Wave Definition and 999 Threads

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. Hamiltonian

    I Writing the wave function solutions for a particle in a 2-D box

    The final wave function solutions for a particle trapped in an infinite square well is written as: $$\Psi(x,t) = \Sigma_{n=1}^{\infty} C_n\sqrt{\frac{2}{L_x}}sin(\frac{n\pi}{L_x}x)e^{-\frac{in^2{\pi}^2\hbar t}{2m{L_x}^2}}$$ The square of the coefficient ##C_n## i.e. ##{|C_n|}^2## is...
  2. jim mcnamara

    Ordovician mass extinction second wave - deep sea anoxia

    https://www.nature.com/articles/s41561-021-00843-9 Popular science version: https://scitechdaily.com/uncovering-the-surprising-secrets-behind-Earth's-first-major-mass-extinction/ Nature paper discusses causes of the second "wave" of mass extinction at the end of the Ordovician (~445mya) Really...
  3. C

    Resultant Frequency and Wavelength of Interfering Sound Waves

    ##-w1## and ##-w2## are to shift the cosine graph to the right, and ##\frac{2pi}{\lambda}## is to stretch the graph. But I can't seem to draw an appropriate ##y1+y2## graph (quite irregular) and I struggle to find the resultant frequency and wavelength. Also, why is there angular frequency in a...
  4. I

    How can I plot the function g(x) = sin(πn/L) x and its corresponding g²(x)?

    Summary:: We are currently studying basics of quantum mechanics. I'm getting the theory part but it's hard to visualise everything and understand. We are given this question to plot the function so if someone could help me in this. Plot the following function and the corresponding g²(x) g(x)...
  5. rudransh verma

    Car traffic producing shock wave

    I don’t get where exactly the lengths start and end in figure.
  6. R

    How to find the amplitude of oscillations of a string with 5 beads?

    Hi, First of all, I'm wondering if a beaded string is the right term? I have to find the amplitude of the modes 2 and 3 for a string with 5 beads. In my book I have $$A_n = sin(\kappa p)$$ or $$A_n = cos(\kappa p) $$ it depends if the string is fixed or not I guess. where $$\kappa = \frac{n\pi...
  7. Mayhem

    Particle in a box: Finding <T> of an electron given a wave function

    If ##\hat{T} = -\frac{\hbar}{2m}\frac{\mathrm{d^2} }{\mathrm{d} x^2}##, then the expectation value of the kinetic energy should be given as: $$\begin{align*} \left \langle T \right \rangle &= \int_{0}^{L} \sqrt{\frac{2}{L}} \sin{\left(\frac{\pi x}{L}\right)}...
  8. B

    I Equation to graph a sine wave that acts like a point on a unit circle

    I need an equation to graph a sine wave that act like a unit circle but only positive numbers. so I need it to be 0 at 0, A at 90 , 0 at 180, A at 270, 0 at 360, and A at 450 and so on and so on... Now I know sin(0) is 0 in degrees and sin(90) 1 and I know if you Square a number is...
  9. S

    Amplitude of standing wave for higher frequency

    I understand the part where there will be more nodes produced because number of wave produced will increase (let say from half wave to one wave). But I don't understand the part where the amplitude will be less. How can number of nodes (or frequency) affect the amplitude of standing wave...
  10. Seanskahn

    I Behavior of a curved 2D sheet and a curved 1D wire under acoustic wave

    Good day. We know how simple objects, such as 1D wires behave when a simple harmonic wave travels along a wire, or two wires knotted togethe.We also know what happens if you excite a circular thin disc with a single frequency. Are there some material I can read on, that considers the effect...
  11. U

    I Phase Speed of Wave in non-relativistic Doppler Shift Derivation

    Consider the situation where an observer at rest on the ground measures the frequency of a siren which is moving away from the observer at speed ##v_{Ex}##. Let ##v_w## be the speed of the sound wave. Let ##\lambda_0##, ##f_0##, ##\lambda_D##, and ##f_D## be the wavelengths and frequencies...
  12. S

    How Do Different Equations Affect the Initial Direction of a Traveling Wave?

    But in the notes from teacher, the equation is ##y=A \sin (kx - \omega t)## for wave traveling to the right and ##y=A \sin (-kx - \omega t)## for wave traveling to the left When I transform the equation of the wave traveling to the left using trigonometry: $$y=A \sin (-kx - \omega t)$$ $$y=-A...
  13. physics1999

    I Particle and wave model understanding -- help please

    How does the photoelectric effect prove the wave-particle wrong? Higher intensity does not mean higher energy. If we were to assume the wave-particle model, an increase in intensity means an increase in the amplitude of the wave right? The energy of light is never dependent on amplitude, it is...
  14. C

    Delaying/shifting the start of a square wave inverter

    I am trying to create a two phase type setup where I have a square wave in the multi-gigahertz frequency. However, I want the second wave to start once the first one reaches 90 degrees. How can the circuit be configured to do this? Will a phase shifter do or can a square wave be phase shifted at...
  15. U

    A transverse wave traveling through a medium versus a particle of the medium

    I imagine a particle traveling across 1 wave cycle. The total vertical distance traveled across the wave cycle is 4 x the amplitude of the wave. The total vertical distance traveled in 1 minute: 5 cycles in 1 second, thus 5x60 cycles in a minute then 4 x amplitudes effectively traveled per...
  16. V

    Best layman non mathematical interesting book on Ray and wave optics

    A book on optics which is less mathematical maybe a similar one to physics for poets or gamow gravity classics
  17. A

    Propagation Wave Expressions and Wave Velocity

    Hello everyone, I would really appreciate some help on the following problem on plane waves and propagation. Not too sure if my attempt at writing the propagation wave expressions are correct, and how to handle the arbitrary function f(u). For the velocity, the wavelength is not specified, so is...
  18. .Scott

    B ARC Centre reports HF Gravitational Wave Antenna

    The full title of the publication is: Rare Events Detected with a Bulk Acoustic Wave High Frequency Gravitational Wave Antenna It is published in Physics Review Letters and reported in Phys Org. They have created a small piezo-electric device (< 2cm, though it gets bigger once you create an...
  19. Tymothee Waldner

    I Schrödinger wave function: How to use it to get 3-D atomic orbitals?

    Hi, I am 16 year old and I am very interested in Physics. This summer I solved Schrödinger equation using griffiths' introduction to quantum physics and other sources. I achieved to get an exact solution of the wave function but I would like to plot it in a programm in order to get the 3d...
  20. redtree

    B Difference between a continuously differentiable function and a wave

    What is the difference between an absolutely continuously differentiable function and a wave? Are all absolutely continuously differentiable equations waves?
  21. V

    B Potential energy in standing wave compared to traveling wave

    From hyperphysics, "The unique point in the case of the traveling wave in the string is the element of the string that is at the maximum displacement as the wave passes. That element has a zero instantaneous velocity perpendicular to the straight string configuration, and as the wave goes "over...
  22. Sciencemaster

    I Exploring Wave Function Collapse and Measuring Particles

    Hello! Let's say we have a wave function. Maybe it's in a potential well, maybe not, I think it's arbitrary here. This wave function is one-dimensional for now to keep things simple. Then, we use a device, maybe a photon emitter and detector system where the photon crosses paths with the wave...
  23. Hallucinogen

    I Common features of set theory and wave functions?

    I would like to know if any of you think there's any sort of connection, analogy, or common features between, sets in set theory and wave functions in QT? Wave functions lack trajectories, so do sets. Wave functions also distribute over areas, as sets can do. To my understanding, wave...
  24. jackiepollock

    B How does polarisation in nature work?

    Why are lights reflecting off horizontal surfaces like the road, water, or snow horizontally polarized? How does the process happen?
  25. baby_1

    Phase velocity in oblique Angle propagation (Plane wave)

    Hello, Regarding the wave oblique angle propagation and based on Balanis "Advanced engineering Electromagnetic" book on page 136 ( it has been attached) I need to know why the phase velocity in x direction is not important to keep in step with a constant phase plane( Just equation 4-23). I...
  26. S

    I How Do You Calculate Day-Specific Phase Shifts in Excel for Sine Waves?

    Hi, I have created a sine wave with the following options: 1.) - changing the period/length in days of the sine wave (Cycle Length in Days) 2.) - calculating the start value of the "dummy" so that the sine wave always starts with -1 (Dummy Start at Cycle Trough) when the phase shift is set...
  27. baby_1

    Attenuation and Phase constant values in wave equation

    Regarding wave equation we are faced with this form $$\nabla^2 \vec{E}=j\omega \mu \sigma \vec{E}-j\omega \mu\varepsilon \vec{E}=\gamma ^2\vec{E}$$ where $$\gamma ^2=j\omega \mu \sigma -j\omega \mu\varepsilon $$ $$\gamma =\alpha +j\beta $$ where alpha and beta are attenuation and phase...
  28. sarahjohn

    Time Dependence of Wave Function

    I started out by finding the w (omega) value for all of the three states but I'm not sure where to go from there.
  29. D

    I Is there a way to calculate the frequency of an electron wave?

    According to de Broglie, the wavelength of an electron wave is L=h/p. Is there a way to calculate the frequency of such a wave? Thank you!
  30. K

    A Thermal shock wave question from my hydrodynamics simulation

    This is a fluid dynamic simulation. The top area has 100 degrees Celsius. The bottom area has 0 degrees Celsius. And both are filled with an ideal gas which is 1-atmosphere pressure. Two areas are connected through the left small line. Another part is blocked. So heat transfer can only happen...
  31. B

    Show that the given electric field is a plane wave

    A wavefront is defined as a surface in space where the argument of the cosine has a constant value. So I set the argument of the cosine to an arbitrary constant s. ## k(\hat{u} \cdot r - c t) + \phi = s ## The positional information is is in r, so I rearrange the equation to be ## \hat{u}...
  32. Buzz Bloom

    I Find GR Equation: Collapsing Orbit & Gravitational Wave

    I recall some time ago seeing a GR equation describing the rate of orbital energy loss from the moving objects in orbit generating gravitational waves. I can no longer find this equation again. I am hoping someone can help me.
  33. The Baron

    What Happens to the Wavelength of Light as it Passes Through Water?

    I have a question, say a wave of light is emitted, and it passes through water, changing it's wave length to 380nm inside the water, once it comes out of the water, to vacuum will the wavelength remain at 380nm or will it change?
  34. J

    B RC Low Pass Circuit Sine Wave Response

    Hey Everyone, I am trying to gain a level of fundamental understanding of an RC circuit sine wave response through the mathematics and was wondering if someone could help me work it out. Fundamentally a sine wave is represented by the equation y=-ky'' . When a sine wave is used as the input...
  35. U

    I Why is Scalar Massless Wave Equation Conformally Invariant?

    It can be shown mathematically that the scalar massless wave equation is conformally invariant. However, doing so is rather tedious and muted in terms of physical understanding. As such, is there a physically intuitive explanation as to why the scalar massless wave equation is conformally invariant?
  36. bubble-flow

    Where are the pressure nodes on a standing acoustic wave in water?

    I have calculated the wave length of a 36 kHz acoustic wave in 20 °C water to be around 41.16mm. Suppose I have a transducer that produces a 36 kHz acoustic wave and a small water container with a length of 41.6 mm. How will the standing acoustic wave look like, which is produced by the...
  37. J

    Engineering Calculating the DC value of the output voltage for a full wave rectifier

    I need help with part (a)... I know that the root-mean-square voltage is the dc-equivalent voltage for an AC waveform and what my book labels "##V_{dc}## is actually the average voltage. Hence I am assuming the question is asking me to find ##V_{rms}## ... Is my assumption that the...
  38. practicaleducator

    Calculating Electromagnetic Wave Intensity in a 30 sq m Room

    Hi, If I build a machine that its sole purpose is to radiate xx Hz of electromagnetic wave, how do I calculate the intensity of the waves? Let's say I put it in the room of 30 sq meters. Thank you.
  39. S

    Position of speaker in front of tube to produce stationary wave

    That is part of the article. I want to ask about step 4. I know the basic theory of how stationary wave is formed (superposition of incoming and reflected wave) and also basic concept about stationary wave in open and closed tube, something like this: But I don't know the reason why in step 4...
  40. F

    Can a continous wave laser be converted to a more powerful pulsed laser?

    Can a continuous wave laser weapon be converted to a Ultrashort Pulsed Laser like the one mentioned in this article?: https://www.forbes.com/sites/davidhambling/2021/03/11/us-army-develops-laser-machinegun-firing-light-bullets/?sh=6555843768a3 Israel is also developing laser weapon for...
  41. Arman777

    Wave equation for Schwarzschild metric

    I am trying to find the $$\nabla_{\mu}\nabla^{\mu} \Phi$$ for $$ds^2 = (1 - \frac{2M}{r})dt^2 + (1 - \frac{2M}{r})^{-1}dr^2 + r^2d\Omega^2$$ I have did some calculations by using $$\nabla_{\mu}\nabla^{\mu}\Phi = \frac{1}{\sqrt{-g}}\partial_{\mu}(\sqrt{-g}g^{\mu \nu}\partial_{\nu}\Phi)$$...
  42. P

    I How does a standing wave form?

    I understand how waves undergo superposition. However, for a standing wave, the reflected wave is a mirror opposite of the incoming wave. By the superposition principle, won’t the 2 waves add up to 0, at all points?
  43. E

    Location of the particles when 1.5 periods of a sound wave have passed

    qn iv. I understand that when 1.5 periods pass, every compression will become rarefaction, and every rarefaction will become compression(someone please correct if wrong) but the answer key shows something else. I'm interpreting the answer key drawing to be 1 compression and 4 rarefactions...
  44. Haorong Wu

    I Weak Gravitational Field & Wave Eq. - Analyzing Effects on Massless Scalar Field

    A massless scalar field in a curved spacetime propagates as $$(-g)^{-1/2}\partial_\mu(-g)^{1/2}g^{\mu\nu}\partial_\nu \psi=0 .$$ Suppose the gravitational field is weak, and ##g_{\mu\nu}=\eta_{\mu\nu}+\epsilon \gamma_{\mu\nu}## where ##\epsilon## is the perturbation parameter. And let the field...
  45. P

    I Good resources for learning a little about the wave vector

    Hi, I am looking for a short document discussing the usage of the wave vector. Any recommendations? Thank you!
  46. B

    Solving the wave equation for standing wave normal modes

    ## \frac {\partial^2 \psi} {\partial t^2} = v^2 \frac {\partial^2 \psi} {\partial x^2} ## has solution ## \psi (x, t) = \sum_{m=0}^\infty A_m \sin(k_mx + \alpha_m)sin(\omegat + \beta_m) ## The boundary conditions I can discern $$ \psi (0, t) = 0 $$ $$ \frac {\partial \psi} {\partial x} (L, t)...
  47. Z

    B Which one is correct? (the Matrix or Wave formulation of QM)

    hello matrix and wave formulation of QM are equivalent theories i.e they yield the same results Which one is most frequentely used by professional scientists in solving real problems and why ?
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