Wave Definition and 999 Threads

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...

For the half harmonic oscillator the ground state wave function is of the form x*exp(-x^2/2) But sir how to check it's parity and with respect to with point As this function is valid for positive x only Thank you

I am currently reading through 'Optics' by Eugene Hecht chp 2 page 20, he talks about the function of the wave and the direction of travel of the wave i.e ##\psi(x)=f(x-t)## and right at the bottom of the page he say this: Equation (2.5) is often expressed equivalently as some function of ##t -...

There are some things that confuse me about electromagnetic waves, and I haven't found good answers anywhere. Consider the following equation: E=E0 e i(wt-kx) (here E and E0 are vectors, I couldn't find the right symbols). The things that confuse me are the following: 1° We say that the power...

I have seen few examples on Doppler effect and i am confused about one such. We are standing on ground. If the source of sound S moves and Object O is stationary. We would presume the frequency as well as wavelength of sound be changed to the obeject O. But if O moves towards or away from S...

Homework Statement $$\Psi = Ae^{\frac{i}{\hbar}(px-\frac{p^2}{2m}t)}$$ where ##p = \hbar k## and ##E = \hbar \omega = \frac{p^2}{2m}## for a nonrelativistic particle. Find ##\Psi'(x',t')##, E' and p', under a galilean tranformation. Homework Equations $$\Psi'(x',t') = f(x,t)\Psi(x,t)$$ where...

Homework Statement The wavefunction at t = 0 is given by $$\Psi = N*e^{-\frac{r}{a_0}}$$ where ##r = |\mathbf{x}|##. ##a_0## is a constant with units of length. The electron is in 3 dimensions. Find the approximate probability that the electron is found inside a tiny sphere centered at the...

Is the simple pendulum considered to be an example of oscillatory motion or periodic motion or both?

Homework Statement A beam of light of vacuum wavelength λ = 550nm passes from water (refractive index 1.33) into air (refractive index 1.00). (a) What is the critical angle? (b) Suppose the beam is totally internally reflected. At what angle of incidence would the decay length of the...

When a non-polarized electromagnetic wave cross a polarizer filter, its intensity drops to a half. Then this now polarized wave cross a polarizer such that it has 90 degree compared to the other. The wave is completely vanished. But if we put another polarizer with, let's say 45 degree in...

Homework Statement Homework Equations See above in the question The Attempt at a Solution I know that I need to be using a summing amp with the sinusoidal terms but I am struggling to calculate the input values that I need, also I think I need a capacitor in place of R6 but I'm not...

i know it's an absurd question, but why are longitudinal waves called waves although they aren't wave-like?

Hello! (Wave) I want to show for the initial value problem of the wave equation $$u_{tt}=u_{xx}+f(x,t), x \in \mathbb{R}, 0<t<\infty$$ that if the data (i.e. the initial data and the non-homogeneous term $f$) have compact support, then, at each time, the solution has also compact support. I...

Homework Statement The sound source of a ship’s sonar system operates at a frequency of 18.0 kHz. The speed of sound in water (assumed to be at a uniform 20°C) is 1482 m/s. What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling...

How can we prove that ##k^\mu=(\frac{\omega}{c}, \vec{k})## is a four-vector? One way is to consider the invariance of light velocity. If we postulate ##k^\mu## to be a four-vector then the scalar product of ##k^\mu\,x_\mu=\vec{k}\cdot\vec{r}-\frac{\omega}{c}\,t## is invariant, if it constant...

I don't really know where my brain is taking me on this one. I was wondering a couple things.. You set up everything for a Slit Experiment. You shoot an atom and observed it before the slit, then somehow collected the particle. It loops back and shoots it out again, this time with the particle...

Interference pattern made by light shows the wave nature of light and photoelectric effect shows particle nature of light. So, what is light? According to the photoelectric effect, light consists of photons with energy E and momentum ## \vec p##. According to the interference pattern, we...

Hi. I'm reading a paper "Transmission of light through a single rectangular hole in a real metal" and the author refers to the incident light shown below as "p-polarized" without further specification. Note that ax > ay. Is there any convention in regarding a certain polarization as...

I'm trying to get a sense of the current state of knowledge regarding the relationship between gravity and quantum phenomena. For example, if you had a super-sensitive gravity detector, would that count as a "measurement" in the double-slit experiment in the same way that a particle detector...

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...

In this article, researchers have used electrons to image light as both particle and wave at the same time. https://phys.org/news/2015-03-particle.html

Homework Statement A monochromatic plane wave with wavelength 500µm is propagating through a dissipative medium with refractive index 1-0.0002i. It approaching the edge of the medium, and will pass out into free space. If the angle of incidence is not 90°, how much will the wave deflect as it...

If you created the following double slit experiment would you still see interference? 1) Modify the slits so that the path from photon source through one of the slits to the detector is much shorter than the path through the other slit. 2) put a shutter in front of the photon source so that you...

In these notes, https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes11.pdf, in the middle of page 5, it is mentioned: We will be interested in bound states namely, energy eigenstates that are normalizable. For this the energy E of the states...

h is plank constant and v is frequency. I was using this to derive the TDSE. But I ran into problem because to substitute k^2 in E=h^2/8mpi^2 * k^2, I can use single derivative of psi squared or double derivative, both of which tend to give the correct answer. So, is my assumption of energy...

Homework Statement Monochromatic light of wavelength, λ is traveling in air. The light then strikes a thin film having an index of refraction n1 that is coating a material having an index of refraction n2. If n2 is larger than n1, what minimum film thickness will result in minimum reflection of...

Homework Statement A transverse traveling wave on a string starts at x = 0 and travels towards x = ∞. The wave has an amplitude of 1.20 m, wavelength of 4.60 m and travels at a speed of 14.3 m/s . At time t = 0.0 s the displacement at position x = 0.0 m is 1.20 m. (b) Calculate the displacement...

Homework Statement I've just read that light can behave like a wave at times, and a particle at other times. How does the light from the Sun traveling towards Earth behave? A wave? A particle? Or both? And is it in any sense something that actually starts at the Sun, travels across space and...

I have recently started learning about waves. We didn't really formally describe what a wave is, but instead started by looking at a concrete example namely harmonic sinusoidal waves in 1d. We then introduced the wave equation in 1d and showed that the sinusoidal waves indeed satisfy this...

I've read that, in general, the energy of a wave, as opposed to what's commonly taught, isn't strictly related to the square of the amplitude. It can be seen to be related to a Taylor series, where E = ao + a1 A + a2A2 ... Also, that the energy doesn't depend on phase, so only even terms will...

I need help with this question. The energy of wave related to its amplitude but not to frequency. If we talk about wave as disturbance carring energy we can imagine a swinging rope that gives potential energy to body by pushing it up. Bigger amplitude means getting high and increasing Potential...

When a layman like myself hears the term 'Wave function collapse' is brings to mind physical things. A wave of some sort physically getting smaller or shrinking. Obviously that's not what it is but it does sound like it. In reality, if I have it right it's just a fancy way of saying a...

Let us say I have a moving charge. At each point x,y,z in it's path from understanding there is a transverse electromagnetic wave being radiated (could also be viewed as a photon). The electric field at any point x1,y1,z1 in the path is disturbed. The moving charge does the same thing all...

I've been reading about Quantum Field Theory. It strikes me that since the 1920's, physicists have changed the name "wave" to "field". I can't tell the difference between today's "fields" and what was described a "wave" in quantum theory in the early 1900's. So in quantum physics, is there a...

Can anyone tell me what a Gaussian Wave Packet is? What happens to the atoms inside a Gaussian Wave Packet? Can more than one Gaussian Wave Packet Exist in the same place? Thank you,

Im just starting to try to break into and understand quantum physics and so this question may be a completely absurd but I am curious as to whether or not its been proven that a particle really does act like a wave until observed or if the "spin" of two entangled atoms actually changes opposite...

Hello! (Wave) I want to prove that if for the initial value problem of the wave equation $$u_{tt}=u_{xx}+f(x,t), x \in \mathbb{R}, 0<t<\infty$$ the data (i.e. the initial data and the non-homogeneous $f$) have compact support, then, at each time, the solution has compact support. I have...

I noticed HF radio waves travel farther and easier when the sun is out rather then during the night. Why?

I've seen somwhere a claim that Hamilton-Jacobi euqation is the only formulation of classical mechanics which can treat motion of particle as wave motion. There was something about hamilton prinicpal function, hamilton characteristic function and one of these change in time like wavefront or...

Hi this is my first question and love these Forums. I have a Independent research task due next term. My idea was: Seeing the change of wave length of light as it passes through different substances. My question is: How do i measure the wave length? Because I could use a spectrometer but my...

Homework Statement Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width? Homework Equations [/B] I solved for Ψ(x, t): $$\Psi(x,t) =...

I need to know what is the typical extention of the (spatial) wavefunction of an atomic nucleus in a crystal, in particular I am interested to the case of a Germanium cristal. Please together with the actual number of the size of the nuclei wavefunctions, let me know the references (articles or...

Subatomic particles can take the form of a wave or a particle. While in wave form, it is not like a physical wave, but rather a probability wave, (i.e. a wave of information about where the particle is probably located etc.) And while in particle form, a photon, for example, can knock electrons...

Hi everyone, I'm kind of new in the QM world and I'm having difficulties understanding the superposition and the measurement principles together with the have function collapse. This is how I understand these principles: Superposition: While not measuring, the particle is in a superpsotion of...

I would like to get your ideas on what Australian professor at ANU David Chalmers' proposes that consciousness arises out of certain configurations of complex states (Integrated information theory) and then the existence of that consciousness collapses the wave function. Specifically, why isn't...

I find the de Broglie-Bohm pilot wave theory interesting but what I still feel missing in the descriptions I could find so far is that it reformulates what we already know but nobody speaks of new testable predictions that could eventually distinguish it from other interpretations (such as a new...

These are from Griffith's: My lecture note says that I am having quite a confusion over here...Does the ##\Psi## in the expression ##\langle f_p|\Psi \rangle## equals to ##\Psi(x,t)##? I understand it as ##\Psi(x,t)## being the component of the position basis to form ##\Psi##, so...

Hey everyone, I’m trying to simulate a 1D Shallow Water wave in FORTRAN using the Lax Wendroff Method. The case is fairly simple. I have a wave generator on one end of a water pool and a wall boundary on another. The waves start traveling towards the wall and are ‘reflected off’ the wall. The...

Homework Statement I am having a issue understanding this question I have solve the PDE below, but I can't understand where or how you the characteristic frequency, what more confusing is that I don’t know if that lambda is just a constant or a wavelength. Homework EquationsThe Attempt at a...

A photon acts like a wave and a particle. In the double slit experiment the photon seemingly interferes with itself which is troublesome to me. To help better understand this, I would rather think of the photon as a particle and the wave as something that is independent of the photon where the...