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.
OK, so I'm trying to work out a few ideas regarding locality. I've studied at the undergrad level in the past (including quantum), but with professors that slaved away at proving math constructs and never bothered to indulge in clarifying the context of any concepts, so I'm pretty weak here...
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...
I am having trouble with doing the inverse Fourier transform. Although I can find some solutions online, I don't really understand what was going on, especially the part that inverse Fourier transform of cosine function somehow becomes some dirac delta. I've been stuck on it for 2 hrs...
Homework Statement
Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m1. The end portions of stretched string oscillates in the transverse direction with a frequency of 20 Hz and an amplitude of 0.005 m. Wave , which travels along the string, made in 0.1 second, 0.4 m long...
My textbook explained that it would be hard to see the wavelength properties of a tennis ball because we would have to find a very tiny slit in which to pass the tennis ball through. The wavelength of the tennis ball can be calculated using debroglie formula: wavelength = h/p
I was wondering if...
If I’m not mistaken, a system can be described as a wave if it follows the wave equation.
On Wikipedia, the general solution for the one-dimensional wave equation is written as u(x,t) = F(x - ct) + G(x + ct).
I don’t see the connection between this solution and what I understand waves to be...
I've wondered this for a while but not known how to ask the question,
If light is a transverse wave, then what is it transverse to?
To elaborate, light travels in three-dimensions, radially. To me, this seems analogous to the sound wave, with pulses of pressure moving longitudinally to the...
So, my game is coming along.
My psychic energy shielding protects against EM radiation. The energy used for shielding gets depleted based on the type of EM radiation (the wavelength) and according to the amplitude of the radiation the energy shielding is exposed to.
I can't find many numbers...
I understand that waves are function of space and time in nature, so E(x,t) will be fundamental description of a wave. I notice that often people denote a wave as E(t) for instance, an envelop function of a pulse. For this case, E is an oscillation at a fixed spatial point x? So that the point x...
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...
Hi everyone! Sorry for the bad english!
So, just a quick doubt... Does things collapse from a wave of probability into a quantum field or is the wave in the quantum field the probabilistic wave itself?
An example to make it clearer:
Suppose we have an atom, it enters an atom interferometer, it...
1. Homework Statement
Consider a potential field
$$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$
The eigenfunction of the wave function in this field suffices...
Consider a potential cavity
$$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$
The eigenfunction of the wave function in this field suffices
$$-\frac{\hslash^2}{2m}\frac{d^2\psi}{dx^2}+\frac{\hslash^2}{m}\Omega\delta(x-a)\psi=E\psi$$...
Just when I thought there couldn't be any more quantum interpretations (I think @Demystifier listed 9 in his recent thread)... :smile:
Lee Smolin and several others (Cohen, Cortês, Elitzur) have published a pair of related papers discussing dBB/Bohmian Mechanics and its ability to explain the...
How do I setup an integral to integrate over the following equation:
V(t) = 1/(R*C) integral to t Vin(t) dt
This is the capacitor voltage over time formula.
I want to integrate over a sine wave from 9 to 81 degrees. Frequency of 120Hz, amplitude of 120V.
The formula I used in wolframalpha is...
Dear community,
I am Pedro de la Torre, now doing my PhD on Cosmic ray propagation.
Now, I have started to study reacceleration due to interactions of CR with plasma waves. My problem is that I do not find neither a good book or any kind of review with a detailed demonstration on the...
I am trying to understand the following:
1. Have gravitational wave constructive and deconstructive interference phenomena already been observed or is it that only after making LIGO kind of experiments more advanced, that we might be able to observe such phenomena in the future?
2. Can't...
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...
Homework Statement
Homework Equations
v = d/t
Solve for t. t = d/v
The Attempt at a Solution
In my General Physics 2 course we are doing sound waves I have the answer to the problem which is 90.8m I am trying to understand the concepts of sound wave. So please correct me if I am wrong,
1...
Dear Everybody,
I do not know how to begin with the following problem:
you are asked to solve the wave equation subject to the boundary conditions ($u(0,t)=u(L,t)=0$), $u(x,0)=f(x)$ for $0\le x\le L$ and ${u}_{t}(x,0)=g(x)$ for $0\le x\le L$ . Hint: using the...
Dear Everybody,
I am confused about how to start with the following problem: using the solution from ex. 3:
$u(x,t)=F(x+ct)+G(x-ct)$
"For data u(x,0)=0 and ${u}_{t}=\frac{x}{(x^2+1)^2}$ where x is from neg. infinity to pos. infinity."
Thanks
Cbarker1
Dear Everyone,
Hi. I do not how to begin for the following question:
Ex. 5. Using the solution in Ex. 3, solve the wave equation with initial data
$u(x,t)=\frac{1}{{x}^2+1}$ and $\pd{u}{t}(x,0)=0$ for $x\in(-\infty,\infty)$.
The solution, (I have derived this solution in Ex. 4), that is...
I have a few questions about the wave equation and the D'Alambert solution:
0) First of all, I'm a bit confused with the terminology. Wikipedia says that THE wave equation is a PDE of the form: ##\frac{\partial^2 u}{ \partial t^2 } = c^2 \nabla^2 u##, however there are other PDEs that have...
Homework Statement
A. Two identical speakers, with the same phase constant, are arranged along a 1D track. One speaker remains at the origin. The other speaker can slide along the track to any position x. You are on the track at x=10 m. You hear interference maxima when the adjutable...
Suppose a linear polarized light wave front is incident on a double slit. What happens if one places a quarter-wave polarizer in front of only one slit in the double slit experiment? Does one obtain the usual inteference fringes? Or the diffraction pattern only? Else?
Hi,
a simple question related to the gravitational wave detection.
The net effect of gravitational wave is basically the stretching of the space including all the measurements tools (meter sticks just to illustrate the concept) that could be used to detect it. I am aware of laser...
Homework Statement
This is just a question about a question in Serway & Jewett's "Physics for Scientists and Engineers 3rd Ed". It's Objective Question 3 from Chapter 18, building on Example 18.1 from the text.
Two identical loudspeakers placed 3.00 m apart are driven by the same oscillator...
Basically, we have a transmission line not matched to load R. So there is a forward wave and a reflected wave. Now when the reflected wave reaches back to source 'S', does it get absorbed by the source? Does that mean the source 'S' gets back some of the power (equal to the reflected power) that...
Is the wave function for the positron the complex conjugate of the wave function for the electron? I've tried to google this, but I can't seem to get a definite answer from a reliable source. It seems that antimatter is derived in quantum field theory which does not concentrate on wave...
Is anyone did experiment on wave function collapse in double slit experiment. Could you please share information about that, and also share research paper about that experiment.
What kind of observation done here, what kind of equipment used for that?
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...
Answer is probably not, but is there some connection between the inhomogeneous wave equation with a constant term and the spacetime interval in Minkowski space?
$$
1) ~~ \nabla^2 u - \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \sum_{i=0}^2 \frac{\partial^2 u}{\partial x_i^2} -...
We want to solve the equation.
$$H\Psi = i\hbar\frac{\partial \Psi}{\partial t} $$ (1)
If we solve the following equation for G
$$(H-i\hbar\frac{\partial }{\partial t})G(t,t_{0}) \Psi(t_{0}) = -i\hbar\delta(t-t_{0})$$ (2)
The final solution for our wave function is,
$$\Psi(t) =...
Hi.
We tried to make some quantitative measurements with a Pasco ripple tank system, a video camera and software for video analysis. We generated circular waves and tracked the propagation of a crest, from which the software computed the phase velocity:
We used 5 Hz, 10 Hz and 20 Hz...
Homework Statement
The problem is shown on the photo. And the actual answer is A. 0.5s, and I thought it would be B. 1.0s
Homework EquationsThe Attempt at a Solution
Here is my thought,
The journey from A to B is just a half period, then the whole period would be 4s, as a result, the time it...
We know that skin depth in a conductor is found using the following expression,
(Credits: http://farside.ph.utexas.edu/teaching/315/Waves/node65.html)
Basically, as the wave propagates in a conductor, it's electric field strength reduces and reaches 1/e of it's initial value at the skin depth...
Hi, there is no particular question that I need help on, just something my lecturer told us in lesson which I couldn't quite understand so i'd like to check my understanding on this. I know that the speed of a soundwave is 'c' in undisturbed flow. Suppose the flow velocity is 'U'. If the...
Does a single photon travel in two different waves at once? If photons are particles like the Photoelectric Effect, Compton Scattering, and Blackbody radiation all suggest, how do polarizing filters block light completely? Is a particle from a radio antenna actually that large in size?
I am interested in the derivation of Schrödinger’s wave equation from the Klein Gordon equation. I have looked in Penfold’s ‘The Road to Reality’, the open University’s Quantum Mechanics books, Feynman’s lectures, the internet, but not found what I want. Everyone seems to take it as a given...
In classical electrodynamics energy of a wave is proportional to its intensity , this theory fails when Hertz did experiment on photoelectric effect. Is my statement is correct? If not correct me.
For this problem at t=0
Ψ(x,0)=Ψ1-Ψ3
Where Ψ1 and Ψ3are the normalised eigenstates corresponding to energy level 1 and 3 of the infinite square well potential.
Now for it's time evolution it will be Ψ1exp(-iE1t/ħ)- Ψ3exp(-iE3t/ħ)
And taking the time given in the question the time part of the...
Homework Statement
Homework Equations
For this question my ans. is coming option (3) since the time part of the wave comes out to be same for both the energy states which is (-1)^(-1/8) and (-1)^(-9/8) respectively (using exp(-iEt/ħ)).
But the correct option is given option (4).
Am I right...
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...
For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) traveling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the...
Homework Statement
There's a bucket, filled about halfway with water. The water itself is completely still. A perfect sphere with mass m and volume v are given. The depth of the water, and the radius of the bucket (which may be considered perfectly cylindrical) are both given. In short, you...
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 ?