Wave equation Definition and 544 Threads

Homework Statement The differential equation describing the motion of a stretched string can be written \frac{\partial ^2 y}{\partial x^2} = \frac{\mu}{T} \frac{\partial^2 y}{\partial t^2} μ is the the mass per unit length, and T is the tension. (i) Write down the most general solution you...

Homework Statement Solving Normalized case of schrondinger wave equation Homework Equations The Attempt at a Solution This type of question is not normalized case of solving using schrondiger equation. Any example of solving normalized case using schrondinger equation ? How...

Hi, I have a test tomorrow and I'd like you to guys help me please. Solve the following: $\begin{align*} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0. \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1. \\ &...

I'm trying to prove the conformal invariance (under g_{\mu\nu}\to\omega^2 g_{\mu\nu}) of \bar{\Box}{\bar{\phi}}+\frac{1}{4}\frac{n-2}{n-1}\bar{R}\bar{\phi} I've found that this equation is invariant upto a quantity proportional to...

Homework Statement Show that the wave equation u_{tt}-\alpha^{2}u_{xx}=0 can be reduced to the form \phi_{\xi \eta}=0 by the change of variables \xi=x-\alpha t \eta=x+\alpha tThe Attempt at a Solution \frac{\partial u}{\partial t}=\frac{\partial \xi}{\partial t}\frac{\partial...

Homework Statement Hello, I have problems with expressing a reflected wave mathematically. In my printed notes I found the following formulas for reflected waves: a) For a fixed end: incoming wave: y_1(x,t)=e^{-i(kx+ωt)} reflected wave: y_2(x,t)=re^{i(kx-ωt)} where r is the reflection...

Homework Statement Homework Equations The Attempt at a Solution b) I could figure it out if kz was changed to kx... Double Derivative of E(r, t) with respect to x is = 0 Double Derivative of E(r, t) with respect to t is = -ω2*E0*cos(kz - wt + ∅0) Multiply the second term by k2/ω2...

Homework Statement Hello, as in topic, i am looking for simpliest wave equation i can get, i don't really need to know what it is etc., i only need it to be as simple as possible. Homework Equations The Attempt at a Solution I think that simpliest wave equation will be just y =...

Homework Statement Consider an electromagnetic wave hitting a metallic surface with conductivity σ at normal incidence. a) Derive the wave equation describing this situation. Hint: Use Ohm’s law, J = σE to eliminate the current. b) Solve the wave equation for the electric field to...

i am an A-level physics student (high school if you're american) and for a research topic i have chosen wave particle duality. i have been able to explain the ideas of diffraction, double slit experiments, photo electric effects and electron diffraction easily enough, but we are expected to take...

Hi there, I'm a mechanical engineering student who's extremely interested in going into physical oceanography after finishing undergrad. I'm trying to find a good source for the wave equation as it relates to physical oceanography, as well as orbital paths of particles, and have yet to find...

This thing is driving me mad, I thought I figured it out already, but it seems I was wrong. Any help would be appreciated. Homework Statement "Under what conditions does the sum of two sinusoidal waves also satisfy the wave equation?" The sum wave is D(x,t) = A_{1}sin(k_{1}...

I need to use the Fourier transform to solve the wave equation: $\begin{aligned} & {{u}_{tt}}={{c}^{2}}{{u}_{xx}},\text{ }x\in \mathbb{R},\text{ }t>0, \\ & u(x,0)=f(x), \\ & {{u}_{t}}(x,0)=g(x). \end{aligned} $ So I have $\dfrac{{{\partial }^{2}}F(u)}{\partial...

Hello all, Homework Statement We can represent a mechanical transverse wave by Y=Asin(kx-wt+∅). Now imagine this wave traveling (towards right as velocity is positive) and meeting up with two cases Case 1) Rigid wall. Case 2) Free end. The way gets reflected completely( ignoring transmission...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}}+t,\text{ }t>0,\text{ }x\in \mathbb R, \\ & u(x,0)=x \\ & {{u}_{t}}(x,0)=1. \end{aligned} $ Okay first I should set $v(x,t)=u(x,t)-\dfrac16 t^3,$ then $u(x,t)=v(x,t)+\dfrac16 t^3$ so $u_{tt}=v_{tt}+t$ and $u_{xx}=v_{xx}$ so...

I have $u_{tt}=u_{xx},$ $x\in\mathbb R,$ $t>0,$ $u(x,0)=0$ and $u_t(x,0)=\chi_{[-1,1]}(x).$ What does mean the last condition? In such case, how to solve the equation then? Thanks!

I need to apply D'Lembert's method but in this case I don't know how. How to proceed? Determine the solution of the wave equation on a semi-infinite interval $u_{tt}=c^2u_{xx},$ $0<x<\infty,$ $t>0,$ where $u(0,t)=0$ and the initial conditions: $\begin{aligned} & u(x,0)=\left\{ \begin{align}...

Homework Statement An infinite string obeys the wave equation (d2z/dx2)=(ρ/T)(d2z/dt2) where z is the transverse displacement, and T and ρ are the tension and the linear density of the string. What is the velocity of transverse traveling waves on the string? The string has an initial...

Hi, I have a general question about linear wave equation: Is solving the linear wave equation is equivalent to compute the output of a linear system where source is the input? Thanks in advanced! Chao

Hi, I have a understanding of what is eigen value and eigen function. But I am unable to correlate the same with Schrodinger wave equation. Can you please help me to clarify the concept? Thanks!

Homework Statement Verify that Acos(kx-ωt) and Bsin(kx-ωt) are solutions of the one dimensional wave eqn. if v=ω/k. Does f(x,t)=(ax+bt+c)^2 represent a propagating wave? If yes what is its velocity? Homework Equations I know the partial differ. eqns. for the wave equation are d^2...

Hi, I am confused about my solutions to the following governing equation: u_{tt}-c^2u_{xx}=F_{xx} For F=A(x)sech^2\left(\frac{x-c_gt}{B}\right) Where c,c_g,B \in \mathbb{R} and A(x) is a linear function. Also, we have c_g<c. Substituting physical values for the parameters, I...

the harmonic wave equation is given by y(x,t)=Rsin{2\pi/\lambda(vx-t)+\phi} where R is amplitude \lambdais wavelength v is velo of wave \phi is initial phase. Could you please tell as well as explain me what are the parameters x and t where there in units of length and time respectively.

hi , can anyone please explain to me what is wavefunction - and can we apply schordinger wsve equation to simple pendulum. thanks

Homework Statement A transverse harmonic wave travels on a rope according to the following expression: y(x,t) = 0.18sin(2.2x + 17.1t) The mass density of the rope is μ = 0.146 kg/m. x and y are measured in meters and t in seconds. Homework Equations I do not know what to use...

Homework Statement Show ψ(x,t) = f(x-at) + g(x+at) satisfies the wave equation (a^2)*(∂^2ψ/∂x^2)-(∂^2ψ/∂x^2)=0 Homework Equations The Attempt at a Solution I think i just take the derivative twice and end up with something like the second derivative = a^2*second derivative...

For a wave equation η(u,v) = f1(u) + f2(v) where u = x - ct and v = x + ct, consider an initial displacement η = η0(x) and an initial velocity ∂tη = \dot{η_{0}}(x). I'm a little confused with the velocity initial condition; shouldn't the time derivative of η0(x) be 0?

Homework Statement Consider the second order wave equation u_{tt} = 4u_{xx} There are initial and boundary conditions attached, but I'm less concerned with those for the moment. I think I can figure those out if I can figure out where to get started. Rewrite this as a system of first order...

Homework Statement If a system satisfies the equation \nu^2 {\partial^2 \psi\over \partial x^2}={\partial^2 \psi\over \partial t^2}+a{\partial \psi\over \partial t}-b\sin\left({\pi x \over L}\right)\cos\left({\pi \nu t\over L}\right) subjected to conditions: \psi(0,t)=\psi(L,t)={\partial...

D'Alembert's solution to the wave equation is u(x,t) = \frac{1}{2}(\phi(x+ct) + \phi(x-ct)) + \frac{1}{2c}\int_{x-ct}^{x+ct} \psi(\xi)d\xi where \phi(x) = u(x,0) and \psi(x) = u_t (x,0). I'm trying to understand this intuitively. The first term I get: a function like f = 0 (x/=0), = a (x=0)...

Homework Statement Consider an isotropic medium with constant conductivity \sigma. There is no free charge present, that is, \rho = 0. a)What are the appropriate Maxwell equations for this medium? b)Derive the damped wave equation for the electric field in the medium. Assume Ohm's...

Homework Statement Write down an equation to describre a wave \psi(x,t) with all of the following properties a) It is traveling in the negative x direction b) It has a phase velocity of 2000ms-1 c) It has a frequency of 100kHz d)It has an amplitude of 3 units e) \psi(0,0)= 2 units...

Hi there. I was trying to understand this deduction of the one dimensional wave equation developed at the beggining of the book A first course in partial differential equations of H.F. Weinberger. You can see it right here...

Consider a string of length 5 which is fixed at its ends at x = 0 and x = 5. The speed of waves along the string is v = 2 and the displacement of points on a string is defined by the function f(x,t). At the initial time the string is pulled into the shape of a triangle, defined by f(x,0) =...

(Note: although arising in QM, this is essentially a calculus question) Ѱ (x) = A sin (n╥x/a) 1 = ∫ l Ѱ (x) l^2 dx with limits of integration a to 0 1 = ∫ A^2 sin^2 (n╥x/a) dx with limits of integration a to 0 Indefinite integral ∫ sin^2 x dx = x/2 - sin2x/4 I know this integral...

I have just completed Atomic Structure from my textbook. In that a Schrodinger Wave Equation is mentioned and after that it is written that it is not in the scope of this book to solve this equation. I want to know what is so hard in the schrodinger wave equation that it is not of my level?

Homework Statement As I know wave equation has d^2/dt^2,but Schrodinger's equation has only d/dt (Time-dependent). Why these eq has different thing(d/dt, d^2/dt^2)? I assume if Schrodinger's equation has d^2/dt^2(not d/dt), eigenfunction of Schrodinger's equation is not stable along with...

How did Schrodinger derive the wave equation? Does it have a physical interpretation? And, what are its scope of applicability and limitations?

in electromagnetic books, we see by the aid of vector calculus, we can reach to wave equation from Maxwell 's equations. is it possible to reach to Maxwell 's equations from wave equations? in the other word, in electromagnetic books we get Maxwell 's equations as phenomenological...

Homework Statement Well, I'm not sure if this is a correct subforum to post my problem, but to me it does seem to me as an academic problem. One I can not solve, apparently. Well, anyway. I'm solving the 1+1 radial wave equation using finite difference. I shifted my grid, so that the origin...

Hello everyone and greetings from my internship! It's weekend and I'm struggling with my numerical solution of a 1+1 wave equation. Now, since I'm eventually going to simulate a black hole ( :D ) I need a one-side open grid - using advection equation as my boundary condition on the end of my...

Homework Statement Show that the electromagnetic wave equation \frac{\partial^{2}\phi}{\partial x^{2}} + \frac{\partial^{2}\phi}{\partial y^{2}} + \frac{\partial^{2}\phi}{\partial z^{2}} - \frac{1}{c^2}\frac{\partial^{2} \phi}{\partial t^2} is invariant under a Lorentz transformation...

Hello, My question is about method of characteristics used in solving wave equation. I've found a book on dynamics of structures, and what I cannot understand is a part when it is talked about method of characteristic. Can somebody try to read the shoert article attached below and see if...

Hi, I want to solve the following wave equation: u_{tt} - c^2 u_{xx} = f(x,t)u What is the best way to do it? I don't think I can use Duhamel's principle since I have a u in the forcing. Doing a change of variables of the form w=x+ct, v=x-ct Seems to make things worse. Any ideas...

Homework Statement (A) [PLAIN]http://remote.physik.tu-berlin.de/farm/uploads/pics/Gekoppeltes_Pendel_01.png What happens when you swing pendulum P1? (B) How does the position of the spring affect the outcome? (C) If the length of the string of one pendulum was longer than the...

For a traveling wave u(x,t) = u(x-ct) How is the relation below hold? u_{x}u_{xt}=-u_tu_{xx} I don't understand why there is (-) sign . Thanks in advance ! PS. Here is the URL of the book I am having trouble with https://www.amazon.com/dp/0198528523/?tag=pfamazon01-20...

Wave Equation (urgent) Sounds waves in a pipe of varying cross-section are described by the wave equation v2 d/dx .(1/A.dAu/dx) = d2u /dt2 Where A = 0.2 +0.3x simplify the equation My attempt at a solution Sub in A: v2 d/dx ( 1/(0.2+0.3x) . d(0.2+0.3x)u/dx) =d2u/dt2 Not to...

This is the problem, it says to solve the solution to the vibrating string problem. \frac{\partial^2 u}{\partial t^2}=\frac{\partial^2 u}{\partial x^2} u(0,t)=u(1,t)=0,t>0 u(x,0)=x(1-x),0<x<1 \frac{\partial u}{\partial t}(x,0)=sin(7\pi x),0<x<1 The solution form I obtained (without showing my...

For a real stretched string, the wave equation is (partial deriv)^2 (u)/partial deriv t^2 = (T/mu) (partial deriv)^2 (u)/partial deriv x^2 - B/mu(y) where T is the tension in the string, mu is its mass per unit length and B is its "spring constant". Show that the wave given by u =...

Hello everybody! I have a really silly question concerning wave equation: consider the problem \left\{ \begin{matrix} u_{tt} &=& u_{xx} & x \in \mathbb{R}\\ u(x,0) &=& 0 & \\ u_t(x,0) &=& x(1-x)\chi_{\left[0,1\right]}(x)& \end{matrix} \right. the solution is given by d'Alembert's...