In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities, sometimes as described by a wave equation. In physical waves, at least two field quantities in the wave medium are involved. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.
The types of waves most commonly studied in classical physics are mechanical and electromagnetic. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium. Other examples of mechanical waves are seismic waves, gravity waves, surface waves, string vibrations (standing waves), and vortices. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields which sustains propagation of a wave involving these fields according to Maxwell's equations. Electromagnetic waves can travel through a vacuum and through some dielectric media (at wavelengths where they are considered transparent). Electromagnetic waves, according to their frequencies (or wavelengths) have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.
Other types of waves include gravitational waves, which are disturbances in spacetime that propagate according to general relativity; heat diffusion waves; plasma waves that combine mechanical deformations and electromagnetic fields; reaction-diffusion waves, such as in the Belousov–Zhabotinsky reaction; and many more.
Mechanical and electromagnetic waves transfer energy, momentum, and information, but they do not transfer particles in the medium. In mathematics and electronics waves are studied as signals. On the other hand, some waves have envelopes which do not move at all such as standing waves (which are fundamental to music) and hydraulic jumps. Some, like the probability waves of quantum mechanics, may be completely static.
A physical wave is almost always confined to some finite region of space, called its domain. For example, the seismic waves generated by earthquakes are significant only in the interior and surface of the planet, so they can be ignored outside it. However, waves with infinite domain, that extend over the whole space, are commonly studied in mathematics, and are very valuable tools for understanding physical waves in finite domains.
A plane wave is an important mathematical idealization where the disturbance is identical along any (infinite) plane normal to a specific direction of travel. Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic motion at one frequency. In linear media, complicated waves can generally be decomposed as the sum of many sinusoidal plane waves having different directions of propagation and/or different frequencies. A plane wave is classified as a transverse wave if the field disturbance at each point is described by a vector perpendicular to the direction of propagation (also the direction of energy transfer); or longitudinal if those vectors are exactly in the propagation direction. Mechanical waves include both transverse and longitudinal waves; on the other hand electromagnetic plane waves are strictly transverse while sound waves in fluids (such as air) can only be longitudinal. That physical direction of an oscillating field relative to the propagation direction is also referred to as the wave's polarization which can be an important attribute for waves having more than one single possible polarization.
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'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...
Hello! (Wave)
I want to solve the equation $u_t+uu_x=0$ with the initial condition $u(x,0)=1$ for $x \leq 0$, $1-x$ for $0 \leq x \leq 1$ and $0$ for $x \geq 1$. I want to solve it for all $t \geq 0$, allowing for a shock wave. I also want to find exactly where the shock is and show that it...
Is there a difference between Schrodinger's equation and the wave function? In the beginning of the second edition by David J. Griffiths he compares the classical F(x,t) and Schrodinger's equation and I am having trouble understanding the connection.
Just for my knowledge, not to confuse the OP, why would you say, for example, the double slit experiment does not show both of these properties in one measurement method?
[Mentors' more: this thread was forked off from another thread]
Homework Statement
I have the wave function Ae^(ikx)*cos(pix/L) defined at -L/2 <= x <= L/2. and 0 for all other x.
The question is:
A proton is in a time-independent one-dimensional potential well.What is the probability that the proton is located between x = − L/4 and x = L/4 ?
Homework...
Hello! (Wave)
I want to prove that if the initial data of the initial value problem for the wave equation have compact support, then at each time the solution of the equation has also compact support.
Doesn't the fact that a function has compact support mean that the function is zero outside...
Before quantum mechanics, light was generally seen as a wave and matter as particles (biliards). From e.g. the discovery of the photoelectric effect, one saw that light can also be seen as a particle. From e.g. the double slit experiment, one makes the interpretation that matter can also be seen...
Homework Statement
1. Homework Statement [/B]
The displacement y of standing wave that is obtained by a superposition of waves :
Y1 = 3 sin (2##\pi##(0.5t - 0 25 x))
Y2 = 3 sin (2##\pi##(0.5t + 0 25 x))Homework Equations
Formula for standing waves
Y = 2Asinkx coswt
The Attempt at a Solution
Y1...
I have a question regarding a theoretical analysis of Ultrasonic waves :
The next picture represents a system of transducers sitting on fixed boards:
Datum:
* there are 4 transducers ( represented by blue color , indexed by letter ' T ' ) , each outputting Ultrasonic wave (represented by...
Hello,
I am wondering if it is possible to determine the kinetic energy and potential energy of a quantum system just by investigating the graph of its wave function. Suppose we are given the graph of some wave function Ψ(x), i.e. a function which is an eigenfunction of the hamiltonian. I think...
Homework Statement
A radio speaker produces sound when a membrane called a diaphragm vibrates, as shown above. A person turns up the volume on the radio. Which of the following aspects of the motion of a point on the diaphragm must increase?
a) the max. displacement only
b) the average...
I collected this data by moving a sound level meter slowly through a total length of 0,75 meter between two speakers pointing towards each other. The wavelength of the sine waves was 0,343 meters and the frequency was 1000 Hz. The sound level meter measured the sound in dbA 20 times a second...
Find the wave equation U(x,t) of a vibrating string with linear density d, tension p, initial velocity zero, weight L and initial displacement
U0(x) = a1*sin(2*pi*x/L)+a2*sin(4*pi*x/L).
Guys, please help me with this task. I did the following procedure:
The U(x,t) solution must me a sum of...
<Moderator's note: Moved from a technical forum and thus no template.>
I've done an experiment on standing waves on a string.
By graphing √T vs λ (where T is tension and λ is wavelength) using the linearized equation √T = (1/√μ) f ⋅ λ, I was able to get this data:
μ = .000256 kg/m
slope = 1.78...
Hope, I do not violate any forum rules here, this is not a discussion topic, mostly. I am just asking for help looking for a specific article/work.
I just remember reading somewhere that there is a QM theorem or article saying smth. in a sort that if the same physical "ontic" state would be...
For the harmonic oscillator, I'm trying to study qualitative plots of the wave function from the one-dimensional time independent schrodinger equation:
\frac{d^2 \psi(x)}{dx^2} = [V(x) - E] \psi(x)
If you look at the attached image, you'll find a plot of the first energy eigenfunction for...
I am having a problem with understanding concepts related to the speed of a wave. Here are my thoughts laid out:
1) The speed of a wave is dependent only on the medium
2) When a wave crosses from a less dense medium into a more dense medium (or visa versa) the speed of the wave is always...
Hello,
Came across https://drive.google.com/file/d/1bpB7BcVf1yQLiwg9quAn2vlhu8-i6Zy_/view and I'm not sure about one thing
For the 2 parts of the equation with sin, is it:
1. [...sin(kx)]sin(wt)
or is it:
2. [...sin(k)*x]sin(w)*t
Thank you
-DR
Homework Statement
I have a simple problem relating to the superposition of plane EM waves that I'd to try out using complex notation. Could anyone run through the work to see if my understanding is right?
Many thanks in advance!
The incident E bit of the wave is
$$\vec{E}_I = E_0 \sin(ky -...
A subatomic particle can either be a wave or a particle.
When it is a particle, what actually is it? is it literally like a tiny physical ball rattling around? (If not, then what is it?)
And when it is a wave, what is it?
From my understanding, when a particle behaves like a wave, the...