# 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. ### B "Brain waves"

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

35. ### 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. ### 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. ### 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. ### The Simple Pendulum

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