Wave equation Definition and 544 Threads

Homework Statement I have a problem that I'm trying to make sense of. Note y_t is the partial derivative of y with respect to t and y_tt is the second order partial derivative of y with respect to t, etc. The complete problem statement is the following: Show that for the equation...

a. As the wavelength of a wave in a uniform medium increases, its speed will _____. a. decrease b. increase c. remain the same The correct answer is c?? I thought that the change in wavelength always incrases the speed of the medium? What does it mean by uniform medium? Can anyone...

The problem is, rather briefly: Show that the wave equation is INVARIANT The equation is given as: [the Laplacian of phi] - 1/(c^2)*[dee^2(phi)/dee(t^2)] dee being the partial derivative.. phi is a scalar of (x, y, z, t) Now, i want, and think i should be able, to solve this problem...

Homework Statement Express the solution P(t, x1) = cos(!t − kx1) as the superposition of two complex exponentials. Show that each complex exponential is also a solution of the 1-D wave equation. Homework Equations just that THETA=P !=w whoops, made a type The Attempt at a...

Homework Statement Consider a medium where \vec{J_f} = 0 and {\rho_f}=0, but there is a polarization \vec{P}(\vec{r},t). This polarization is a given function, and not simply proportional to the electric field. Starting from Maxwell's macroscopic equations, show that the electric field in...

Homework Statement Consider the simplified wave function: \psi (x,t) = Ae^{i(\omega t - kx)} Assume that \omega and \nu are complex quantities and that k is real: \omega = \alpha + i\beta \nu = u + i\omega Use the fact that k^2 = \frac{\omega^2}{\nu^2} to obtain expressions for \alpha and...

Homework Statement Consider the simplified wave function: \psi (x,t) = Ae^{i(\omega t - kx)} Assume that \omega and \nu are complex quantities and that k is real: \omega = \alpha + i\beta \nu = u + i\omega Show that the wave is damped in time. Use the fact that k^2 =...

Hello everyone. I'm asked in a problem to prove that a given general solution is valid for the wave equation \nabla^2 p - \frac{1}{c_0^2} \frac{\partial^2 p}{\partial t^2} = 0 . The given solution was p(x, t) = A_1 f_1 (x - c_0 t) + A_2 f_2 (x + c_0 t). I just need a check of work here. I...

Hello, I have a couple of questions about my assignment. Here are the assigned questions plus my attempts. 1) One end of a rope is tied to a stationary support at the top of a vertical mine shaft 80.0 m deep. The rope is stretched taut by a box of mineral samples with a mass of 20.0 kg...

lol my head is about to explode! :P i think this is similar to a previous question i asked but i can't quite get it none the less... http://img137.imageshack.us/img137/7796/picture11gf9.png now what i did was to following this ...

Hi everyone, I'm having a bit of trouble with this pde problem: http://img243.imageshack.us/img243/9313/picture3ui3.png i get the answer to be u(x,t)=0 but i am guessing that's not right. is the general solution to this problem: u(x,t) = f(x+ct) + g(x-ct) ?? thanks sarah :)

Could someone help me out on the following questions? Q. Consider the free vibrations of a string of length L clamped at x = 0 and constrained at x = L such that u_x \left( {L,t} \right) = - ku\left( {L,t} \right),k > 0. (a) Show that the eigenvalues are given by the positive roots of...

A series of waves traveling at 200m/sec are being generated by a 50hz source. A point at the very top of the crest of a certain wave is ? meters away from a corresponding point 4 crests away. The only equation I have is V=lambda*F. Is there a way to get the distance w/ this or am I missing...

I am having trouble understanding the solution to the wave equation: this is thought of as the final solution to the PDE: but I see that: is a solution to the function. But what I don't get is why D'Alembert's Solution isn't in terms of sines and cosines like that solution right above...

I would like to know how to derive the wave equation for a 3 dimensional case, I was looking it up on wikipedia, and their explination wasn't very comprehensive, I was wondering if anyone knew of any other website that would be able to let me fullly understand it. Edit: not the shrodinger wave...

Sir, Does the equation, y = a[log(x – vt)] Represent a traveling wave? I think the answer is No, because it is not a harmonic function. Is it right?

Sir, Consider a progressive wave represented by the equation, y = A[sin(wt – kx)] If it is reflected from a wall, what will probably be the equation of the reflected wave? I think it is y = A1[sin(wt + kx)] Is it...

Hi, I want to know how to get rid of the time part of the homogeneous wave equation: \newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } } \nabla^2\psi-c^{-2}\pd{\psi}{t}{2} = 0 I've read that this can be done using a Fourier transform, with the following given as the...

Could someone please help, i think this is gauss's law but I am not sure how to answer it as they give me a wave equation and i don't know how to put magnetic field in as well. Help would be much appreciated Question suppose that an appropriate device is used to genereate an...

I believe the PDE Utt-v^2*(Uxx+Uyy+Uzz) can be used to desribe air pressure, and how this pressure changes during time (with a given pressure in t=0) My question is, does this equation also takes into account effects of movement of particles? Such as wind? Can it describe wind? Or do we need...

What happens when you make the x varible in the wave egn to some power m(dx/dt) + k x^n =0 What happens when n increases/decreases?

Hello everyone! I'm having troubles understanding why I'm not getting this right...the problem is: A sinusoidal wave is traveling on a string with speed 10. cm/s. The displacement of the particles of the string at x = 25 cm is found to vary with time according to the equation y = (5.0 cm)...

Hi, I'm having a little bit of difficulty understanding exactly what to do to get to an answer in section a of this problem. It asks to show that the given function satisfies the wave equation... I have the wave equation. How do I go about 'showing' that it satisfies the wave equation? Do I...

Wave Equation problem..! Help...! Hi can anyone solve this?? I couldn't figure out how to use it Question Use the wave equation to find the speed of wave given by y(x,t)=(3.00 mm) sin [(4.00/m)x-(7.0/s)t) ] I guess the wave equation is , (d^2y) 1 (d^2y)...

In the wave equation, what is u, is it the amplitude? If it is, how can it be a vector?

An infinite string vibrates according to the homogenenous wave equation u_{tt}-u_{xx} = 0 with initial data given by u(x, 0) =f(x) and u_{t}(x, 0) = g(x) for -infinity<x<infinity where both f and g are smooth functions that are positive on the intervals -4<x<-3 and 2<x<3 and both zero...

A rod of uniform elastic material of length 1/2 lies along the X axis with its left end fixed at x=0. At time t=0, an identical rod hits the riht end of the first rod with a speed of v. The second rod is thereafter kept alongside the first rod, and neither end is fixed. If the Young's Modulus...

for a free particle, the wave equation is a superposition of plane waves, \psi(x,0)= \int_{-\infty}^{\infty}g(k)\exp(ikx)dk and g(k)= \int_{-\infty}^{\infty}\psi(0,0)\exp(-ikx)dx one is the Fourier transform of the other. some cases to solve this is when we assume a small delta k, so...

Please correct me if I am wrong. Solutions to the linear wave equation: \large\frac{\partial \Psi}{\partial t} = \frac{1}{c^{2}}\frac{\partial \Psi}{\partial x^{i}} are sinusoidal waves of constant wavelength, i.e. they describe light traveling in a flat space. But when light...

1/sin(phi) * d/d\phi(sin(phi) * du/d\phi) - d^2u/dt^2 = -sin 2t for 0<\phi < pi, 0<t<\inf Init. conditions: u(\phi,0) = 0 du(\phi,0)/dt = 0 for 0<\phi<pi How do I solve this problem and show if it exhibits resonance? the natural frequencies are w = w_n = sqrt(/\_n) =2...

If you remember, when in textbooks* they derive the wave equation by considering a small element of string and applying Newton's 2nd law on it, they make the assumption that the angles the tension makes at the two ends of the element with the horizontal is smallish, such that sin ~ tan. Without...

Every "spacially periodic" function [i.e. s.t there exist P s.t. f(x+P,t) = f(x,t)] of the form f(x,t) = X(x)cos(wt) is a solution of the wave equation.

The question says to show that the wave function picks up a time-dependent phase factor, e^\left(-i V_0 t / \hbar \right) , when you add a constant V_0 to the potential energy. And then it asks what effect does this have on the expecation value of a dynamical variable? Assuming I only...

Hi, I have the following question on my problem sheet, and I just want to check that my answer to it is correct as I need to use the result in a later problem. If someone could confirm it is correct, or point out mistakes/erros that would be great. ======= Q. Derive the wave equation for E...

"The Wave Equation IS the electron" Hello everyone, I've heard it said that well, "the Wave Equation IS the electron". Can anyone explain this to me? I know what the Wave Equation is (even solved a few of them) and have a degree in Chemistry but I probably would not be able to follow...

Assume the well known PDE of an infinite length string D^2(y)/Dt^2 = c^2* ( D^2(y)/Dx^2) where y=y(x,t) is the transverse displacement of the string. D/Dx= partial derivative with respect to x D/Dt= partial derivative with respect to t c= velocity of the wave According to Morse and...

Hi, We were told to show that the magnetic flux density B obeys a homogenous wave equation. This case applies to electromagnetic waves in a homogenous, linear, uncharged conductor. Now I know that the wave equation for magnetic flux density is as follows. [ tex ] \nabla^2-\epsilon\mju \frac...

Can someone show me that f(x, t) = A\cos(K(x-vt) + \phi) is in fact a solution of the wave equation? I kind of know how to show it by using calculus, but is there other way to show it? Thank you very much!

can anyone give me the most simple for someone with little diffrential equations back ground, on the proof for where the 1D wave equation was developed, i mean what's the proof for it. The 1D wave equation is a partial diffrential equation \frac{\partial^2\psi}{\partial x^2} =...

Hi, I recently came across a proof for the De Broglie wave equation in a book, which went as follows: E of photon = mc2 = m*c*c = (m*c)c = (p)c ( ie - momentum*speed of light) = (p)(f*lamda) Therefore, hf =...

Hi friends... Sometime back, I encountered the Self Consistent Field Method in Quantum Mechanics, which is used to compute wave functions in complex atoms. The book I read this from is "Practical Inorganic Chemistry" by Clyde and Day. The method is explained through an argument about the...

according to quantum mechanics there are many possiblities for a anything to happen...for example if there is a soap on the table..it exists only when we see it...only when we 'actualize' the wave-function...but what about the characteristic smell of the soap doesn't that make it exist? Does...

I have a wave equation Ytt=c^2 Yxx - g where g is a constant. The boundary conditions are Y(0,t)=Y(L,t)=0 with initial conditions Y(x,0)=0 and Yt(x,0)=0 I tried to solve it by Laplace transfoming the PDE in time and everything worked fine until I got to the point where I had to inverse the...

Hello, everyone I am new to this forum, I hope I am posting this at the right place. I am in my first year of college at Concordia University, and taking chemistry right now. But my main interest is physics. So when we were learning about the equation, I wanted to know more detail information on...