe that the ...


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Here is a good explanation from a textbook: https://openstax.org/books/college-physics/pages/27-5-single-slit-diffraction


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There are a few critical issues that I did not find in the other answers which are worth noting here. Landau Interactions Landau interactions are specifically tied to the term $\mathbf{k} \cdot \mathbf{v}$, where $\mathbf{k}$ is the wave vector and $\mathbf{v}$ is the particle velocity. The physical interpretation of this term is that longitudinal electric ...


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A way of intuitive thinking about Landau daming is from the point of view of the electrostatic wave (or Langmuir oscillation). This will also clarify a bit why the whole mathematical apparatus is needed. Short Intro to Electrostatic Waves Without a magnetic field, in an electrostatic field you can consider the Vlasov equation and derive a dispersion relation ...


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This wikipedia article explains the physical picture rather well. Landau damping results from the energy exchange between the electromagnetic wave and the plasma particles, its main feature being the dependence on the distribution of the particles. As an analogy, perhaps a bit far-fetched, one could compare Landau damping with the interaction of an ...


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The farther the wave goes, the more it spreads out, and the weaker it becomes. In a perfect world, that wave never vanishes no matter how far it goes- it just keeps getting weaker and weaker. But our world is not perfect, in that the physical field in which sound propagates (the air) contains the weakened remnants of all other sound waves traveling through ...


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I understand that EM waves are self-perpetuated due to the interactions between changing electric and magnetic fields as described by Maxwell's third and fourth equations, but I'm stuck conceptually on what they are if there are no electrons or conductors around. people were stuck like you begininning of the 20th century thinking the EM waves required a ...


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You've come to a long time phyilosophical question: does a field actually "exist"? We cannot measure fields. There is no instrument able to measure a "field". The instrument you use to measure electric field is actually based on forces. The instrument detects an electric force and then it deduces the value of the $E$ field. In an empty ...


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The Cosmic Microwave Background (aka CMB) is light radiated from hot glowing matter as it cooled from the Big Bang. It took a few hundred thousand years for the universe to cool enough that electrons could stick to protons, forming neutral H atoms. Before this, the universe was full of free charges, which absorbed light. After this, the universe was ...


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Classically, there would be no hard limit. In a perfectly silent, classical universe, you could imagine a device to detect the wave. But practically, the strength would eventually decay below the ability of your device to discriminate it from other sources of noise (including those from within the device). In QM, any detector has a lower and lower ...


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Electromagnetic waves are made of photons. These will continue to travel along geodesics unless they scatter or are absorbed. Currently the main model of cosmology has an infinite Universe so if this is correct a photon could keep travelling indefinitely if it is not absorbed.


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It is only in the simplest cases (called "linear") that overlapping waves simply add without disturbing one another. In more general cases waves add in more complicated ways and then they can affect one another. With electrons, the wave associated with each individual electron only adds in a simple way with itself. This is observed for example when ...


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Isn't the same principle [super-position] applicable to the electron? Yes is is. Diracs equation gives us the quantum field that describes the electron-positron field. Despite its name, it is not a quantised field. A better name for it would be a relativistic classical field. It is akin to the electromagnetic field. And hence we have super-positions. The ...


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We can say with certainty that an electron exhibits both particle-like and wave-like behaviours. Experiments suggest that an electron is a point-like fundamental particle (ie one with no internal structure) with a radius of less than 10−22 metres. However, electrons can also be diffracted as if they were waves, the wavelength being dependent upon the ...


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The wave function of a particles is described by the Schrödinger equation, which is compatible with the principle of superposition. However, the wave function has no physical meaning - it is its squared the probability, and the square of the wave function does not agree with the principle of superposition. Check Eisberg's book, for example, or Morrison's.


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$\hat{x}$ and $\hat y$ are linearly independent vectors. The sum of two vectors is the sum of their components in order. So $$\vec E_1 + \vec E_2 = A\sin(kz-\omega t)\hat x - A\sin(kz+\omega t)\hat y$$.


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A half-wave dipole is fed with the signal at its mid-point. Consider the current distribution along the antenna. Some current has to flow in and out at the middle, or power cannot be transferred. But at the ends the current has nowhere to flow. So the current distribution along the dipole takes on a distinct "hump" shape, basically half a sine wave....


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An antenna, in general, is NOT a resonator (contra @oliver). The purpose of the antenna is to be a direction dependent impedance transformer that matches the wave impedance of the transmission line connecting the transmitter/receiver to space (air) having impedance $\sqrt{\frac{\mu_0}{\epsilon_0}}=377\Omega$ in all direction. In other words, the apparent ...


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Electromagnetic waves in vacuum and air very accurately are subject to what is called the superposition principle, which in turn derives from the linearity of the equations of electrodynamics. The superposition principle says that waves that travel in different directions don't disturb each other waves with different frequencies/wavelengths don't disturb ...


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An antenna is a resonator. If you are not feeding it with its natural frequency, it is not going to oscillate with sufficient amplitude. Of course you can always think about increasing voltage, but usually everything in technology is about efficiency. Imagine you would have to carry a heavy car battery and a high voltage generator with your smartphone in ...


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To talk about "the" wavefunction doesn't really make sense. There are many wavefunctions in the Hilbert space of this system for example. Usually what is meant with this language are the eigenstates of some model Hamiltonian H. In the nearly free electron model, we consider non interacting electrons with the effective Hamiltonian $$ H = \frac{p^2}{...


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So how can we calculate the speed of light for different frequency? It depends on how much prior information you want to require of your calculation. In the simplest case you may just look up an approximate formula for the speed of light in your medium of choice as a function of wavelength or (less common) frequency. Of course, this relies on somebody ...


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This question can be reformulated as: “Does the index of refraction of a given medium depend on wavelength” (inverse of frequency), the answer is given by Cauchy’s formula: https://en.wikipedia.org/wiki/Refractive_index


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Let say u have a USB cable and wish to connect from wall to your PC, but if the distance is short. Then you won't mind to untangle the cable, since it would connect anyhow. But if the same USB cable needs to connect a cell phone which is much further from wall, then u would think of stretching or minimizing coiling of cable, so that it could compensate to ...


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It's actually correct (and, IMHO, better) to use the equation you used. The problem solution uses a couple of approximations that are basically correct but lead to small enough errors that the final answer differs at 2 significant figures. Using $s \sin \theta = n \lambda$ as you did, you would obtain $\theta = 0.1865...^\circ$. This is a direct ...


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In this problem, fixed end is at $x = l$. Corresponding boundary condition has a form $$ y(x = l, t) = 0. $$ Solutions to the wave equation with this boundary condition have the following form $$ y(x,t) = f(kx-\omega t) - f(k(2l-x)-\omega t). \quad (1) $$ In this problem, $f(kx-\omega t) = A\sin(kx-\omega t)$. For $t$ large enough, in the $x<l$ area, only ...


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The dispersive response is a feature of heterogeneous material. As your material includes heterogeneities and your wavelength in order of heterogeneities length scale, the dispersion phenomena are observed. Anisotropic material has another effect on the received wave pattern.


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I can't mention so I write it here: First, it depends on "metal alloys" and ultrasonic frequency and wavelength. Metal alloys are crystalline material. Heterogeneity, in any form, could appear in this structure. Alloys generally have heterogeneities. If the wavelength of your elastic wave in order of heterogeneities length scale, a dispersive wave ...


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Yes, several quantities vary with distance from the source. One useful quantity is the radiant flux (the amount of energy passing through a given area in a given amount of time -- basically how 'bright' it looks from your position). In fact, for a source that is spherically symmetric or far enough away that we can regard it as spherically symmetric, the ...


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Intensity changes because energy of the wave is absorbed by the medium in which it propagates. Also the wavefront appear different. Far away from a source, waves have plane parallel wavefront, like light from the stars.


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In mainstream physics, both the photon and the electron are point particles. The photon does not have an amplitude. It has energy $E=hν$ where $ν$ is the frequency of the classical electromagnetic wave built up by a large number of photons. See how in the double slit experiment one photon at a time, the points accumulating show the interference pattern of ...


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Everything seems to be right except the calculation of $λ$. that will be perceived by the observer is given as $λ=\frac{V}{f’}$ (all three are relative or apparent i.e. as perceived by the observer) So instead of $V$, we write $V-U$ (since the observer is moving away the relative velocity will become slower, you’ve written $V+U$) this is the mistake you’ve ...


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The formula of Doppler Effect goes as follows:$$f_o=\Bigl( \frac{ v\pm v_0}{v\pm v_s}\Bigl).f_s$$ Here , $f_o$=frequency measured by observer $f_s$=frequency of source Note: When observer moves away from source - sign is used in numerator and if observer moves towards source + sign is used in numerator. When source moves away from observer + sign is used in ...


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This is a long comment: Here is a simple plane electromagnetic wave: 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. The electric and magnetic fields in such a wave are in-phase with each other, ...


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A few years later, I had this effect in real life again and observed it in a bit more detail. It turns out this is an optical illusion. The rotation wave "nodes" are actually just the points where the slackline band is currently parallel to the line of sight. The actual wave seems to have only one node roughly in the middle, which is then the same ...


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You are picking up just the phase point where the fields interfere constructively, meaning that the amplitude add up, but in the total volume where the field is present there are points where the electric field of the two waves interfere destructively and other constructively: $I = 2I_0(1 + \cos\chi) = 4I_0(\cos^2(\frac{\chi}{2}))$. Then the intensity ...


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I think you can delete "at the point under examination". It is not required. Also you could replace "phase velocity" with "propagation velocity". Then the statement would apply to most, or all, waves including pulses. Re. I'm not sure I understand what "at the point under examination" means. I guess it refers to the ...


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Your question is unclear as an electron as far as is known is a point particle. Still it seems that you are asking about the diffraction in the limit of vanishing slit width. If the slit width is smaller than the wavelength, the optical path difference as function of angle of transmission becomes to small to cause destructive interference. In the limit the ...


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In the formula $f'=\frac{v_{sound}\pm v_{observer}}{v_{sound}\pm v_{source}}f$ expressing the Doppler effect, $v_{sound}$ is the speed of the waves (sound in this case) in the medium (this quantity is independent of the speed of the medium), while $v_{observer}$ and $v_{source}$ are speeds of the observer and source measured with respect to the medium. ...


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Consider an oscillating electric charge (part of an oscillating current). The moving charge introduces a transverse distortion into its (preexisting) radial electric field (strongest when moving most rapidly). As part of a current it also produces a magnetic field (wrapped around the direction of motion), also strongest when the charge is moving most ...


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A standing wave doesn't necessarily travel with less frequency on a longer string, as the string tension and string density affect wave speed, as stated by AFG with the formula: $v=\sqrt{\frac{T}{\mu}} \qquad \qquad(1)$ where $T$ is the tension in the string and $\mu$ is the linear density of the string. The velocity of waves on the string is also given by ...


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I realize that the truly correct answer to this question is perhaps to simply say that if there is a wave solution to Maxwell's equations, then a necessary property of that solution is that the electric and magnetic fields will be at right angles to each other and will be in phase. I was looking for a more intuitive type understanding. Please tell me if ...


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Since the times of maximum charge separation (electric field) and maximum current (magnetic field) are out-of-phase in a oscillating dipole, the question makes perfect sense. The answer is to look at the exact dipole solution: $${\bf E}=\frac 1{4\pi\epsilon_0}\Big[ \frac{\omega^2}{c^2r}(\hat{\bf r}\times{\bf p})\times\hat{\bf r}+ \big[ \frac 1 {r^3}-\frac{i\...


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The propagating wave has complex power density (Poynting vector) $\mathbf S = \mathbf E \times \mathbf {\bar H}$. Any phase shift between the fields $\mathbf E $ and $\mathbf H $ is reactive and does not correspond real power. Recall the analogous case of $V\bar I$ from circuit theory.


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The frequency needed to produce a resonant standing wave on a string fixed at the far end will depend on the length of the string. You will need an integer number of anti-nodes in the pattern.


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If the double slit experiment is done with a very low intensity light source, it is found that all the energy of each photon is absorbed at a single detector element. The electromagnet wave packet of each photon passes through both slits, and the recombination determines the probability that the energy will be absorbed at a particular location.


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In a sinusoidaly forced RLC circuit, the maximum charge and energy on the capacitor occurs at a frequency just below resonance. The current changes very little, but there is more time on each cycle to charge the capacitor. The maximum voltage and energy on the inductor occurs just above resonance. The rate of change of the current is a little higher. The ...


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