Wave equation Definition and 544 Threads

Homework Statement Homework Equations In question. The Attempt at a Solution To be clear it's part (vi) that's unclear to me. In order to ignore the cosine term it has to reduce to 1. This can happen, only if k(x1+x2)/2 = ωt Is this a correct assumption ? Also, it is known that k = 2∏/λ...

What do the components of the following equation represent : http://www.mediafire.com/view/?0we6f9jkw26qi9o To be clear, this represents a wave of the form Acos(kx-wt) after being reflected off a wall. I understand that the ∅ represents the phase change of the wave after hitting the...

I don't completely understand how equation 4.4.4 was derived and determined. I understand the derivation behind the basic wave equation 4.3.4 but not what happened in 4.4.4. Why is there a need for all the negative signs ? Would a simple phase change suffice ? Please do be a bit detailed in...

equation -- Wave Equation Derivation Question Hello, my teacher says that if, on a wave equation f(x-ct)=f(e) then \partial_{ee}= \partial_{tt}- c^2 \partial_{xx} but i think that \partial_{t}=\frac{\partial }{\partial e} \frac{\partial e}{\partial t}=-c\frac{\partial }{\partial e} and...

f(z,t)=\frac{A}{b(z-vt)^{2}+1}... \frac{\partial^{2} f(z,t)v^{2} }{\partial z^2}=\frac{-2Abv^{2}}{[b(z-vt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(z-vt)^{2}}{[b(z-vt)+1]^{3}}=\frac{\partial^2 f}{\partial t^2} \frac{-2Abv^{2}}{[b(z-vt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(z-vt)^{2}}{[b(z-vt)+1]^{3}} this...

Homework Statement Given that the the One Dimensional wave equation is \frac{∂^{2}y(x,t)}{∂x^{2}} = \frac{1}{v^{2}} \frac{∂^{2}y(x,t)}{∂t^{2}} is y(x,t) = ln(b(x-vt)) a solution to the One Dimensional wave equation? Homework Equations Shown above. The Attempt at a Solution So my Professor...

Hi, so the problem is this: I am trying to solve (analytically) the wave equation with c=1: u_{xx}=u_{tt} on x,t>0 given the initial conditions u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt) I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms...

Homework Statement Just looking back through my notes and it looks like I'm missing some. Just a few questions. For one example in the notes I have the wave utt-c2uxx + u3 = 0 and that the energy density 1/2u2t + c2/2u2x + 1/4u4 I have that the differential form of energy conservation...

i've just learned de broglie wave equation in chemistry which tells that matter can act as wave. if an electron is moving at a certain speed(v) at which its wavelength is comparably in meters. If a football is made to move at the same speed (v),will it behave as a wave? Since Football also has...

Question 1 Basically I have no idea how to calculate the z part of the equation since x and y are assumed to be propagating in the z direction.

Hey! How to transform the equation \bigtriangleup\vec E=\operatorname{div}(\operatorname{grad}(\vec E))=\epsilon_0\cdot\mu_0\cdot\frac{\partial^2\vec E}{\partial t^2} in Einstein Notation? Thank you all for your help!

I have been trying to research the best way to solve the Schrodinger wave equation numerically so that I can plot and animate it in Maple. I'd also like to animate as it is affected by a potential. I have been trying for weeks to do this and I don't feel any closer than when I started. I have...

Homework Statement Dear Guys, Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic waves? Please help! Manish Germany Homework Equations The Attempt at a Solution it is of the form g(ax+bt). which is the general form for harmonic wave. but what bothers me is the...

Dear Guys, Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic wave? Please help! Manish Germany

I'm trying to learn more about the physics of guitars. I followed through the derivation of the transverse wave equation and that makes sense, but it seems like several of the simplifying assumptions might not apply. There are a lot of approximations with small angles and small slopes. I...

Homework Statement Prove that the electromagnetic wave equation:  (d^2ψ)/(dx^2) + (d^2ψ)/dy^2) + (d^2ψ)/(dz^2) − (1/c^2) * [(d^2ψ)/(dt^2)]= 0 is NOT invariant under Galilean transformation. (i.e., the equation does NOT have the same form for a moving observer moving at speed of...

in solving the schrodinger wave equation, there arises this differential equation (d^2/dx^2) ψ + (1/x) (d/dx )ψ + (a/x)ψ + (b/x^2)ψ + cψ = 0 Please any leads on how to solve this equation will be highly appreciated.

A harmonic wave traveling in +x-direction has, at t = 0, a displacement of 13 units at x = 0 and a displacement of -7.5 units at x = 3λ/4. Write the equation for the wave at t = 0. Homework Equations The equation for a harmonic wave is r = asin(kx-vt+θ) a being the amplitude k...

Homework Statement Hello all, stuck on a question involving a formula for a wave that doesn't make much sense to me. Assuming that a wave on a string is represented by: y(x,t) = y_i*sin((2∏/λ)(vt-x)) Where y is transverse displacement at time t of the piece of string at x. The...

Homework Statement Please have a look at the picture attach, which shows the proof of the D'alembert's solution to the wave equation. If you can't open the open, https://www.physicsforums.com/attachment.php?attachmentid=54937&stc=1&d=1358917223 click onto this...

I read in the book regarding a point charge at the origin where Q(t)= \rho_{(t)}Δv'\;. The wave eq is. \nabla^2V-\mu\epsilon\frac{\partial^2 V}{\partial t^2}= -\frac {\rho_v}{\epsilon} For point charge at origin, spherical coordinates are used where: \nabla^2V=\frac 1 {R^2}\frac...

Hello, is it possible for one to assume a straight-line propagation of an e.m. wave and constant velocity c? If so, is it possible to simplify the wave equation utt=c2uxx by expressing the spatial variable x through the time variable t? x must be a function of t, since the motion is...

Hello, this is a problem I've been trying to do but I'm not sure it is right. Particularly the A_n and B_n terms. Thanks https://docs.google.com/open?id=0BwZLQ_me50B8M0sxelVrbTBhYVk

For the wave equation I managed to get the coefficient of f: a1=2 and the coefficient of g: \frac{12pi}{2pi*2}=B2 Is these answers right, since my B2 does not match the answer I was given. Thank you

Does anyone know where I find second order damped wave equation worked where the overdamped, underdamped, and critically damped cases are all taken into account? I found resources where they throughout the overdamped and just focus on the underdamped.

$$ u(x,t) = \frac{1}{2}\int_{x - t}^{x + t}g(s)ds = \begin{cases} t, & (x,t)\in R_1\\ \frac{1}{2}(1 - x + t), & (x,t)\in R_2\\ \frac{1}{2}(x + t + 1), & (x,t)\in R_3\\ 1, & (x,t)\in R_4\\ 0, & (x,t)\in R_5,R_6 \end{cases} $$ where \begin{alignat*}{3} R_1 & = & \{(x,t):-1 < x - t < 1\text{ and }...

$$ u_{tt} + 3u_t = u_{xx}\Rightarrow \varphi\psi'' + 3\varphi\psi' = \varphi''\psi. $$ $$ u(0,t) = u(\pi,t) = 0 $$ $$ u(x,0) = 0\quad\text{and}\quad u_t(x,0) = 10 $$ \[\varphi(x) = A\cos kx + B\sin kx\\\] \begin{alignat*}{3} \psi(t) & = & C\exp\left(-\frac{3t}{2}\right)\exp\left[t\frac{\sqrt{9...

Given The 1D wave equations p_{x}'' - (1/c_{0}^2)p_{t}'' = 0 u_{x}'' - (1/c_{0}^2)u_{t}'' = 0 ρ_{x}'' - (1/c_{0}^2)ρ_{t}'' = 0 and linearised continuity and momentum equations ρ_{t}' = -ρ_{0}u_{x}', ρ_{0}u_{t}'=-p_{x} how may one derive the following two equations? u=p/ρ_{0}c_{0}...

\begin{alignat*}{3} u_{tt} & = & c^2u_{xx}\\ u(0,t) & = & 0\\ u_x(L,t) & = & 0\\ u(x,0) & = & \frac{x}{L}\\ u_t(x,0) & = & 0 \end{alignat*} Let's start with $u_t(x,0) = 0$. Then $$ u_t(x,0) = \sum_{n = 1}^{\infty}B_n\frac{\pi c}{L}\left(n + \frac{1}{2}\right)\sin\left[\frac{\pi x}{L}\left(n +...

Well title says it all pretty much. My question is if one set of boundary conditions uniquely specifies the solutions to the wave equation. My speculation comes from the fact that my book introduces electromagnetic in a bit weird way I think. It shows how Maxwells equations lead to the wave...

1. Solve the Heat equation u_t = ku_xx for 0 < x < ∏, t > 0 with the initial condition u(x, 0) = 1 + 2sinx and the boundary conditions u(0, t) = u(∏, t) = 1 (Notice that the boundary condition is not homogeneous) 3. Find the solution of the Wave equation u_tt = 4 u_xx with u(0...

Homework Statement Show that the boundary-value problem $$u_{tt}=u_{xx}\qquad u(x,0)=2f(x)\qquad u_t(x,0)=2g(x)$$ has the solution $$u(x,t)=f(x+t)+f(x-t)+G(x+t)-G(x-t)$$ where ##G## is an antiderivative/indefinite integral of ##g##. Here, we assume that ##-\infty<x<\infty## and ##t\geq 0##...

Hi there, This is a problem concerning hyperbolic type partial differential equations. Currently I am studying the book of S. J. Farlow "Partial differential equations for scientists and engineers". The attached pages show my problems. Fig. 18.4 from case two (which starts in the lower part...

http://imageshack.us/a/img824/1121/asdasdaw.png I am having trouble completely understanding what the question wants. I know it is quite clear but the part I am having trouble is the following. It says 'pretend' w(x,t) is a solution to the 2D equation, just independent of y, then to...

I was studying a book on QM and found out that the wave function for a free particle of completely undetermined position traveling in positive x direction is given by e^(2(pi)i(kx - nt)) where n is the frequency i have been trying a lot to derive it but till now i can't . Can anyone help me

Homework Statement Solve the boundary value problem \frac{\partial ^2 u}{\partial t^2} = c^2 (\frac{\partial ^2 u}{\partial x^2}+\frac{\partial ^2 u}{\partial y^2}), 0<x<a, 0<y<b, and t>0 for the boundary conditions u(0,y,t) = 0 and u(a,y,t) = 0 for 0 \leq y \leq b and t\geq0...

I am new to quantum mechanics and trying to combine the pieces. If I am looking into the quartum world, first I prepare a mechanism with which i can bring the properties and behavior of the particles i.e. an experiment to study them, but the information i emphasize to look on in the experiment...

hi, It is a bit confusing, because when I say "wave equation" the connotation it invokes in my mind is if I apply the equation I will find the function of the wave I'm exploring. Of course I know now this is wrong.. it is the other way around, I have to know my wave-function in advance and...

Consider the classical wave equation...

How did schroedinger arrive at the wave equation? I recently read in a book about the concept of wave packets using Fourier analysis and the wave equation was derived by forming a differential equation of the Fourier integral. But some books say that there is no formal proof of the...

Suppose that along a stretch of highway the net flow of cars entering (per unit length) can be taken as a constant $\beta_0$. The governing equation of motion is then $$ \frac{\partial\rho}{\partial t} + c(\rho)\frac{\partial\rho}{\partial x} = \beta_0 $$ where $$ c(\rho) = u_{\text{max}}\left(1...

Hello, I am studying wave mechanics and I managed to derive the linear wave equation with a string. Now I don't understand the significance of the equation or why I can use a string oscillating to make it general and apply to all sorts of waves Edit: this one \frac{\partial^2...

Consider the quasi-linear 1-D wave equation $$ \frac{\partial\rho}{\partial t} + 2\rho\frac{\partial\rho}{\partial x} = 0 $$ with the piecewise constant initial conditions $$ \rho(x,0) = \begin{cases} \rho_1, & x < -x_0\\ \rho_2, & -x_0 < x < x_0\\ \rho_3, & x > x_0 \end{cases} $$ where $\rho_1...

Traffic is moving with a uniform density of \rho_0. $$ \frac{\partial\rho}{\partial t} + c(\rho)\frac{\partial\rho}{\partial x} = \beta_0 $$ where $$ c(\rho) = u_{\text{max}}\left(1 - \frac{2\rho}{\rho_{\text{max}}}\right). $$ Show that the variation of the initial density distribution is given...

Homework Statement Given an equation for a wave \psi(x,t) = A e^{-a(bx+ct)^{2}} determine the direction of its propagation if you know \psi(x,t) = f(x \pm vt) and use this to find its speed. Homework Equations The Attempt at a Solution I figured I would just rearrange the expression in...

Homework Statement Let y_{1}(x,t)=Acos(k_{1}x-ω_{1}t) and y_{2}(x,t)=Acos(k_{2}-ω_{2}t) be two solutions to the wave equation \frac{∂^{2}y}{∂x^{2}}=\frac{1}{v^{2}}\frac{∂^{2}y}{∂t^{2}} for the same v. Show that y(x,t)=y_{1}(x,t)+y_{2}(x,t) is also a solution to the wave equation. Homework...

Homework Statement I've just derived the 1D wave equation for a continuous 1D medium from a classical Hamiltonian. I simply wrote Hamilton's equations, where the derivatives here must be functional derivatives (e.g. δ/δu(x)) since p and u are functions of x, and I got the wave equation (see...

Homework Statement Solve the initial boundary value problem u_{tt}=c^2u_{xx} u(-a,t)=0,\quad u(a,t)=0,\quad u(x,0)=\sin(\omega_1 x)-b\sin(\omega_2x) where a, b, \omega_1, \omega_2 are positive constants. Homework Equations d'Alembert's solution The Attempt at a Solution...

I've been searching online for the past week but can't seem to find what I am looking for. I need the analytic solution to the wave equation: utt - c^2*uxx = 0 with neumann boundary conditions that are not homogeneous, i.e. ux(0,t) = A, for nonzero A. also, the domain i require the...

Hi all, apologies if this has been answered elsewhere - I was unable to find an answer using the search function. Homework Statement "Expressed in terms of wavenumber and angular frequency, the equation for a traveling harmonic wave is: y = Asin(kx-ωt). Express this function in terms of (a)...