Propagation Definition and 457 Threads

Hi! Dealing about wave propagation in a medium and dispersion, wavenumber k can be considered as a function of \omega (as done in Optics) or vice-versa (as maybe done more often in Quantum Mechanics). In the first case, k (\omega) \simeq k(\omega_0) + (\omega - \omega_0) \displaystyle \left...

Hi, I'm a second year undergrad and we've covered the heat equation, \begin{equation} ∇^{2}\Psi = \frac{1}{c^{2}}\frac{\partial^2 \Psi}{\partial t^2} \end{equation} and the wave equation, \begin{equation} D∇^{2}u= \frac{\partial u}{\partial t} \end{equation} in our differential equations...

This is a question that has been bugging me for a little while. If sound propagation in air changes from an adiabatic to an isothermal process (for example via the use of fiberglass or other heat conducting material), the wave velocity is lowered due to the reduction in the bulk modulus of air...

Hello! Starting from a gaussian waveform propagating in a dispersive medium, is it possible to obtain an expression for the waveform at a generic time t, when the dispersion is not negligible? I know that a generic gaussian pulse (considered as an envelope of a carrier at frequency k_c) can be...

Suppose I have some observables \alpha, \beta, \gamma whose central values and uncertainties \sigma_{\alpha}, \sigma_{\beta}, \sigma_{\gamma} are known. Define a function f(\alpha, \beta, \gamma) which has both real and complex parts. How do I do standard error propagation when imaginary...

Can carbon nanotubes support electron propagation perpendicular to the axis? That is, can there be circular current flow on the tube's perimeter, not just the linear flow parallel to the axis? Because I reading that it's generally considered a 1-dimensional conductor.

I am a senior physics and mathematics major, and this is my last semester. As a result, I am taking advanced physics lab, which feels more like a grad school experiment than an undergrad. One of the labs deals with the modal analysis of three spring-mass systems placed vertically as shown in the...

Hello :) I have 2 questions about the beam propagation of an Ti:sapphire-laser: Picture 1: The cw argon ion laser brings the beam to mirror (1). Then...? Then the beam (100% of it), go to the birefringent plate (4), gets then reflectet to the first mirror again (1) , which reflects it to the...

For a point in space if we have the values of E and H fields at a certain instant of time, we can tell the direction of the propagation of these values, which is the direction of the cross product vector E x H. Is this phenomenon time asymmetric or not ?

Does anyone have an open source code or know how to code propagation of multi gaussian beams through multiple interfaces using the ABCD matrix approach? And this is using ultrasound and not optics. Please let me know if anyone can help out in this

The integral form of Maxwell's equation pertaining to induced electric fields is: ∮E(t0)⋅dℓ= −dΦ(t)/dt|t=t0Say for a long time, in some circular region there has been no B or E fields present. Then, there is a sudden constant increase of B field introduced in the middle. I know that information...

Hi, I'm looking at an Italian high-school physics textbook. The subject is uncertainty propagation, and the target is 9th grade students. The book is allegedly by J.S. Walker, but I'm not sure how much it was "redacted" by the Italian editor. I am a little puzzled by two rules that are stated...

Homework Statement The problem is about calculating the error on the area of a rectangular field. What is known is that the sides of the rectangle are 120 m and 180 m, and they have been measured with a 10 m measuring tape. The tape has a sensitivity of 2 cm.Homework Equations Since the area...

Homework Statement I am trying to express ##T(\phi(x1)\Phi(x2)\phi(x3)\Phi(x4)\Phi(x5)\Phi(x6))## in terms of the Feynman propagators ##G_F^{\phi}(x-y)## and ##G_F^{\Phi}(x-y)## where ##G_F^{\phi}(x-y) =\int \frac{d^{4}k}{(2\pi)^{4}}e^{ik(x-y)} \frac{ih}{-k.k - m^2 -i\epsilon} ## and...

Homework Statement Let t = f(g, h, A, Δm, Γ, r). For t = 2 s, the propagated error is σ = 0.02 s. Can the error of 1/t2 be simply determined using the known error in t = (2 ± 0.02) s, or must the variance formula (with all the partial derivatives and errors of each dependent variable) be...

Hi all, Whew, last question for a while: I think I already know the answer, but want to confirm (e..g, I think this thread basically answers the question, https://www.physicsforums.com/threads/propagation-of-wavefunction.152053/) As an example, let's say I have an electron (in free space or...

Hi, I'm having quite a bit of trouble finding the propagation of uncertainty (using partial derivatives) of the volume of a hollow cylinder. The examples in my tutorial only demonstrates how to find the propagation of uncertainty on simple operations such as x + y, x/y, etc... 1. Homework...

What kind of spacetime structure can make the lines of a soliton-like field propagate in higher-dimensional space-time that do not diverge as they converge on the target. Does General Relativity make this just completely impossible? Or is there a solution of General Relativity that allows this...

Hi, I have been trying to use imaginary time propagation to get the ground state and excited states eigen function but the results I got is different from the analytical solution. I know that to get excited states, I should propagate 2 or more orthogonal functions depending on the number of...

speed? This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky. In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite...

Hello, I have a set of N samples, each of which yields the measurable variables A and B. I am interested in computing the mean and standard error of the ratio A/B within the group. The catch is that I need to do background subtraction on both A and B, and the two different background values BGA...

I have a physical quantity A defined as ##A=(74.5 B^2*(M+N))^{1/3}## where B, M, N and relative uncertainties are given. And M and N are dependent on B. Could you show me how to calculate and estimation for the uncertainty on A? Thanks a lot

Hello Everyone, my question is that what's the formula or equation to find flexural wave propagation speed along the beam?? Please guide with this, I am kind of stuck in this problem. Thanks in advance,waiting for the response...

I read Weyl tensor helps on propagating gravitational effects. Ricci is local depending on mass energy at that point and would vanish at other points. Weyl propogates the gravity effects (for example gravity at any point between Earth Moon is due to Weyl Tensor). I didn't quite get it...

I am just wondering why there is a discrepancy between two different methods for error propagation. For example, if you have ## Q = (a)(b)(c) ## then the relative error in Q is simply the square root of the sum of the squares of each of the terms being multiplied together, correct? But what if...

Homework Statement Hello, I have the following operation that I want to perform: f=\frac{\bar{X}}{100-\sum \bar{Y}_j}*K \bar{X} and \bar{Y} are averages with variances S_{X}^2 and S_{Y_j}^2 and K is a constant. How will the error propagate? Homework Equations According to...

Homework Statement In a region of empty space, the magnetic field is described by ##\vec{B} = B_0e^{ax}\sin{(ky-\omega t)} \hat{z}##. Find the speed of propagation ##\vec{v}## of this field. Homework Equations ##\Delta \vec{B} = \frac{1}{v^2}\frac{d^2\vec{B}}{dt^2}## , ##k=\frac{\omega }{...

Before the recent LIGO result, there was already not much doubt that gravitational effects propagated at c, but the evidence was indirect. To what extent does the LIGO result test this directly, and how will this be improved in the future? The H1 and L1 instruments are separated by 3002 km...

Homework Statement Based on wave attenuation and reflection measurements conducted at 1MHz, it was determined that the intrinsic impedance of a certain medium is , and the skin depth is 2m. Determine: a) The conductivity of the medium b) The wavelength in the medium c) The phase velocity...

Hello! I still would like to thank those who participated to my previous thread about group velocity and dispersion. Now there is a (maybe) simpler question. A sinusoidal, electro-magnetic plane wave in the vacuum propagates in a certain direction with the following wavenumber, which is supposed...

Hi all, I am interested in finding the power of a laser diode as function of the distance z, assuming a free space propagation. I think to have enough information to work it out but I am stacked at the moment. Given: the initial power, P0 = 1mW beam width clip (e-2 = 13.5%), wx = 3μm, wy =...

Hi... If we consider propagation of sound through a medium other than vacuum, we mean, when sound is produced by a vibrating speaker diaphragm, it gives periodic jolts to the molecules and atoms present in the medium or air. These "pushes" are transferred to all adjacent atoms until finally few...

If waves require a medium or some kind of force carrier to propagate, how exactly do matter waves propagate?

I need to clear up my (mis)understanding about QFT. Does QFT show how a particle propagates through spacetime? (Or maybe this is the realm of QM) Or does QFT only specify how a particle propagates as a particle through time without reference to where in space it is? But... if QFT specifies how...

I know that the time-evolution operator in quantum mechanics is ##e^{-iHt}##. Is this also called the Schrodinger time-evolution operator? Also, can you guys explain why the amplitude ##U(x_{a},x_{b};T)## for a particle to travel from one point ##(x_{a})## to another ##(x_{b})## in a given...

Moderator's note: Thread moved to homework section. Thus no template. I have an exercise in which I have to calculate the Area from the following measurements: L = 22.1 ± 0.1 cm W = 7.3 ± 0.1 cm Of course, A = W * L = 161.33 but since I have a measurement with just 2 significant digits the...

Say I have a 0-10 lbf load cell that can measure the force it takes to lift an object. The load cell is accurate to 1% of the full scale. I take 5 measurements and get the following readings: 5.2, 5.1, 4.9, 5.0, & 4.8, all in lbf. Now I am asked to give the mean with the associated...

I'm trying to understand how a vibrating body produces oscillations in sound pressure. I've been through derivations and solutions of the wave equation for a string, but I don't understand the transition from waves on a string to sound pressure waves. How are the waves on a string or drum...

What is the most accurate way to think of a photon moving through space? 1) Should we think of it as an entity that travels as an integrated corpuscle that parts the "quark sea" of empty space and maintains it's internal integrity as it moves from point A to point B, or.. 2) Should we think...

Shankar ("Principles of Quantum Mechanics", 2nd ed.) shows that the free particle propagator "matrix element" is given by (see p. 153): ## \qquad \langle x | U(t) | x' \rangle = U(x,t;x') = \left(\frac{m}{2\pi\hbar it}\right)^{1/2} e^{im(x-x')^2/2m\hbar} ##, which can be used to evaluate the...

The Transverse resonance method is used to determine the propagation constant of a wave in several waveguides, like the rectangular waveguide, or also dielectric waveguides. It takes advantage of the fact that a standing wave is present along a certain direction (transverse with respect to the...

Hello Forum, I have a lot of questions concerning Wave propagation, but I will not pose them all into one thread, because of my experience, that part of them will be overlooked. So let's get started: 1. Phase shift, E-B- Independence Consider a plane wave generated by a distant dipole...

I tried posting this question in this forum a couple of weeks ago, but didn't get an answer to my question. I'm going to try posting it again using the formatting template so that it is hopefully clearer. I am also not sure if this is the right forum to be posting this in. It is a problem I ran...

Hi, I'm trying to make sense of a wave propagation problem. It's a 1D problem, modelling propagation of density perturbations which travel like waves in a fluid. The problem is governed by the mass and momentum equations and density is related to pressure using the bulk modulus of the fluid...

In the propagation of non-monochromatic waves, the group velocity is defined as v_g = \displaystyle \frac{d \omega}{d k} It seems here that \omega is considered a function of k and not viceversa. But in the presence of a signal source, like an antenna in the case of electro-magnetic wave or a...

Hi, I am trying to find the error propagated by calculating the sum of a set of mass flow rates collected over the same length of time. The sum of mass flow rates can be calculated with two approaches, since the collection time is the same for all of them. Approach (1) is adding up all of the...

Homework Statement Write down the equation for a plane wave traveling in perpendicular to the plane x+y+z=constant traveling in the direction of increasing x, y, and z. Homework Equations From the given information how do I determine the unit vector that goes next to E(0)? How do I determine...

Homework Statement Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra. I am having trouble finding information on how to calculate and propagate errors when the quantities in my equations are not independent...

Homework Statement The complex amplitudes of a monochromatic wave of wavelength ##\lambda## in the z=0 and z=d planes are f(x,y) and g(x,y), redprctively. Assume ##d=10^4 \lambda##, use harmonic analysis to determine g(x,y) in the following cases: (a) f(x,y)=1 ... (d) ##f(x,y)=cos^2(\pi y / 2...

Homework Statement Suppose you measure three numbers as follows: Homework Equations x= 200. +-2. y= 50. +-2. z= 40. +-2. where the three uncertainties are independent and random. Use step-by-step propagation to find the quantity q= x/(y-z) with its uncertainty. The Attempt at a...