Wave equation Definition and 544 Threads

Homework Statement I have the damped wave equation; u_{tt} = 4 u_{xx} -2 u_{t} which is to be solved on region 0 < x < 2 with boundary conditions; u(0,t) = 2, u(2,t) = 1. i must; 1) find steady state solution u_{steady}(x) and apply boundary conditions. 2) find \theta(x,t)...

Hi! I was reading some notes on relativity (Special relativity) (http://teoria-de-la-relatividad.blogspot.com/2009/03/3-la-fisica-es-parada-de-cabeza.html) and it says that the classical wave equation is not Galilean Invariant. I tried to show it by myself, but I think there is some point that...

What is the meaning of the wave equation...in English??! Everybody knows one dimensional wave equation \frac{\partial^2u}{\partial t^2} = c^2 \frac{\partial^2u}{\partial x^2} This together with verious boundary and initial condition give various solution of u(x,t). Also it can be transform...

My lecturer said that a standing wave is formed when two waves that travel in the opposite have the same frequency. He said that if the waves are y1 and y2, then the resulting wave y can be given as the sum: y = y1 + y2. y = Asin(\omegat - kx) + Asin(\omegat + kx). (1) Where the...

Hi to all! I need to solve following equation: \frac{\partial^2 u}{\partial t^2} + 2 \beta \frac{\partial u}{\partial t} -c^2\nabla^2u=0 It describes a damped wave on a x-y plane. 2\beta is damping factor and c is wave speed. I haven't had any luck finding a PDE class that looks...

Hey, I've come across a part in my notes which I can't figure out. Essentially it says: \frac{\partial^{2}y}{\partial t^{2}} = v^{2} . \frac{\partial^{2}y}{\partial x^{2}} is space and time invariant. Whereas: \frac{\partial y}{\partial t} = -v . \frac{\partial y}{\partial x} is not...

1. Homework Statement consider the differential d²ψ(x)/dx²=k²ψ(x); for which values of a is the equation e^(a*x) is a solution to the above equation. 2. Homework Equations 3. The Attempt at a Solution I have been working on this problem but I do not know how relate the 2...

Homework Statement consider the differential d²ψ(x)/dx²=k²ψ(x); for which values of a is the equation e^(a*x) is a solution to the above equation. Homework Equations The Attempt at a Solution I have been working on this problem but I do not know how relate the 2 equations, or if...

Water Waves -- Universal Wave Equation Homework Statement Attached. Homework Equations v=fλ The Attempt at a Solution f= cycles/time f= 45/60 f= 0.75 Hz The trouble I am having is wondering if λ is 28 m or do i have to do something else to find λ?

Hi, Why the wave equation is \frac{\partial^2 u}{\partial^2 x}=c^2\nabla^2 u? Where does it come from?Thanks.

In what conditions do we use time dependent and time independent Schrodinger's wave equations?

Homework Statement Ok so hope someone will be able to help... I've used the D'Alembert method to solve the wave equation and have got that the general form should be y(x,t) = f(x+ct) + g(x-ct) Now I am also told that the time dependence at x=0 is sinusoidal.. that is, y(x,0) =...

how do i show that v(x,t)=u(x,t)-ue(x) satisfies the wave equation? =( i get that ue(x)=gx2/2c2 + ax + b where a and x are just constants but how does this satisfy the wave equation?

Homework Statement The ends (x=0,x=L) of a stretched string are fixed, the string is loaded by a particle with mas M at the point p (0<p<L). 1. What are the conditions that the transverse displacement y must satisfy at x=0, x=p and x=L? 2. Show that the energy of the system is E(t) =...

In am studying PDE and I have question about D'Alembert solution for one dimension wave equation. I am going to reference Wolfram: http://mathworld.wolfram.com/dAlembertsSolution.html [SIZE="6"]1) I want to verify the step of \frac{\partial y_0}{\partial t} of step (14) of the page...

Homework Statement A stretched string occupies the semi-infinite interval -\infty<x\leq0. y(x,t) := f(x-ct) + f(-x-ct) is a solution of the wave equation. What boundary condition does y satisfy at x=0? Describe what is going on in terms of incident and reflected waves. Homework...

In relativity, the scalar wave equation in the coordinate system (x,y,z,ict) is \frac{\partial^2\phi}{\partial x^2}+\frac{\partial^2\phi}{\partial y^2}+\frac{\partial^2\phi}{\partial z^2}+\frac{\partial^2\phi}{\partial (ict)^2}=0 In 3D classical mechanics, the Laplace equation is:{when...

Y=a+b because Y,aa+Y,bb=0

Homework Statement Show that the wave equation becomes \left(1-\frac{V^{2}}{c^{2}}\right)\frac{\partial^{2}\psi'}{\partial x'^{2}}-\frac{1}{c^{2}}\frac{\partial^{2}\psi'}{\partial t'^{2}}+\frac{2V}{c^{2}}\frac{\partial^{2}\psi'}{\partial t' \partial x'} = 0 under a Galilean transform if the...

I'm not understanding something here. Maxwell's wave equation is: Laplacian of E = (1/c^2) * second partial of E (sorry, I don't know how to write symbols) But the second partial derivative is the Laplacian. So how can you scale the laplacian of E by a number and get the laplacian of E as...

1. Solve the wave equation u_(tt) = 4u_(xx) on the interval [0, π] subject to the conditions u(x, 0) = cos x, u_t(x, 0) = 1, u(0, t) = 0 = u(π, t). Homework Equations 3. Hello. This appears to be a common separation of variables question. Only problem is after using...

Homework Statement Solve, u_{t} = u_{xx}c^{2} given the following boundary and initial conditions u_{x}(0,t) = 0, u(L,t) = 0 u(x,0) = f(x) , u_{t}(x,0) = g(x)Homework Equations u(x,t) = F(x)G(t) The Attempt at a Solution I solved it, I am just not sure if it is right. u(x,t) =...

Homework Statement I am trying to calculate the angular momenta for \psi(x,y,z) = A(ar^2 + bz^2) A is given as a constant. Homework Equations The Attempt at a Solution I know that z=r\sqrt{4\pi/3} * Y_0^1 What I have so far is:- \psi(x,y,z) = r^2Aa +...

Hello, I want to use Galerkin method to solve 3-D wave equation \nabla^2 u+k^2 u=0, with the following boundary conditions: at z=z_1 plane, u=g, and when x,y,z go to the infinity, u becomes 0. My question is how to choose the basis function \phi_n for u: u=\sum \lambda_n \phi_n. As my...

Hi, I have this electrodynamics problem sheet on the paraxial approximation, and I am not getting very far with it. It starts off talking about a laser beam traveling in the z-direction, and says that a scalar wave has the form F(r,w)eiwt. The first part of the question ends with me proving...

In the wave equation u(x,t), what does u represent?

a wave equation is given as A = A cos (kx - ωt) so why if someone describes the wave equation to be A = A sin (ωt - kx) , the argument of the sin function changes by a minus sign? and is there a meaning to it? also i still don't really understand why the minus sign in the first equation...

I need help solving 3Utt+10Uxt+3Uxx=sin(x+t) I have found the homogeneous part, which is U(x,t)=f(3x-t) +g(x-3t), but I don't know where to go from there. Any help would be much appreciated!

I am unable to determine the relationship between x and t in the following equation. y\left(x,t\right)=A\sin\left( kx-\omega t \right)\\ If \nu=\frac{x}{{t}} then the numbers within the bracket goes to zero; because kx=\omega t for all points on y(x,t). Can anyone...

Homework Statement a) Assuming the presence of sources (J flux density) and (p charge density) , write out Maxwell’s equations in the time domain in terms of and only for a lossless, but inhomogenous medium in which ε = ε(r) , μ = μ(r). b) Derive the vector differential...

Homework Statement \Psi(x) = \frac{C}{a^2 + x^2} Homework Equations I know to do this I need to solve for: \int_{-\infty}^{\infty} \left|\Psi(x)\right|^2 = 1 The Attempt at a Solution I'm not sure how to do it for this function. I've tried various methods to solve C^2...

Homework Statement Show that Y(x,t) = cos(kx)exp(-iwt) is a solution to the time-dependent Schrodinger wave equation. where k is the wavenumber and w is the angular frequency Homework Equations Hamiltonian of Y(x,t) = ihbar d/dt Y(x,t) The Attempt at a Solution When I plug...

Problem: Applied Partial Differential Equations (Richard Heberman) 4ed. #12.3.6 Consider the three dimensional wave equation \partial^{2}u/\partial t^2 = c^2\nabla^2 u Assume the solution is spherically symetric, so that \nabla^2 u =...

[b]1. Homework Statement [/b Determine whether the function D=A sin kx cos \omegat is a solution of the wave equation. Homework Equations D=Asin (kx-\omegat) The Attempt at a Solution sorry completely lost please help

This comes from Jackson's Classical Electrodynamics 3rd edition, page 613. He finds the Green's function for the covariant form of the wave equation as: D(z) = -1/(2\pi)^{4}\int d^{4}k\: \frac{e^{-ik\cdot z}}{k\cdot k} Where z = x - x' the 4 vector difference, k\cdot z = k_0z_0 -...

The Shroedinger equation defines the time evolution of the wave function. If we observe a region of large gravitational fields where observed time has slowed, the wave function will be observed to evolve slowly. In the limit of a Black Hole it will stop evolving altogether. Still quantum...

Hello, I have a question about the following problem: Given a wave equation \Psi(n,t) where t is the time, and n is an integer. What is the Fourier transform? I'm trying to reproduce this paper: One-dimensional Quantum Walks by Ambainis et al...

I was interrested in the general solutions to the wave equation depending on only one spatial coordinate. For one linear coordinate, the general solution is: a f(x-ct) + b g(x+ct) For one radial spherical coordinate, the general solution is: a f(r-ct)/r + b g(r+ct)/r I thought that...

Hi there, i would like everyone to evaluate my working here, this is my attempt to wave equation / vibrating system using vector approach. please correct me if i had made some mistakes. Your help is much appreciated, Thanks, and have a nice day. :smile: Regards, Daniel.

1D wave equation -- bizarre problem! I am trying to write a solver for a 1D wave equation in python, and I have run into a bizarre problem that I just can't find a way out of. I start with the wave equation, and then discretise it, to arrive at the following, phi(i,j+1) = deltat2/deltax2...

I know that we can find the speed of the wave in shallow water by: c^2 = gh but how do we derive it?

Hey Everyone, So I've been working on some very basic QM mathematics. Basically I've worked out the wave equation for a particle in one dimension (briefly) like so: -\frac{\hbar 2}{2m}\psi"(x) + V(x)\psi(x) = E\psi(x) V = 0 for 0 < x < L ; (L = "Length" of the Boundary) =>...

Homework Statement The displacement of the wave traveling in + x direction is: Y(x, t) = 0.35 (m) Sin (6x- 30t); where x is in meter and t is in second. If the wave reaches its maximum displacement after 0.04 sec, what is the value of x corresponding to y (max). Homework Equations...

Homework Statement How can I find out if a function is a solution of a wave equation such as: (a) xt (b) log(xt) (c) x² + c²t² The Attempt at a Solution Is it simply differentiating the funtion with respect to 'x' twice and equating this to the product of 1/c² and...

I am trying to derive the wave equation for 'Second Sound in superfluid Helium-4 using the basic tenets of the two-fluid model. I am following the derivation in a book which has intermediate steps along the way - I am trying to fill in the gaps. I am almost there - there is only one step that I...

Let u be a solution of the wave equation utt-uxx=0 on the whole plane. Suppose that ux(x,t) is a constant on the line x=1+t. Assume that u(x,0)=1 for all x in R and u(1,1,)=3. Find such a solution u. I need help trying to incorporate the ux(x,t) is a constant on the line x=1+t

A transverse wave on a rope is given by y(x, t)= (0.750\; {\rm cm})\, \cos ( \, \pi [(0.400\;{\rm cm}^{ - 1})x+(250\; {\rm s}^{ - 1})t]) Find the period. This should be simple, but I keep getting the wrong answer in Mastering Physics. I can't find any explanation in my book, and it's...

I'm reposting this because there was a problem with the title/LaTeX last time. Homework Statement Solve the wave equation (1) on the region 0<x<2 subject to the boundary conditions (2) and the initial condition (3) by separation of variables.Homework Equations (1) \frac{\partial^2...

Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance... For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain...

Hi, I was wondering if anybody could help me understand a derivation connected to the double-slit experiment that I came across within an introduction to quantum theory paper. I was interested in understanding this approach because it seems to provide a useful correlation of the meaning of the...