Wave Definition and 186 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. P

    B "Brain waves"

    Can I say, by any means, that a "brain wave" is, in fact, a wave of some kind?
  2. Aethermimicus

    I What is the function of the air cavity inside drums?

    I'm trying to understand the function of the air cavity inside drums. I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.' Then what are the resonance...
  3. samy4408

    I Question about electromagnetics (waves and particles)

    I saw that we can talk about the light as particles (photons ) or as an electromagnetic wave , the question is that do we represent other electromagnetic waves (like microwaves or radio waves ) as particles (like we do with light ) ?
  4. R

    Total (net) reflection of a wave moving through 3 different impedance regions

    I know for a wave moving from left to right, ##\psi_i = Ae^{i(\omega t - k_1x)}## The first reflection where ##Z_1## is ## R_{12}Ae^{i(\omega t - k_1x)}## The second reflection. The wave moves from 2 to the limit between 2 and 3 then reflect... Thus, ##T_{12}R_{23}T_{21} Ae^{i(\omega t - k_1 x...
  5. 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...
  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. 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...
  8. 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?
  9. 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?
  10. 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!
  11. A

    I Can the energy in two waves cancel out? If so, why?

    I know the answer would be yes, but why? In class, I learned that energy is scalar and cannot be negative (at least in undergraduate class). Thus adding two sources of energy should result in a higher level of energy in general. But here for wave, if we have 2 waves that do destructive...
  12. L

    I Connecting wave equation with a non-constant force only in bounds

    Hi hi, I'm confused about how to mix this two concepts, actually the wave equation: ##\frac {\partial^2 u} {\partial t^2} = v_x^2 \frac {\partial^2 u} {\partial x^2} + v_y^2\frac {\partial^2 u} {\partial y^2} + force## The equation will apply the rule all over the space, but I have the next...
  13. I

    B Particles with small Wavelengths passing through huge slits?

    I´´m confused. How can a single photon in the lightspectrum with wavelength of a few hundert nanometers go through both slits in the double slit experiment at the same time. I understand the wave- particle duality and the concepts in principle. My confusion is in the context of little wavelength...
  14. S

    B Conversion of Lux into W/m^2

    For a physics project, I'm planning to investigate the relationship between the number of slits in a diffraction grating and the intensity of the central maxima. The light meter which I'm planning to use to measure the intensity gives me a result in LUX. I know the wavelength of the red laser...
  15. Kaushik

    Reflection of a wave by a rigid boundary

    I found this on the internet. Source How does the crest reach the end of the medium? As the other end is fixed there is no way the crest can reach the interface. Isn't it? My book gave an alternative explanation. It stated that as there is no net displacement at the interface, we can use the...
  16. Kaushik

    B Laplace's correction

    Laplace pointed out that the variation in pressure happens continuously and quickly. As it happens quickly, there is no time for heat exchange. This makes it adiabatic. But newton believed it to be isothermal. Why isn't it isothermal but adiabatic? Why is there a change in temperature?
  17. Jason-Li

    Comp Sci Fourier analysis & determination of Fourier Series

    ANY AND ALL HELP IS GREATLY APPRECIATED :smile: I have found old posts for this question however after reading through them several times I am having a hard time knowing where to start. I am happy with the sketch that the function is correctly drawn and is neither odd nor even. It's title is...
  18. A

    Wave on a piano wire

    angular frequency= 50 rad/s= 2*pi*frequency frequency= 7.96 Hz k=2*pi/wavelength k=2*pi/(2*1.6m) = 1.96 velocity=angular frequency/ k velocity=50/ 1.96 = 25.5 m/s For some reason this velocity is wrong
  19. ContagiousKnowledge

    General solution of the spherical wave equation

    Since the spherical wave equation is linear, the general solution is a summation of all normal modes. To find the particular solution for a given value of i, we can try using the method of separation of variables. $$ ψ(r,t)=R(r)T(t)ψ(r,t)=R(r)T(t) $$ Plug this separable solution into the...
  20. A

    Tension of a cello string

    wavelength of string= 2*L wavelength of string=2*0.70m= 1.4m velocity of string= frequency * wavelength velocity of string= 220Hz * 1.4m= 308 m/s tension= (308m/s)^2 * 0.00196 kg/m =186N Is the tension correct?
  21. K

    Waves: Calculate the sound intensity from two speakers

    Two similar speakers are connected to a stereo system that emits a signal of frequency 𝑓. However, the signal to speaker B is inverted so that positive voltage becomes negative (but with the same absolute value) and vice versa for negative voltages that become positive. A sound intensity meter...
  22. Z

    Can ultrasonic waves be stopped or mitigated?

    Summary: After use of Ultrasonic energy we need to mitigate the propagation of mechanical waves, need a solution to stop propagation or at least mitigate it. Hello Scientists, After use of Ultrasonic energy we need to mitigate the propagation of mechanical waves, need a solution to stop...
  23. Fdtroya

    Standing wave node counter

    Summary: Make a circuit that counts the number of nodes in a standing wave generator I have a an assignment to complete this Term, the assignment consist in making a machine that would produce standing waves in various frequencies, (for example the typical motor connect to a string with...
  24. jdou86

    Wanting to understand the linearity of wave equations

    dear yall with tranditional wave equation on the gre book it says by the linearity in function f which represents wave. it leads to the principle of superposition. I get an intuition about with a standing wave with cos(x)cos(t) you can break it down to pair of left and right moving waves. i...
  25. michael872940

    Can I determine mass & spring k from graph of wave, t, a, & vectors?

    Classical problems for hookes law generally give either mass or spring constant. What if I have a graph of a wavelike structure that is oscillating which I can use to measure for example: T (period), t (time), Δx (displacement), v (velocity), a (acceleration) and other variables is this...
  26. P

    How to solve this sound problem (minimum sampling rate required)

    Summary: The problem: If one wants to make a digital record of sound such that no audible information is lost, what is the longest interval, Δt, between samples that could be used? ( it gives a hint that humans can hear sound waves in the frequency range 20 Hz to 20 kHz. It should be a very...
  27. F

    I How to Determine a Photon's Wavefunction After it Collapses?

    Suppose one measures the position of a photon without destroying it. From my understanding, the wavefunction of the photon should collapse, and will return to a more spread out state over time. How would one calculate this, specifically the rate at which the wavefunction spreads out from the center?
  28. P

    I Gravitational waves and density of matter

    From what I have read gravitational waves are caused by the acceleration of massive object causing ripples in space time. What specifically causes this, and how does general relativity predict these. Does it have to be a high density of matter, or a large amount of it. How do these waves affect...
  29. LarryS

    I Does wave superposition consume time?

    In Classical Mechanics, waves produced in linear systems, like EM waves, obey the Superposition Principle in which the wave amplitudes of, say two input waves, “add up” to create one output wave whose varying amplitude is the sum of the two input waves. One example would be Young’s Double Slit...
  30. S

    Amplitude relation with periodic time

    Homework Statement Ql: Which sound wave will have its crests farther apart from each other - a wave with frequency 100 Hz or a wave with frequency 500 Hz? Homework Equations Frequency= 1/ periodic time The Attempt at a Solution I did it like that: I just found the periodic time for each...
  31. Cathr

    Finding Fresnel coefficients from the interface conditions

    Homework Statement We have an incident electric field, and there are two cases: 1) the field is polasised perpendicularly to the incidence plane (TE) 2) polarised in the plane (TM) Here I must be able to correctly apply the limit conditions, to find the Fresnel formulas that give the...
  32. C

    Police Radar Wave Question

    Homework Statement [Answer is V = 25m/s, however, how do I get that answer? Thank you!] A police cruiser sets up a novel radar speed trap, consisting of two transmitting antennas at the edge of a main north-south road. One antenna is 2.0 m [W] of the other. The antennas, essentially point...
  33. A

    Clear formula for water penetration by wave frequency

    I want a clear formula for clear water (and salty water) penetration by giving only the radio wave frequency . I searched the web , the formulas on the web are so complicated . Are there any simple formula available for that ?
  34. G

    Are superpositions of waves with different c still waves?

    Hi. As far as I know, superpositions of waves are normally considered to be waves too, even in dispersive media. But how can they still be solutions of a wave equation of the form $$\left(\frac{1}{c^2}\frac{\partial^2}{\partial t^2}-\Delta\right)u=0$$ if ##c## isn't the same for all of them...
  35. P

    Studying De Broglie-Bohm theory books/material recommendations...

    Hi PF, im finishing my bachelor soon and I would really like to do my thesis in De Broglie-Bohm theory. I know its a controversial topic but i refuse to accept the statistical crazyness of qm(i passed qm already). Im not a super good student so I´m asking you for some books on this theory, or...
  36. S

    Progressive wave

    The answer is B but I don't understand how. Surely, the string at point P is moving upwards. This video gave a solution but the part that they have indicated as down is a different part of the string and not P.
  37. Y

    Phase angle and Phase in Simple harmonic motion

    I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula: y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π) phase angle = θ = ωt + θ0 phase of wave = φ = t/T + θ0/2π But I...
  38. B

    The Simple Pendulum

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

    B Why longitudinal waves are waves?

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

    A Questions about the energy of a wave as a Taylor series

    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...
  41. Lyakhnitskiy Dmitriy

    B Energy of a wave

    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...
  42. A

    Duration of electromagnetic disturbance

    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...
  43. Kenneth Boon Faker

    B What is the difference between a wave and a field?

    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...
  44. W

    I What is a Gaussian Wave Packet?

    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,
  45. Vicol

    Hamilton-Jacobi equation and particle-wave motion

    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...
  46. Kenneth Boon Faker

    A question about wave/particle duality

    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...
  47. T

    B What, in essence, distinguishes light from matter?

    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...
  48. H

    New wave after superposition (interference)

    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...
  49. C

    I Analysis of Ultrasonic Waves at a point

    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...
  50. J

    Motion of point when sound volume goes up

    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...