Wave equation Definition and 543 Threads

Homework Statement So I don't really understand what the professor means by "show why the displacements y(x,t) should satisfy this boundary value problem" in problem 1. Doesn't that basically boil down to deriving the wave equation? At least in problem 2 he says what he wants us to show...

Homework Statement So I don't really understand what the professor means by "show why the displacements y(x,t) should satisfy this boundary value problem" in problem 1. Doesn't that basically boil down to deriving the wave equation? At least in problem 2 he says what he wants us to show...

Homework Statement phi(x,t) = A e *[-a(bx+ct)*2] I'm trying to find the speed of the equation Homework Equations f(x+vt) +vt which means it is in the negative x-direction f(x)= e^-ax^2 plugging in x'=x+vt A e *[-a(bx+ct)*2] where a= constant A= amplitude...

Is it correct to state that a progressive wave, originates when a simple harmonic motion is imparted continuously to adjacent particles from one direction to another moving with a velocity v. Using this idea, substituting (t - x/v) instead of t is the simple harmonic motion function...

I have been thinking about this. For a wave equation, the acceleration of a point on a drumhead is proportional to the height of its neighbors $$U_{tt}=\alpha^2\nabla^2U$$ The heat equation, change in concentration or temperature is equal to the average of its neighbors...

Homework Statement 3 tuning forks of frequencies 200, 203, 207 Hz are sounded together.find out the beat frequency. Homework Equations Beat frequency= n1-n2 (n=frequency). The Attempt at a Solution I know that beat frequency is the difference in the frequencies of two superposing notes. But...

Text books often give an expression like Asin(kx-ωt) as a solution of the wave equation, but they don’t show how to arrive at this solution. Other textbooks, which go through the complete solution process of the wave equation, determine the coefficients using Fourier series. My goal was to get...

This question concerns a section from the book Modern Physics by James Rohlf. http://srv3.imgonline.com.ua/result_img/imgonline-com-ua-twotoone-Bs4zgy7pruqG.png He shows that the form of the Wave equation for light remains invariant under a Lorentz boost (4.42)...

As an exercise, I am trying to solve the 2nd-order wave equation: $$ \frac {\partial ^2 E}{\partial t^2} = c^2 \frac {\partial ^2 E}{\partial z^2} $$ Over a domain of (in SI units): ## z = [0,L=5]##m, ##t = [0,t_{max} = 5]##s, ##c = 1## m/s and boundary/initial conditions: ## E(z[0]=0,t) =...

Given the equation ##\frac{d^2 \psi (x)}{{dt}^2}+\frac{2m}{{\hbar}^2}(E-V(x))=0## the general solution is: $$\psi (x)=A_1 e^{ix \sqrt{\frac{2m}{{\hbar}^2}(E-V(x))}} +A_2 e^{-ix \sqrt{\frac{2m}{{\hbar}^2}(E-V(x))}}$$ If we have an infinite potential well: ## V(x)=\begin{cases} \infty \quad x\ge...

Hello to everybody, I am solving some examples related to wave equation of shear horizontal wave in cylindrical coordinates (J.L Rose: Ultrasolic Waves in Solid Media, chapter 6), which is expressed as follows: ∇2u=1/cT2⋅∂2u/∂t2 The Laplace operator in cylindrical coordinates can can be...

Hello! So if I want to describe dΨ(x)/dt can I use 1D wave equation?

Homework Statement [/B] I found a couple of assignements for a physics course I will take later this year- so I started looking into them a bit in advance. It concerns wavefunctions. I'm a bit rusty on my trigonometric identities So I would love if someone could try to help me solve these two...

I have been reading these notes on Rindler coordinates for an accelerated observer. In Rindler coordinates, the hyperbolic motion of the observer is expressed through the coordinate transformation $$t=a^{-1}e^{a{{\xi}}}\sinh a{\eta}\\ {}x=a^{-1}e^{a{{\xi}}}\cosh a{\eta}.$$On a space-time...

Homework Statement In some places, the wave equation is y=Asin(wt-kx) and in other places they have y = Asin(kx-wt) and they treat them as if they are equal. How are they equal? They also had y=-Asin(wt-kx). What is the difference between all 3? Homework Equations As above The Attempt at a...

Homework Statement I'm reading through the derivations of the linear wave equation. I'm following everything, except the passage I highlighted in yellow in the below attachment: Homework Equations I'm not understanding why partials must be used because "we evaluate this tangent at a...

hi, I know the wave equation in terms of minkowski metric, and we use ordinary derivative in that equation. I also know this wave equation in terms of general metric form using covariant derivative, but I do not know the derivation of it. Could you spell out the steps of derivation?? How do we...

Hi. Is the superposition of two different monochromatic waves in a dispersive medium still a wave (i.e. a solution of a wave equation) if the phase velocity is not the same? Since the wave equation contains the phase velocity, the two individual waves are solutions of different wave equations...

How could you that y(x,t)=ƒ(x/a + t/b), where a and b are constants is a solution to the wave equation for all functions ,f ? many thanks.

Hello, I have a wave of the form y = Asin(x-vt) + Asin(x+2vt) which I substituted into the wave equation to find out if it satisfies it. It didn't because of the speed of the left traveling wave being equal to 2v. What I got was: A[-sin(x-vt)-sin(x-2vt)] = 1/v2 * A[-v2sin(x-vt) -...

Hi there. First of all, sorry for my bad english. I ´m trying to solve next exercise, from Vibrations and Waves in Continuos Mechanical Systems (Hagedorn, DasGupta): Determine the eigenfrequencies and mode-shapes of transverse vibration of a taut string with fixed ends and a discrete mass in the...

Homework Statement From the derivation of v(x,t) and i(x,t) I am stuck on how the inverse Fourier transform of e^(-jwx/u) was calculated. I am trying to understand how the PDE was fully solved here: http://fourier.eng.hmc.edu/e84/lectures/transmission_line/node1.htmlHomework Equations Not...

Homework Statement Consider the wave equation: u_{tt} - c^2u_{xx} = f(x,t), \hspace{1cm} for \hspace{1cm} 0 < x < l \\ u(0,t) = 0 = u(l,t) \\ u(x,0) = g(x), u_t(x,0) = f(x) \\ Find a nontrivial solution. Homework EquationsThe Attempt at a Solution Here's what I did, but I have little...

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 }{...

Homework Statement For a 1-dimensional simple harmonic oscillator, the Hamiltonian operator is of the form: H = -ħ2/2m ∂xx + 1/2 mω2x2 and Hψn = Enψn = (n+1/2)ħωψn where ψn is the wave function of the nth state. defining a new function fn to be: fn = xψn + ħ/mω ∂xψn show that fn is a...

Homework Statement derive the following wave equation ∇2H = 1/c2 (∂2H/∂t2) Homework EquationsThe Attempt at a Solution I'm not sure how to derive it. I suppose I can break it into a whole bunch of partial derivatives because of the del squared operator and then just lump the three partial...

Homework Statement Show that the funtions y(x,t) and g(x,t) satisfy the differential equation of a wave unimensional. What function is a wave?Homework Equations y(x,t)=x² +v²t² ; d(x,t)= 2Acos(kx)cos(wt) frac{d²y}{dt²}=2v² frac{d²y}{dx²}=2 The Attempt at a Solution frac{d²y}{dt²}=2v²...

Homework Statement Consider the homogeneous Neumann conditions for the wave equation: U_tt = c^2*U_xx, for 0 < x < l U_x(0,t) = 0 = U_x(l, t) U(x,0) = f(x), U_t(x,0) = g(x) Using the separation of variables, find a nontrivial solution of (1). Homework Equations Separation of variables The...

Homework Statement Wave equation: ytt=yxx Initial conditions: Y(x,0) =f(x) = x (0 ≤ x < 1) 2.5(5-x) (1 ≤ x < 3) 0 (Otherwise) and yt(x,0) = 0 Boundary condition: y(0,t) =0 Semi infinite domain: 0 ≤ x < infinity Homework Equations d'Alembert solution...

Homework Statement i want to prove that the functions u(r,t)=(1/r)f(r-v*t) and u(r,t)=(1/r)f(r+v*t) satisfy the wave equation in spherical coordinates, i have tried a lot to solve it but in each time i would face a problem. Homework Equations wave equation : grad^2(u)=(1/v)*(partial ^2...

From my understanding, all the wave equation says is the transverse acceleration of a particle on wave is equal to the the curvature of the of the wave at that point-particle times the propagation speed squared. Am i missing something?

$$\frac{\partial^2}{\partial t^2}u(x,t)=c^2\Delta u(\vec{x},t)\qquad \vec{x}\in \mathbb{R}^n$$ is known as the wave equation. It seems not very trivial, so is there any derivations or inspirations of it? To solve this equation, we have to know the initial value and boundary conditions...

What's the solution to the wave equation for circular waves on a two-dimensional membrane? The waves have a constant wavelength throughout. For spherical waves, you have to multiply the amplitude by 1/r. I tried 1/√r for circular waves but it didn't work. :blushing:

First, we know for every wave function $$p(x)=\psi(x)^*\psi(x)$$ indicates the probability density of a particle appearing at the point x. So if we calculate $$P=\int _M p \text{d}x$$ this gives the probability of the particle appearing in the range M. On the other side, I was thinking about...

Homework Statement I'm currently following the textbook Advanced Engineering Mathematics by Erwin Kreyszig. I'm learning the derivation of the Wave equation using the method shown in the book, but when I reached the final part of the derivation, the working just confuses me. (1/Δx)[ (u/dx)|...

Hi, following the attached paper I try to find the general solution of the following wave equation: \frac{1}{a^2} \frac{\partial^2 \phi}{\partial t^2} + \frac{2M}{a}\frac{\partial^2 \phi}{\partial x \partial t} + \overline{\beta}^2 \frac{\partial^2 \phi}{\partial x^2} =...

hi, my question is , when do we need to have vector wave equation. So far in Maxwell equation you can find scalar as well as vector wave equation, I figure out when we are looking for the scattering we need vector wave equation. Second isn't simple to work out scalar potential and then by its...

I am modelling a 1D fluid wave propagation problem and I needed to know how I can check that my results are energy conservative. please reply, urgent. thank you.

Homework Statement Is the function y(x,t) = Ae(−β2x2−2βxt−t2) + Be(−x2+2αxt−α2t2) a solution to the wave equation ∂2y / ∂t2 = v2 (∂2y / ∂x2) Homework Equations ∂2y / ∂t2 = v2 (∂2y / ∂x2) The Attempt at a Solution I have found the solution through finding the partial derivatives (∂2y / ∂t2...

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...

I came across this expression for the wave equation: \nabla^2E + \mu\sigma\frac{\partial{E}}{\partial{t}} - \frac{n^2}{c^2}\frac{\partial{E}}{\partial{t^2}} = 0 My question is what kind of medium is it for/where did it come from?

Homework Statement A 1D wave function ψ(x,t) satisfies these initial conditions: ψ(x,0) = 0 for all x ∂ψ/∂t (x,0) is v for -a≤x≤a 0 otherwise Plot ψ(x,t) as a function of x at time t=a/v. Homework EquationsThe Attempt at a Solution I know the 1D wave equation is given by...

Homework Statement [/B] Don't know if this goes here or in the advanced bit, thought I'd try here first! I know the general solution of a 1D wave equation is given by d'Alembert's formula ##u(x,t) = 0.5[u(x+vt,0) + u(x-vt,0)] + \frac{1}{2v} \int_{x-vt}^{x+vt} \frac{\partial u}{\partial...

Hey guys the Idea of simulating the DSE with a program caught my interest but I just had a few questions regarding the DSE Is there a function that models the probability of finding an electron at a certain point ONCE It's BEEN FIRED FROM AN ELECTRON GUN? like an amplitude function squared or...

Hello, I am working through Hughston and Tod "An introduction to General Relativity" and have gotten stuck on their exercise [7.7] which asks to prove the following non- linear wave equation for the Riemann tensor in an empty space: ∇e∇eRabcd = 2Raedf Rbecf − 2Raecf Rbedf − Rabef Rcdef I have...

So the equation is f(x,t) = f(x-vt,0) = A sine k(x-vt). Now Since x is displacement of wave from origin, t is time taken for that,wouldn't 'x-vt' always be equal to 0 ? If x-vt is 0, Y = A sine k(x-vt) will also be zero. So am I writing the equation wrong?

Homework Statement There's a derivation here that I'm looking at, and I've hit a snag. At (1) about 15 lines down the page, the author divides by Δx and takes the limit as Δx goes to 0. I understand what he did on the right side of the equation, but on the left side of the equation, by what...

Homework Statement Homework Equations y (x,y) = 2YmSin(kx)Cos(wt)The Attempt at a Solution I am having trouble at setting up the standing wave equation for this problem. Once I set up the equation, I know that part a b c d is just plugging in the numbers. From what I learned, I know that...

Hello! I need to understand one seemingly simple thing in wave mechanics, so any help is much appreciated! When a pulse travels to the right toward an open end(like a massless ring that is free to oscillate only in the vertical direction), then when the wave reaches the end it gets reflected and...

I don't know if this is a silly question? Am I missing simple math? How does a wave depending on amplitude and frequency make it's equation a second order differential equation?