What is Wave: Definition and 999 Discussions

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.

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  1. B

    Textbook 'The Physics of Waves': Derive Complex Solution Form for SHM

    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 -...
  2. PhysicsEnjoyer31415

    B What is a Gravitational wave?

    Many more questions....please enlighten me on this topic. thank you!
  3. S

    Why is the "conscious observer" thing considered?

    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...
  4. ergospherical

    I Is this a Killing vector field?

    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)...
  5. N

    Sound Wave Diagram Help

    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
  6. H

    I Freqeuncy of Matter Waves Approaches Infinity as Velocity Approaches c

    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...
  7. Danielk010

    How do you solve for multiple constants given the wave functions at the boundary?

    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.
  8. L

    Length of string in a standing wave

    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...
  9. N

    I How Does Local Measurement Affect an Entangled System?

    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...
  10. H

    What is the time taken by a pulse generated at the bottom of a string to reach the top?

    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?
  11. flyusx

    Operators On Multivariable Wave Functions

    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...
  12. Danielk010

    How do you prove ##\lambda = \frac {2L} {n} ## given only L?

    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...
  13. hello478

    Wave movement and particle movement

    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...
  14. hello478

    Phase difference between two light waves of the same frequency

    the diagram. i found that the phase difference between them is 100º but how is the answer 260 can someone please explain?
  15. N

    I Sound power, amplitude, frequency, and decibels

    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...
  16. K

    I Why does wave amplitude indicate particle location in QM?

    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?
  17. jinweiiii

    B What is the difference between standing wave and resonance?

    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?
  18. L

    B Does light propagate as a wave of little bullets?

    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...
  19. B

    B Mapping wave forms to sphere, does wave form y=0 have a reflection?

    Zero does not have an inverse. And y=0 does not have an inverse. Does the wave form y=0 for all x have an inverse?
  20. M

    Agree or Disagree? Analyzing Wave Amplitudes

    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...
  21. O

    Radio Wave Induced Firing Of Neurons Through Ca2+ Channel Manipulation

    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?
  22. LarryS

    I Transmission Line EM Wave vs EM Wave in Free Space

    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...
  23. R

    B Interpreting light as Maxwell's EM wave

    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...
  24. J

    A LCAO graphene orbitals wave functions

    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...
  25. H

    I Symmetry and two electron wave function

    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...
  26. jedishrfu

    B FRB & Gravitational Wave Link: Scientists Baffled

    https://www.sciencealert.com/uncanny-coincidence-fast-radio-burst-detected-after-gravitational-wave-event
  27. binbagsss

    A Deriving Non-linear acoustic wave models, equilibrium state assumption

    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...
  28. Like Tony Stark

    Mixed states and total wave function for three-Fermion-systems

    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...
  29. Z

    A Momentum operator -- Why do we use the plane wave solution?

    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?
  30. Philip551

    How can the direction of propagation help in determining the phase of a wave?

    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...
  31. BiGyElLoWhAt

    3d plot of interference from 2 wave sources with 2d grid surface

    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) +...
  32. D

    Misc. DIY 'ECG' Machine: Testing Feasibility of Wave Transference

    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...
  33. A

    Conservation of power in a traveling wave on a string

    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...
  34. Darmstadtium

    I Relationship between the Different Frequency vs Decibel Graph Peaks

    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...
  35. Leureka

    I How does EM wave geometrical attenuation affect atomic absorption?

    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...
  36. homeworkhelpls

    How is Wave Intensity Affected by Half Amplitude and Double Frequency?

    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.
  37. J

    Calculating Wave Amplitude & Wavelength in Water Pools

    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...
  38. uxioq99

    Time Independence of the Momentum Uncertainty for a Free Particle Wave

    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...
  39. M

    Showing that this equation is a solution to the linear wave equation

    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!
  40. M

    Graph for sinusoidal wave travelling to the left

    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!
  41. I

    I Approach to extrapolate a "superpositioned" wave?

    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...
  42. J

    Trying to analyze a half wave rectifier with inductor and DC source

    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...
  43. Astronuc

    NASA NASA - Bimodal NTP/NEP with a Wave Rotor Topping Cycle

    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...
  44. Spinnor

    I Let a standing wave of length L go, get traveling wave of length 2L?

    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...
  45. maxelcat

    Standing wave, phase and antiphase

    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...
  46. loversphisics

    I Proving Behavior of Particle in Infinite Potential: Wave Function?

    Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?
  47. M

    I Can the Transverse Nature of a Wave from an Electron Gun be Observed?

    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
  48. M

    Deriving Wave Function for One-Dimensional Sinusoidal Wave

    Where did they get the equation in circled in red from? It does not seem that it can be derived from the graph below. Many thanks
  49. L

    B Quantum field theory and wave particle duality

    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...
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