# 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. ### 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. ### B What is a Gravitational wave?

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

32. ### 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) +...
33. ### 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...
34. ### 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...
35. ### 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...
36. ### 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...
37. ### 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.
38. ### 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...
39. ### 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...
40. 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!
41. 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!
42. ### 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...
43. ### 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...
44. ### 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...
45. ### 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...
46. ### 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...
47. ### 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?
48. ### 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
49. 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
50. ### 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...