Wave equation Definition and 543 Threads

Homework Statement Wavelength of a tsunami: Propagates toward shore as a sinusoidal plane wave. - determine the peak value of the horizontal particle displacement. Is your answer consistent with the assumption that the water momentum is mainly horizontal? Explain by considering the...

[FONT=Verdana]Hi, In class a few days ago, my teacher gave me a challenge question which they wanted me to answer. I have yet to succeed in finding the correct answer so I would be grateful for anybody who might be able to explain where I am going wrong with this problem! Homework Statement...

Hello everyone I am searching for the answer for the condition (related to the total energy of the particle E) for which any particle will go into the square potential well. I have studied Griffiths's quantum mechanics book Introduction to the quantum mechanics Section 2.5 and 2.6) but still...

Homework Statement Suppose a horizontally stretched string is heavy enough for the effects of gravity to be significant, so that the wave equation must be replaced by ##u_{tt} = c^2u_{xx} - g## where ##g## is the acceleration due to gravity. The boundary conditions are ##u(0,t) = u(l,t) = 0##...

I would like people's opinions on why the negative energy solutions of Dirac's Relativistic Wave equation were simply ignored in 1934 to make things fit. Another related question is with the energy conservation laws as they stand. Why in pair production from a photon at 1.022MeV forming a...

Why would one need to use the Schrodinger's wave equation? What does it give us? I understand that we solve for psi and stuff, but graphically what does it give us, in practical and not theoretical terms? What exactly is a wave function? After solving for psi with the help of the equation, we...

Hai PF, I had a doubt in the sector of partial differential equation using one dimensional wave equation. Actually the problems is below mentioned :smile: A string is stretched and fastened at two points x=0 and x=2l apart. motion is strated by displacing the string in the form...

Homework Statement Show that the function is a solution of the wave equation utt = a2uxx. u = (t)/(a2t2-x2) Homework Equations Quotient rule (f/g)' = (g*f ' - f*g') / g2 The Attempt at a Solution I began with the first and second partials of u with respect to x...

What is the general solution of the following hyperbolic partial differential equation: The head (h) at a specified distance (x) is a sort of a damping function in the form: Where, a, b, c and d are constants. And the derivatives are with respect to t (time) and x (distance). Thanks in advance.

Homework Statement I'm using a couple different textbooks on waves, and it seems they've possibly contradicted one another. I think the problem may be that one deduced the equation for displacement in a transverse harmonic wave y(x,t) through the equation for displacement at t=0 [y(x,0)] and...

I just learned how to derive the wave equation and now I have some questions about it. In my physics text (first year) it simply says (without reason) that the solution to the wave equation is y(x,t) = Acos(kx-wt), where A is the amplitude of displacement, k is the wave number and w is the...

Hello! The wave equation given: {1\over{c^2}} {\partial^2 \phi\over{\partial t^2}} = \Delta \phi with r = \sqrt{x^2+y^2+z^2} needs to be rearranged, so that {1\over{c^2}} {\partial^2 ( r \phi) \over{\partial t^2}} = {\partial^2 (r \phi) \over{\partial r^2}} . Are there any tricks to obtain...

Homework Statement a non uniform string of length L and mass M, has a variable linear density given by μ=kx where k is the distance measured from one side of the string and k is a costant. a) find that M=(kL2)/2 b) show that the time t required to a pulse generated from one side of the string...

We derived the wave equation by applying f=ma to an element of an oscillating string, yielding ∂2y/∂x2 = 1/v2 ⋅ ∂2y/∂t2. In order to get this result it was necessary to assume that the string in question was nearly horizontal, so that the angle formed by the tension vector and the horizontal...

Homework Statement Serway's Physics for Sciencetists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19:[/B] (a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the...

Hi dear people , Hello I waw studying super position of two Sound Waves , traveling in same medium with same frequency , same wavelength and same amplitude while differing in phase . quick derivation : Wave 1 displacement y1= A sin (kx-vt ) and wave 2 displacement y2= A sin (kx-vt-phase...

Consider the wave equation ##\nabla^{2} f - \frac{1}{c^{2}} \frac{\partial ^{2} f}{\partial t^{2}} = \delta(r) \delta(t) ## where there is no wave before ##t=0## The solution will be something up to a constants like ##f=\frac{\delta(r-ct)}{r}##. So we have a dirac delta function that...

Homework Statement Derive from the formulas ##\frac{D^\pm}{Dt}(u \pm F) = 0## where ##\frac{D^\pm}{Dt} = \frac{\partial}{dt} + ( u \pm c) \frac{\partial}{\partial x}## the one-dimensional wave equation in the acoustical limit. \begin{cases} u << c\\ c \approx c0 = const\\ F =...

Suppose you are given a phase spectrum or (/and) equation of the (main) signal only and you are said that the given (main) signal is formed of 3 other signals. Is it possible to compute phases of these three signals from the equation or (/ and) phase spectrum of the (main) signal? Also,what...

Homework Statement A particle is in the state |\psi \rangle = \frac{1}{{\sqrt 3 }}|U\rangle + \frac{{a\sqrt {(2)} }}{{\sqrt {(3)} }}i|D\rangle . The up state |U\rangle = \left( {\begin{array}{*{20}{c}} 1\\ 0 \end{array}} \right) and the down state |D\rangle = \left(...

Please, I've been unable to comprehend how the mathematical wave equation was derived.. Please can anyone explain it to me...

Homework Statement The general wave equation can be shown as: y(x,t) = ymsin(kx-ωt) Homework Equations See above The Attempt at a Solution My question relates to the variables present in this equation. I understand what the amplitude is, its the magnitude of the maximum displacement of...

Homework Statement Please see attached. Part ii) Homework EquationsThe Attempt at a Solution So I try to conserve volume as it suggests in the hint. I take the initial volume of the region to be given by: $$ h \times \delta x \times l = (\delta x + \eta) (h+\Psi) l $$ Where l is just some...

Homework Statement If ##u(x,t)\in \mathbb R, x\in[-\pi,\pi] ## represents a standing wave with ##u(\pm\pi,t)=0## Then what is the most general solution u(x,t)? Homework EquationsThe Attempt at a Solution [/B] Using the separation of variable technique: u(x,t)=P(x)Q(t) I get ##P(x)...

Hi, We were recently testing out waves on a string and completing a lab based on it, and I wanted to provide background information on how the equation v=fλ was formulated. I would greatly appreciate it if someone could direct me to a source on it. Thanks.

Homework Statement Consider a propagating wave packet with initial length L0. Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wave packet is approximately: \begin{equation} \Delta \omega = \frac{v_{g}}{L_{0}} \end{equation} where vg is the group...

Homework Statement Normalize the wave function $$ \langle x|\psi\rangle = \left\{ \begin{array}{l l} Ne^{-kx} & \quad x>0\\ Ne^{kx} & \quad x<0 \end{array} \right..$$ Determine the probability that a measurement of the momentum p finds the momentum between ##p## and ##p + dp## for this wave...

Homework Statement This is Problem 7.6 from Electronic Properties of Engineering Materials by Livingston. "Over a wide range of frequencies, the dielectric constant of a polymer is found to be proportional to the inverse square root of frequency. (a) How does the phase velocity of EM-waves...

Homework Statement Okay, here's the deal:I have been given a second order nonlinear differential equation, and I have also been given the general solution with constants A and B. I am supposed to find the constants A and B. The solution represents a fermion at rest, since the solution does not...

When I deduct the the general form of wave equation, I noticed it has a second order partial derivative form. I am wondering why wave equation has a second order partial derivative form nor a first order partial derivative form?

Hi everybody! Can you explain me how I can obtain wave equation given a metric? For example, if I have this metric $$g_{μν}=diag(−e^{2a(t)},e^{2b(t)},e^{2b(t)},e^{2b(t)})$$, how can derive the relation $$\frac{1}{\sqrt{g}}\partial _t(g^{00}\sqrt{g}\partial _t...

Greetings all and new to the forum here. It's been many years and I've forgotten how to do it, and it should be a basic question, but assuming we have an equation Ex=E_0*cos(wt-kz), how do we translate to sine? I've seen it written sin(kz-wt) or sin(wt-kz), but I've just plainly forgotten how...

Dear forum users, I need some help on the following proof that appears in a book (pp. 84 in Bohren' Absorption and Scattering of light by Small Particles). This is no a home work problem. The problem statement: \vec{M} = \nabla\times\vec{c}\psi, where \vec{c} is some constant vector and \psi...

Hi, I'm trying to wrap my head around the derivation of the wave equation and wave speed. For starters I'm looking at the derviation done on this site: http://www.animations.physics.unsw.edu.au/jw/wave_equation_speed.htm I could maybe explain what I understand at this point Given a string with...

Hi, So in the steady state Schrodinger equation (SE), the E on the RHS (see http://scienceworld.wolfram.com/physics/SchroedingerEquation.html) is the sum of the kinetic and potential energy of the electron. However, is this the same as the 'internal energy'? The statistical distribution used...

Homework Statement given a medium in which p=0, j=0 but where the polarization vector P=P(r,t). Derive the wave equation satisfied by E and B.Homework Equations i started with the 4 basic Maxwells equations ∇ · D = ρ (1) ∇ · B = 0 (2) ∇ × E = −∂B/∂t (3) ∇ × H = J + ∂D/∂t (4) and with the...

I wrote a wave equation simulation in C# a while ago, and while everything works fine, I am running into the expected problem that my simulation boundaries (ie the edges of the grid) reflect the waves coming to them. Obviously I want to keep the grid of reasonable size, so I looked into what...

Homework Statement The question is to sketch for values of t = 0, t =0.25, t = 0.5, t=1 and t = 1.25 for the wave equation Ytt = Yxx in the infinite domain with initial conditions y(x,0) = f(x) = \begin{cases} 1 & \text{if } 0 ≤ x ≤ 1 \\ & 0 (otherwise) \end{cases} Yt(x,0) = 0 Homework...

Can someone please help me in plotting a D'Alembert wave equation solution in MATLAB? I am so confused as how to plot it in MATLAB I need to plot a graph like the one below

Homework Statement Ytt = 1 Yxx with initial conditions of yT(x,0) = 0 y(x,0) = \begin{cases} 1 & \text{if } x \geq 0 \ & \text{if } x \leq 1 \\ 0 & \text{if } otherwise \end{cases} Sketch the solution of this wave equation for 5 representative values of t, when the solution of the wave is...

so H(psi) = E(psi) is the schrodinger equation such that psi is the eigen function of the hamiltonian operator, and since E is the eigen value of the hamiltonian, then this E is the measured E. This is what i understand so far, and i am building on this here. All psi must be eigen function of...

Homework Statement The question is Ytt- c^2Yxx =0 on the doman 0<x< +infinity where initia conditions are y(x,0) = e^-x^2 = f(x) , Yt(x,0) =x*e^-x^2 = g(n) and boundary condition is y(0,t) = 0 and c = 2 Homework Equations D'Almbert solution 1/2(f(x+ct)+f(x-ct))+1/2c∫ g(n) dn over the...

It's the application of Shrodinger wave equation to H-atom and I can't solve the first step. Please help me solve this. I'm not maths student so it's really hard to solve it:( d^2 psi/dx^2+d^2psi/dy^2+d^2psi/dz^2+8π^2m/h^2(E-V)=0 Where x= rsin(theta)cos(phi) y=rsin(theta)sin(phi) z=rcos(theta)...

Homework Statement So it says solve this wave equation : [y][/tt] - 4 [y][/xx] = 0 on the domain -infinity<x<infinity with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2)) Homework Equations I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz The...

Homework Statement Solve u_{tt}(x,t)+2u_{t}(x,t)-u_{xx}(x,t)=18\sin\left(\dfrac{3\pi x}{l}\right) \omega=\frac{\pi n c}{l} Boundary conditions u(0,t)=u(l,t)=0 l<\pi Initial conditions u(x,0)=u_t(x,0)=0 Homework Equations [/B] The general inhomogeneous damped wave equation is u_{tt}(x,t)+2\mu...

Homework Statement Please find question attached. The context is a lecture course on seismic theory for exploration geophysics. Homework Equations The substitution for the elasticity tensor made in my solution is given in the lecture notes. Please find my attempt at the solution attached...

In the equation regarding an array of masses connected by springs in wikipedia the step from $$\frac {u(x+2h,t)-2u(x+h,t)+u(x,t)} { h^2}$$ To $$\frac {\partial ^2 u(x,t)}{\partial x^2}$$ By making ##h \to 0## is making me wonder how is it rigorously demonstrated. I mean: $$\frac {\partial ^2...

Homework Statement http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_Dec_2008_tfy4240.pdf problem 2a) Homework EquationsThe Attempt at a Solution Hi. In problem 2a I was supposed to find a wave equation, however while digging around in maxwell's equations, I found this result...

Hi, I am trying to plot a function subjected to a nonlinear wave equation. One of the method I found for solving the nonlinear schrodinger equation is the split step Fourier method. However I noticed that this method only works for a specific form of PDE where the equation has an analytic...

Suppose that we have the four-vector potential of the electromagnetic field, [texA^i[/tex] The wave equation is given by $$(\frac {1}{c^2} \frac {\partial^2}{\partial t^2}-\nabla^2) A^i=0$$ Now the solution, for a purely spatial potential vector, is given by $$\mathbf{A}(t...