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.
TL;DR Summary: Question on deriving the complex irreducible solution form for simple harmonic motions based on time translation invariant.
Reference textbook “The Physics of Waves” in MIT website:
https://ocw.mit.edu/courses/8-03sc-...es-fall-2016/resources/mit8_03scf16_textbook/
Chapter 1 -...
Question from someone scarcely more knowledgeable on QM than a layperson. To my understanding, early in QM's study, some thought observation by a conscious being was required to collapse a wave function. I was told here that said Copenhagen interpretation(?) is only considered by people like...
There is a gravitational wave spacetime described by$$g = a(u) (x^2-y^2)du^2 + 2du dw + dx^2 + dy^2$$There is one obvious Killing vector field, ##\partial/\partial w \equiv \partial_w##. To find some more, it's suggested to try:$$X = xf(u) \frac{\partial}{\partial w} + p(u)...
I have tried to draw the diagram and would just like feedback on it to know whether it is correct or not.
Please keep in mind this was done roughly. Thanks
I have heard that the phase velocity of matter waves can be represented as c^2/v. But if the wavelength of these matter waves goes to zero as momentum approaches infinity and v approaches c, then does this mean that the frequency of the matter waves approaches infinity, to give the matter wave a...
From my understanding, you can equate ψ1(x) and ψ2(x) at the boundary of x = a, so I plugged in the values of a into x for both equations and I got ψ1(x) = 0 and ψ2(x) = ## (a-d)^2-c ##. I am a bit stuck on where to go from here.
In part (c), I have no problem if the string could stretch, but consider an inextensible string. This could still form a standing wave, according to google.
But then how is the string (the wave) equal to L? So can we actually equate lambda/4 with L? i.e. it is curved and varies with amplitude...
Hi, I am doing my thesis on quantum entanglement and I don't seem to wrap my head around what really happens to an entangled system during a local measurement. I happen to know that information can't travel faster than light I could believe that the collapse of the wave function wouldn't allow...
I have been taught that speed of pulse is v = √(T/μ), but here tension varies at each point therefore I cannot just simply apply the formula. I think integration would be needed, I tried but ended up nowhere. Can someone help me find the time?
I know the way to solve the first part is to find <ψ|Αψ> and compare it with <ψΑ|ψ>. This comparison can be done through an integral representation where we take ψ* and act A on ψ to be the integrand, or act A on ψ* and multiply by ψ for the integrand. If the integrals are the same, then the...
Since I know from the equation the type of particle and the distance L, I thought of equating the first relevant equation to the second equation. Since n = 1, 2, 3 ..., I thought by equating the two equations I could get k = 1, 4, 9... and have the two constants equal each other. The two...
A wave pulse moves along a stretched rope in the direction shown.
Which diagram shows the variation with time t of the displacement s of the particle P in the rope?
A
B
C
D
my answer was c because i thought that the particle would move in the same way the wave was coming...
Hello,
It has been difficult to find a clear answer to this question. I've found some sources stating that the power of a sound wave depends upon both amplitude and frequency. I've found other sources stating that the power of a sound only depends on amplitude. I've found sources stating...
Why do we say that wave amplitude tells us where we are likely to find the particle versus where we are likely to find the wave from the particle? Isn't the later a more accurate description of the QM math?
Hi, I am confused by the two concepts. How are they related? So, my interpretation is that a standing wave can happen without resonance. Resonance happens when a standing wave passes energy to another object, making it vibrate. Is that right? But some say a standing wave is an example of resonance?
According to Einstein light would be a particle and a wave.
So I infer that it propagates in vacuum in form of waves of little bullets (particles).
This explanation is very insuficient.
So tell me how do waves increase in size since it's made of little bullets (particles)... a wave gets...
For this,
The two statements highlighted do not seem to agree. I think the first statement highlighted is referring to A as initial amplitude (which we can denote ##A_i##) of the traveling waves before there constructive interference to form antinodes with an amplitude 2A and nodes of an...
I’ve read that the Ca2+ channels in neurons can be manipulated through the use of certain radio wave frequencies. And the resulting internal/external charge differential will cause the neurons to fire.
Does anyone have any more insight into that?
According to Maxwell’s Equations, the speed an EM plane wave in free space, far from its source, is determined by the electric constant, ε0, and the magnetic constant, μ0, such that c = 1/√( ε0 μ0).
The units of ε0 are capacitance per unit length and the units of μ0 are inductance per unit...
Sometimes I cannot imagine light as the popular Maxwell's blue and red electric and magnetic wave https://simply.science/images/content/physics/Electromagnetism/em_waves/emv.jpg but I found the image below to be the more accurate representation of how light actually looks like as waves...
Hello,
My name is Josip Jakovac, i am a student of the theoretical solid state physics phd studies.
First I want to apologize if my question has already been answered somewhere here, I googled around a lot, and found nothing similar.
My problem is that I need to apply TBA to Graphene. I went...
In the picture below we have two identical orbitals A and B and the system has left-right symmetry. I use the notation ##|n_{A \uparrow}, n_{A \downarrow},n_{B \uparrow},n_{B \downarrow}>## which for example ##n_{A \uparrow}## indicates the number of spin-up electrons in the orbital A. I would...
The standard derivation in obtaining a single wave equation involves making use of the heat equation with a Taylor expansion of the equation of state, then differentiating this equation and the continuity equation with respect to time, and combining with the divergence of the NS equation...
I've already calculated the total spin of the system in the addition basis:
##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...
Why in order to derive the QM momentum operator we use the plane wave solution. Why later on in field theory and particle physics, the plane wave ansatz is so physically important?
Using the equation above I know that I have to find parameters k ##\omega## and ##\phi##.
$$k = \frac{2\pi}{\lambda}$$
and
$$\omega = 2\pi f$$
The problem I've been having is how you would go about finding ##\phi## since by solving:
$$y(0,0)=0 \rightarrow sin(\phi)=0 \rightarrow \phi = 0...
Desired output similar to image, but without the objects and with better wave interference:
I tried plugging the following into wolfram (I specifically want the values to be adjustable):
plot z= H*e^(-m*sqrt((x-a)^2+(y-b)^2))*sin(k*(x-a)+k*(y-b) -w*t) +...
I'm trying to make a DIY 'ECG' machine, except that it'll only record heartbeats on a piece of paper. Basically the piece of paper will be wound round a cylinder like object, which will be being spun slowly by a motor. A pencil at the end of a stick or something will be writing to this piece of...
The statement of the problem is:
Consider a taut string that has a mass per unit length ##\mu_1## carrying transverse wave pulses of the form ##y = f(x - v_1 t)## that are incident upon a point P where the string connects to a second string with mass per unit length ##\mu_2##.
Derive $$1 = r^2...
In the popular answer for the coin-mass question of Physics Stack Exchange,
I am wondering what are the correlation between the first red peak at around 9kHz and the second red peak at 16kHz. I first thought that they are consecutive harmonics but there was no way of proving it as I do not know...
Let's say we have a point source of an EM wave in a vacuum of total energy E, and an absorber atom at some distance from this source, whose first excited state is at the energy B, with B < or = E.
The energy of the wave is constant as a whole, but at each point around the source the energy...
TL;DR Summary: How do i find the intensity of this wave?
I know I is proportional to amplitude / frequency squared, but I don't know what equation this comes from. And I don't know how to answer this.
How would we model/calculate the circular waves in a pool of water (wavelength and amplitude) from a mass falling into it from a given height, and from a fountain of water falling into it continuously?
Is there is a way to describe the initial configuration of the wave based on the stimulus...
Mine is a simple question, so I shall keep development at a minimum. If a particle is moving in the absence of a potential (##V(x) = 0##), then
##\frac{\langle\hat p \rangle}{dt} = \langle -\frac{\partial V}{\partial x}\rangle=0##
will require that the momentum expectation value remains...
For this problem,
Where equation 16.27 is the wave equation.
The solution is
I don't understand how they got the second partial derivative of ##y## with respect to
##x## circled in red.
I thought it would be ##1## since ##v## and ##t## are constants
Many thanks!
For part(a) of this problem,
The solution is,
I don't understand why they assume on the graph where that the waveform is during it's phase. For example, could it not also be correctly drawn as shown in red:
Could it not?
Many thanks!
Hello everyone, sorry if this is the wrong section. In this forum I'm a fish out of the bowl, my knowledge of physics is ages beyond most of the people on there, so please forgive my naivness.
So, here's my problem, I'm a sort of "audio" engineer (won't enter much on detail) and on my free...
I am trying to analyze a half wave rectifier with an inductor and DC source load. I understand the circuit but I guess I do not get the math. I am reading a book and this is the circuit and equations they came up with. I understand how they got from the first equation to the second equation but...
New Class of Bimodal NTP/NEP with a Wave Rotor Topping Cycle Enabling Fast Transit to Mars
https://www.nasa.gov/directorates/spacetech/niac/2023/New_Class_of_Bimodal/
Ryan Gosse, University of Florida, Gainesville, FL...
Consider a very long string between fixed supports of mass density rho and tension T. At a distance 1 meter from one support pinch the string. The pinching does not change the tension. Adjust the mass density or tension so that when we add energy to this section of string we produce the first...
I think I understand that points P and R are pi radians out of phase - reaching their max/min at the same time.
But are P and Q in anti phase?
What is antiphase exactly - is it when they are 180deg out of phase - or is it when they are anything other than totally in phase? I seem to find...
Hi.
What equipment /mechanism / experimental procedure is used to determine that the nature of a wave fired from an electron gun is transverse in transit?
Thanks
Martyn
I recently watched this lecture "Quantum Fields: The Real Building Blocks of the Universe" by David Tong where the professor provides a succinct explanation of QFT in about 6 minutes around the midway mark.
The main point being that there are fields for particles and fields for forces and the...