Wave equation Definition and 544 Threads

How do you use separation of variables to solve the damped wave equation y_tt + 2y_t = y_xx where y(0,t) = y(pi,t) = 0 y(x,0) = f(x) y_t (x,0) = 0 --- These are partial derivatives where y = X(x)T(t) So rewriting the equation I get X(x)T''(t) + 2X(x)T'(t) = X''(x)T(t) which...

Homework Statement I must use the wave equation to to find the speed of a wave. y(x,t) = (3.0mm) sin [(4.00mm^-1)x - (7.00 s^-1)t] Homework Equations Here's the wave equation. It has strange symbols. (∂^2 y) / (∂ x^2) = (1 / v^2) ((∂^2 y)/ (∂^2 t) The Attempt at a Solution...

Homework Statement Homework Equations N/A The Attempt at a Solution Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either. Help appreciated.

Hey there! I'm faced with this problem: http://img7.imageshack.us/img7/4381/25686658nz9.png It's a 1D nonhomogeneous wave equation with a "right hand side" equaling to the dirac delta function in x * a sinusoidal function in t. I have to find its general solution with the constraints...

Homework Statement A steel guitar string with a diameter of .3 mm and 65 cm long has a tension of 100 N. Find the frequencies of the first five modes of vibration and sketch a graph of the associated eigenfunctions. The density of steel,7700 kg/m^3 is needed to find \mu. Homework...

Homework Statement For which values of the constants a and b does u(x,t) = sin(ax)sin(bt) satisfy the wave equation Utt = C2uxx? Homework Equations The Attempt at a Solution I've taken the partial differentials: Ux = acos(ax)sin(bt) Uxx = -a2sin(ax)sin(bt) Ut = bcos(bt)sin(ax)...

This isn't a homework question, but something which has been bugging me. I can't figure it out. Maybe it's late, but it's probably a very stupid question If light shines onto a denser medium, the light slows down in this medium right? If the light slows down, then by the wave equation, v =...

Hi can anyone show me how to derive the linear wave equation mathematically or show me a link? I googled but unfortunately I am unable to find out anything about it. Wikipedia showed a derivation via Hooke's law, but I am not really interested since it is not a general derivation. My text...

paraxial wave equation - Solved Homework Statement When a laser beam traveling is traveling in one direction, we can make the paraxial approximation. Question: Find an expression for the surfaces with constant phase in the beam. Homework Equations From a previous part of the...

Homework Statement Homework Equations http://books.google.co.uk/books?id=4NXHYg70qqIC&pg=PA85&lpg=PA85&dq=paraxial+approximation+wave+equation&source=web&ots=6PbKKzSEz6&sig=bspXdKfxc-IiMV6AmoifMSJTHuk&hl=en&sa=X&oi=book_result&resnum=10&ct=result The Attempt at a Solution I...

Let respectively b = (b1, b2, b3) and e = (e1, e2, e3) denote the magnetic and electric field in some medium. They are governed by Maxwell’s equations which look as follows: (0.1) \partialte = curl b (0.2) \partialtb = − curl e (0.3) div e = 0 (0.4) div b = 0. Show that each bi and each ei...

Hey, I've been asked to find the minimum thickness for a slab of crystalline sapphire. The equation for the half wave plate is : d(ne-no) = (m+1/2)*lambda I found the minimum by using the fact that m=0 It then asks what the other wavelengths are which will allow the plate to act as a...

A particle is in a state described by (\frac{mk}{\pi^2 \hbar^{2}})^{1/8}exp(- \frac{1}{2 \hbar} \sqrt{mk}x^{2})exp(-if(t)) When applying separation of variables here, my book ignores the first fraction and sets g(x) = exp(- \frac{1}{2 \hbar} \sqrt{mk}x^{2}) h(t) = exp(-if(t)) But...

Hi all, I'm interested to find a solution to the wave equation corresponding to Gaussian initial conditions \psi(0,x) = e^{-x^2/2} A solution which satisfies these initial conditions is (up to some constant factor) \psi(t,x) = \int \frac{d^3k}{(2\pi)^3} e^{-k^2/2 + i(k \cdot x -...

What is the integral for the following equation (e^{}ikx)/x

I have made an attempt on this one, but I'm not quite sure that I have done it correctly so far..? I am now heading a (for me:)) massive partial integration, and therefore I think it's better to ask before I start. Homework Statement Find the solution u(x,t) of the inhomogenous wave...

Hey everybody, My professor started our PDE I class in Chapter six, so I am having a hard time with the really basic stuff to get the theory down. One of my questions to answer is to verify a solution by using direct substitution. u(x,t) \ = \ \frac{1}{2}\left[\phi(x+t) \ + \ \phi(x-t)...

Homework Statement Hi all. The wave equation at plus/minus infinity is zero: \left. {\left| {\psi (x,t)} \right| } \right|_{ - \infty }^\infty= 0 Does this also mean that: \left. {\left| {\psi (x,t)} \right|^2} \right|_{ - \infty }^\infty=0 ?

This is a fairly simple question, but the first such question I have done. Inorder to check my work I was hoping somone could show me how to normalize the following. \Psi(x,t) = Ae^{-a[(mx^{2}/\hbar)+it] where m is the particles mass And also that the expectation values of x and x2 would...

I was playing around with some manipulations of maxwell's equations and seeing if I could work out the wave equation for light. I get: (\nabla^2 -{\partial_{ct}}^2) \mathbf{B} = -\mu_0 \nabla \times \mathbf{J} (\nabla^2 -{\partial_{ct}}^2) \mathbf{E} = \nabla \rho/\epsilon_0 + \mu_0...

What is the equation of wave traveling in space making an angle "p" to the horizontal with wave length 'a',frequency 'n',time period 'T'. Please anyone can help me

Hi, Something has been bothering me about deriving the wave equation for a plane EM wave. We were showed this derivation in class and had to reproduce it but something is not making sense to me... The derivation is as follows: Suppose you have a plane EM wave (in a vaccuum) traveling in the...

Hi I have a presentation tomorrow and have to explain a few wave equations. I am using a book to walk me through them but there is one point I don't understand: At one point the book states: Because k=(angular frequency)/c, we will represent the waves of the electric field as: e^i...

Hi All, Question: "How is the wave equation derived? This is the question. Here is my answer. I am trying to ensure that it is correct. "To derive wave equation, we apply Newton's law to an elastic string, concluding that small amplitude transverse vibrations of the string obey the...

wave equation -- vector notation what does the solution to the SE look like if expressed in vector notation? say if we just used phi as a function of x and t.

Does anyone know how to derive the wave equation in curved spacetime? (-g)^{-1\over 2}\partial_\mu((-g)^{1\over 2}g^{\mu \nu}\partial_\nu \phi) = 0 A reference, or an outline of the derivation would be very helpful. Thanks.

Homework Statement How do you find the phase angle of a wave equation given in the form y(x,t) = Acos(kx - wt) thanks Homework Equations The Attempt at a Solution

[SOLVED] Seperation of variables in the 2 dimensional wave equation I'd like to apologize right away for the terrible formatting. I was trying to make it pretty and easy to read but I guess I'm just not used the system yet and I had one problem after another. As you'll see at one point the...

what do you have to do to solve this

Homework Statement I need to solve the following wave equation: [\nabla^2 + \frac{\omega_a^2}{c^2}\epsilon]\mathbf{E_a} = -\frac{4\pi\omega_a^2}{c^2}\mathbf{P}^{(3)} Homework Equations \mathbf{P}^{(3)}=\chi^{(3)}:\mathbf{E_1E_1E_2^*} E_1 and E_2 are two electric fields with...

Homework Statement As a wave passes through any element of a stretched string under tension T, the element moves perpendicularly to the wave's direction of travel. By applying the laws of physics to the motion of the element, a general differential equation, called the linear wave equation...

I Looked around the web for a while and had not found anything so I figured I'd ask you all about this. It's been awhile since I took a PDE course, but given your standard homogeneous /\u = 0 wave equation, does it scale above and beyond the typical 1-2 dimensional cases? If so, what are some...

Homework Statement how to find the speed and direction of propagation from the wave equation? Homework Equations y(x,t)=Aexp{B(x-ct)^2} The Attempt at a Solution

Homework Statement Show that, as long as v = w/k, the wave equation is solved by y(x,t) = Ae^(i(kx-wt)) v=velocity w=angular velocity k=wave number

I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me. I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which...

[SOLVED] Satisfying wave equation Homework Statement Confirm that the following wave satisfies the wave equation and obtain an expression for the velocity of a wave Y=Asin(2x-5t)*e^(-2t) Homework Equations the wave equation is (d^2y/dt^2)=(V^2)*(d^2y/dx^2) The Attempt at a...

Hi! How does one find out dx and dp from the wave equation? Appreciate ur help:)

I've managed to derive from Maxwell's equations the homogeneous electromagnetic wave equation with respect to the magnetic field. (The one that goes Del Squared of H minus (The second order partial derivative of B multiplied by the recipricol of C squared all equal to zero) Hopefully that...

[SOLVED] Calculate time evolution of Schrodinger wave equation Homework Statement At time t=0 particle is in state: \psi\left(x\right)=\sqrt{2}A\phi_{1}(x)+\frac{A}{\sqrt{2}}\phi_{2}(x)+A\phi_{3}(x) where \phi_{n}(x) are eigenfunctions of 1-D infinite potential well. a) Normalize...

Homework Statement Open Question 3.bmp Homework Equations The Attempt at a Solution Open Answer 3.bmp Any help with this would be greatly appreciated

i saw the 'proof' of the wave equation for a sound wave in a medium assuming the wave equation for a dissplacement wave. that is the equtaion s=s_{0} \sin(kx-wt) is supposed to hold for all points for a wave propagating in the x direction. then using this he found out the excess pressure at...

URGENT. Wave Equation question I have a standing wave and it's various parameters. I need to work out the amplitude at a point 3 cm to the right of an antinode. I'm stumped as to how to approach it. A pointer in the right direction would be great!

I have the next theoretical-practical problem. I have to build a tubular bell array (like that at symphonic orchrestas) with tubes (not rods) of aluminium or copper. The principal problem I have is I don't know how to state the wave equation for a tube (I have done it for a string). How I do it...

Homework Statement [(w^2).b - Tk^2]/Qw = tan(kx - wt + P) This can't be solved for all (x,t) with constant values of w and k Can you explain why this is so please? ive used b to represent the mass per unit length, and T is the tension Homework Equations This is the answer to a...

[SOLVED] 1-D Wave Eqn Alright, so this problem is giving me troubles, and I must just be missing the trick. The equation to solve is the one dimensional wave equation with isotropic, homogeneous, etc. (i.e. wave in a vacuum). Which means the PDE is \frac{\partial^2 u}{\partial t^2} = c^2...

Homework Statement Assume that \psi_{1}(x,t) and \psi_{2}(x,t) are solutions of the one-dimensional time-dependent Schrodinger's wave equations. (a) Show that \psi_{1} + \psi_{2} is a solution. (b) Is \psi_{1} \cdot \psi_{2} a solution of the Schrodinger's equation in general...

I know how to write down solutions of wave equation \partial^2_t u(t,x) = \partial^2_x u(t,x) for given initial u(0,x) and \partial_t u(0,x) like this u(t,x) = \frac{1}{2}\Big( u(0,x+t) + u(0,x-t) + \int\limits^{x+t}_{x-t} \partial_t u(0,y) dy\Big), but what about \partial^2_t u(t,x) =...

can someone tell me why this is true \vec{F}=T(\frac{dy(x+\Delta x)}{dx}-\frac{dy(x)}{dx})\cong T(\frac{d^2y(x)}{dx^2})\Delta x and am i correct in understanding the notation in that that dy(x) simply means the same as dy when it is implied dy is a function of x?

It is just a mere question...Can we write the solution of wave equation as f=g[(+-)ct(+-)x]?

First of all I have to say that translating specific words from native language to english, is not easy. So I hope that you realize what is going on: What did I do wrong ? (Traveling waves from: http://en.wikipedia.org/wiki/Waves ).