Wave Definition and 999 Threads

Apologies if this question is better posed in the mathematics section, it is for a quantum mechanics class so I decided to post it here: We are asked to verify that the following equation is a solution to the Schrodinger wave equation for a free particle: Psi(x,t) = Ae^i(kx-wt) - Ae^-i(kx+wt)...

When a spring is fixed at both ends and it is vibrating back and forth, reflection will occur. So where are the nodes and antinodes? Are they at compression or rarefaction region?

Homework Statement I know that for a dispersive wave packet, the group velocity equals the phase velocity, which is given by v=w/k. But how do I calculate the group velocity of a non-dispersive wave packet? I'm supposed to be giving an example with any functional form. Homework Equations...

1. Homework Statement The figure below shows a section of a thin, elastic rod of density ##\rho##, cross sectional area ##A##, and modulus of elasticity ##E##. By considering the net force acting on an element of the rod, derive the wave equation governing its longitudinal motion...

I am interested in discussing those phenomena which can be defined at a point. The wave equation is the simplest example. Is it acceptable to use the term 'wave' to indicate any phenomenon that is defined at a point, and to call the equation that results a wave equation? To illustrate the...

v = [sqrt(D/m)] * L, where D is spring constant, m is mass of spring, L is length of the spring My lecturer give me this formula to find the longitudinal wave velocity on an helical spring. May i know how to derive this formula? < Mentor Note -- this is not technically a homework question, but...

Homework Statement At ##t = 0##, a particle of mass m in the harmonic oscillator potential, ##V(x) = \frac1 2 mw^2x^2## has the wave function:$$\psi(x,0)=A(1-2\sqrt\frac{mw} {\hbar} x)^2e^{\frac{-mw}{2\hbar}x^2}$$ where A is a constant If we make a measurement of the energy, what possible...

https://www.dropbox.com/s/t5lv4nlunn35ok8/phy1.PNG?dl=0 https://www.dropbox.com/s/ktc9pj7qmqhejrv/phy2.PNG?dl=0 https://www.dropbox.com/s/qbjz1p1gokvsgj2/Capture3.PNG?dl=0 I googled "polarizer film diagram" and "malu's law" and "polarizer physics" to obtain the pictures in this thread. I...

Hi, Apologies if this questions is really easy but it is something quite subtle which is annoying me. In my book of quantum physics it gives a wave function of definite momentum: ψ = Aeipx/ħ It goes on to say that since there is a momentum 'p' in the exponential then the momentum is known...

I'm extremely interested in the self resonant frequency of an inductor. This is to be used as a half wave helical antenna on our ham bands. The usual helical is operated as a ground plane but I have not seen a complete set of design equations for the former. The initial problem with this is...

Homework Statement The figure shows two sets of water waves, created by two sources labeled "A" and "B." The solid half-circles represent wave crests from A, and the dashed half-circles represent wave crests from B. Suppose that individual wave crests from either source A or source B alone are...

Homework Statement State the boundary condition which must be met at a point where the string of question 2 is fixed. Hence find the real standing wave solutions to the wave equation, and determine the allowed oscillation frequencies, when such a string of length ##L## is fixed at its ends...

When light from a rarer medium enters a denser medium, the wave gets refracted into the denser medium and so the wavelenght and the speed of propagation decreases ( [v][1] >[SUBv][/SUB2]) but the frequency remains the same. HOW ? [SUBv][/SUB1] / [SUBλ][/SUB1] = [SUBv][/SUB2] / [SUBλ][/SUB2]...

Electron in hydrogen atom is defined by this wave function : Ψ(r,ϑ,φ)=Ar2exp(-2r/a)cos2(ϑ)exp(-3iφ) proton is in the center of the coordinate system.a is a known positive constant. I'm trying to find normalizing constant A. Ψ*(r,ϑ,φ)=Ar2exp(-2r/a)cos2(ϑ)exp(3iφ) I get that ∫∫∫(ψ*)ψdV=1...

Homework Statement The equations for two waves traveling along the same string are $$f_1(x,t)=a\sin(bx-qt)$$ and $$f_2(x,t)=a\sin(bx+qt+\frac{1}{3}\pi),$$ with $$a=3.00\times 10^{-2},b=4\pi m^{-1},$$ and $$q=500s^{-1}$$. (a) Calculate the amplitude and wavelength of the resultant displacement...

Homework Statement Show that the (1,0,0) and (2,0,0) wave functions are properly normalized. We know that: Ψ(1,0,0) = (2/(a0^(3/2))*e^(-r/a0)*(1/sqrt(2))*(1/sqrt(2*pi)) where: R(r) = (2/(a0^(3/2))*e^(-r/a0) Θ(θ) = (1/sqrt(2)) Φ(φ) = (1/sqrt(2*pi)) Homework Equations (1) ∫|Ψ|^2 dx = 1 (2)...

So Heisenberg's Uncertainty says that we can't know both the position and the velocity of a particle accurately, because measuring one will disturb the particle enough that it's no longer possible to accurately measure the other as it was. So one or the other has to remain unknown to us. This...

Suppose at the instant a gravitational wave passes through an interferometer, one of the interferometer's arm get stretched by 1%. Would the wavelength of the photon traveling in the arm also get stretched by 1%? If so, then would the frequency of the photon remain the same and hence increasing...

I am thoroughly confused regarding the modeling and graphic depictions of gravitational wave propagation. These waves must propagate in three dimensions, not in the planar rubber sheet example that is often shown or the ripples on a pond example. Even the recently publicized example of the...

Homework Statement I am trying to solve the given wave equation using separation of variables, u_{tt} - 4u_{xx} = 4 for 0 < x < 2 and t > 0 (BC) u(0,t) = 0 , u(2,t) = -2, for t>0 (IC) u(x,0)=x-x^2 , u_t(x,0)=0 for 0\leq x \leq2 Homework Equations We are told we will need to use, x =...

In classical mechanics and EM, the energy carried by a wave is the amplitude squared. In QM the (complex) amplitude squared of the position-space wave function is the position probability density. Do physicists regard this as anything more than just an interesting coincidence? Has anybody...

So I'm having a introductory study on waves and there's something that i can't understand when dealing with reflections on a fixed end. We have the general solution for the wave equation: ## y(x,t)=f(x-vt)+g(x+vt)## Supposing that the fixed point is in the origin we have the boundary condition...

In Born interpretation of the wave function it notes that the matter itself cannot be measured however the square of its absolute value is measurable. I am lost as to why the product can be measured but not the wave function itself. Can someone provide clarity?

I know to produce an observable inteference pattern two waves must be coherent(same frequency/phase differnce). Do coherent waves therefore always have the same wavelength? Is it possible to have interference between two waves with the same frequency and different wavelengths, and if so what...

Homework Statement I'm asked to show that the two dimensional plane wave (for constant C) \psi \left ( \mathbf{r} \right )=Ce^{-i\mathbf{k}\cdot \mathbf{r}} satisfies the Schrödinger equation: -\frac{\hbar^{2}}{2m_e}\frac{\mathrm{d}^2 \psi\left ( \mathbf{r} \right )}{\mathrm{d}...

Hello, I have found the technology of spintronics very interesting with a great potential for the (hopefully near) future & I am desiring to experiment with spin waves. I am sure there are several ways to create a spin wave or current, one of which involves placing a platinum strip at the end...

Homework Statement A long, heavy rope hangs straight down from a high balcony on an apartment building. The lower end of the rope hangs about 1.0 m above the ground. If you grab onto the lower end and waggle it back and forth with constant frequency f, a wave travels up the rope. What would...

I'm new to electronics, and using my new equiptment I would like to generate a sine signal on my function generator and display it on my oscilloscope. Equipment: * The scope is Rigol DS1054Z * Function generator is a $60 digital chinese. My problem is: When I plug connect the function...

We laymen and newbies are taught the Schrodinger equation was deterministic. So we tend to picture it’s like a classical thing.. some forever thinking it that way where the idea is etched deep in the mind. Yet when we are home with the idea it is deterministic (that is.. when not measured)...

1. “The profile of a transverse harmonic wave, traveling at 1.2 m s^-1 is given by y(x)=(0.02 m)sin[157 rad m^-1)x]. Determine amplitude, wavelength, frequency, angular frequency, and period. Homework Equations y(x,t)=Acos(kx-wt)[/B]The Attempt at a Solution I attempted to change it to a...

Hello guys! I've been learning how to estimate half life using Schrodinger's time-independent wave equation. In class, we divided the energy barrier into five smaller segments just like this webpage http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/alpdet.html#c1 I was wondering if we could...

Homework Statement the last problem on this page: Homework Equations ##v= \lambda f## The Attempt at a Solution I'm guessing I'm looking for the maximum amplitude in a overlapping wavefront diagram like this? ## v=343m/s \\f=512Hz \\343/512=\lambda=0.67m \\3/0.67=4.5m ## So 4.5 wavelengths...

Homework Statement (Problem #1 on this page.)[/B] Homework Equations ##v=\sqrt { \frac { T }{ \mu } } =\lambda f## The Attempt at a Solution I don't think there is enough information, ##v=\sqrt { \frac { Mg }{ m/L } } ## m, the mass of the string is not given

Homework Statement Homework EquationsThe Attempt at a Solution a. ##{ P }_{ avg }=\frac { 1 }{ 2 } \mu v{ \omega }^{ 2 }{ A }^{ 2 }=\frac { 1 }{ 2 } 0.075\frac { 10 }{ 3 } { 0.35 }^{ 2 }{ (10\pi ) }^{ 2 }=15.1W## b. Not sure how to calculate that... I'm guessing it'd be some integral over 1...

I am studying phase and group velocity in non-dispersive and dispersive media. My question is the following: Is there any reason why a dispersive medium simply cannot be modeled as a type of field?

If two electrons are far apart, the antisymmetrization part in the probability amplitude for position is negligible and they behave as classical particles, thus we don't need to consider antisymmetrization. My question is why is this also true when we have a large number of electrons, say...

2 sound waves that are mathematical polarities cancel each other out according to my audio engineering book. I thought energy cannot be destroyed, just changed. Am I wrong? What happens to the energy? Same question could be applied to matter and anti matter right?

Homework Statement [/B] 1. Using the Schematic of a 555 in astable mode from the Wikipedia entry on '555 Timer IC," resistor R1 = 8 kOhms and capacitor C = 3 micro-Farads. Determine the value of R2 so that the output duty cycle is D = 0.7. Note that D is not expressed as a percentage here for...

Hi, In Classical electromagnetic wave.. does it have definite polarization when the EM wave leaves the sun for example? Or is it in superposition and the polarization only exist after measurement just like in QM? I don't understand the Maxwell Equation. Does Superposition in Maxwell Equation...

Homework Statement "The solution ##u(x,t)=f(x+ct)+g(x-ct)## solves the PDE, ##u_{tt}=c^2u_{xx}##. By graphing the solution ##u(x,t)=f(x+ct)## on the ##ux##-plane, please show that as ##t## increases, the graph shifts to the left at a velocity ##c##. Conversely, show that for ##u(x,t)=g(x-ct)##...

When solving problems, particularly in optics, it is often that we represent the wave-function as a complex number, and then take the real part of it to be the final solution, after we do our analysis. u(\vec{r},t)=Re\{U(\vec{r},t)\}=\frac{1}{2}\left(U+U^*\right) Here U is the complex form of...

Homework Statement Homework EquationsThe Attempt at a Solution the point is going down the wave, so shouldn't the answer be D? Why is it B? Thank you! [/B]

Sound waves transmit in atmosphere as dense and thin areas of air. Is there a graph showing the highest and lowest pressure of atmosphere for sound waves of various decibels?

<Moderator's note: Template removed due to replacement in a technical forum.> In the textbook, it said that standing waves only occur at the resonant frequencies of the medium. I don't understand why. My understanding of standing waves is that it is when the medium length (slinky) is a...

How can we work out all the properties of wave from differential equation? And what really does differential equation of wave implies?

Good afternoon! Please help me figure out the mathematics of this simple plane wave question! 1. Homework Statement 2. Homework Equations n1*sin(theta1)=n2*sin(theta2) The Attempt at a Solution I need help calculating the angle of incidence. I found the propagation vector for incidence...

Homework Statement Consider a wave vector which hits a plain boundary between water and air. The wave vector hits the boundary with an angle α1 measured from the vertical axis. The magnetic field amplitude has a y-component only. Also, notice: The z-axis is the horizontal axis, the x-axis is...

Hiya! In school we have tha task to create our own phy lab. I am going to investigate the width of a hair using wave diffraction (a laser maybe?). Does anyone have any creative ideas on how to develop the lab to make it more uniqe and interesting. E.g measuring from different distances. Or...

I just want to know does any random equation of the form y=f (x-vt) reppresent a wave?? If yes why?? And is this true for all cases or is there any condition?

I remember from my physics classes that the wave functions for the hydrogen atoms or an electron in a box showed typical linear wave behaviour. However, when you have a large system's wave function, say for example the universe, will it then show different spatial-dynamic structure? What comes...