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.
Homework Statement
phi(x,t) = A e *[-a(bx+ct)*2]
I'm trying to find the speed of the equation
Homework Equations
f(x+vt) +vt which means it is in the negative x-direction
f(x)= e^-ax^2
plugging in x'=x+vt
A e *[-a(bx+ct)*2]
where a= constant A= amplitude...
Hello,
Sound waves are always introduced as longitudinal mechanical waves: the medium particles oscillate in a direction parallel to the direction of motion of the sound wave. We can only hear sound frequencies between 20Hz and 20KHz. For us to hear these mechanical sound waves, the waves need...
Is it correct to state that a progressive wave, originates when a simple harmonic motion is imparted continuously to adjacent particles from one direction to another moving with a velocity v. Using this idea, substituting (t - x/v) instead of t is the simple harmonic motion function...
I have been thinking about this. For a wave equation, the acceleration of a point on a drumhead is proportional to the height of its neighbors $$U_{tt}=\alpha^2\nabla^2U$$
The heat equation, change in concentration or temperature is equal to the average of its neighbors...
Hi, I want to ask about the Wave behavior of light.
Fine, I know all about the slit experiments and the resultant interference patterns - but I want to ask about the physical context.
So light is the carrier of electromagnetic force, and thus its wave oscillation pattern represents an...
Homework Statement
3 tuning forks of frequencies 200, 203, 207 Hz are sounded together.find out the beat frequency.
Homework Equations
Beat frequency= n1-n2 (n=frequency).
The Attempt at a Solution
I know that beat frequency is the difference in the frequencies of two superposing notes. But...
What are the factors that determine the property of wave penetration of bodies? For instance we can listen to fm radio from inside the walls of a room. But visible light is unable to penetrate the walls.
Similarly some metals reflect some frequency but absorb some. How atomic orbitals play...
Text books often give an expression like Asin(kx-ωt) as a solution of the wave equation, but they don’t show how to arrive at this solution. Other textbooks, which go through the complete solution process of the wave equation, determine the coefficients using Fourier series. My goal was to get...
Is there a relationship between the quantization of an object and its wave function? If an object isn't quantized does it have a wave function? For example, in string theory branes are not quantized, so do they have wave functions?
Do higher dimensional branes, like the super membrane (which is a 2D brane) or the NS5/M5 brane, have wave functions? I know that they become unstable once they are quantized, but does that mean that they do not have wave functions? You will never here about any thing regarding an M2 wave...
Suppose the Copenhagen interpretation is correct. And we reverse time, what happens. If a wave function has collapsed, and we found a particle somewhere. Now, I turn back time( just hypothetically), what would happen? Would the wave function uncollapse and would the particle then appear at some...
Hellow
i want to ask about guessing the trial wave function at variational method of approximation
usually for example at solving harmonic oscillator or hydrogen atom we have conditions for trial wave function
but in fact i want to ask generally how could i make the guessing .. some problems...
Homework Statement
Flat harmonic electromagnetic wave propagates in the positive direction in vacuo axis y. Vector electromagnetic energy flux density is given by: S(y,t)=Sm *cos(wt-ky)2.Wave value: k=(2*π)/λ=0.41 m-1,Amplitude Sm=26 W/m2.Compare this wave with another wave.
Homework Equations...
I don't understand the difference between the Jeans Mass and the fundamental mode. Both are reaching till the horizon but according to me is the Jeans mass not oscillating. So what is the relation between a Jeans mass and the fundamental mode of the acoustic waves?
I selected the Name "Rogue Wave" because I do a lot of boating. Rogue Waves have recently been accepted into the scientific community as a fact of nature. For centuries sailors and captains have spoken of them but, was considered to be "Tales of the Oceans". Science does move at a very slow rate...
Schrodinger developed his famous wave equation which describes how the quantum state of a system changes over time.
But, what was Schrodinger trying to initially prove with his equation?I assume that it has to do with Debrogile's hypothesis.
I know from my classes that we use the Schrodinger...
Homework Statement
The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = sm cos (kx – ωt). Consider a sound wave of frequency 330 Hz and wavelength 0.95 m. If sm= 16 µm, what is the displacement of an element of air located at x = 1.1 m...
Is it possible to build the full wave function for a simple problem in QM, such as an infinite well, without any experimental data ?
I'm learning about QM, and I saw how to compute energy states (the wave function for each allowed energy level) in some usual QM basic problems. But then, I was...
Homework Statement
Many sources of electromagnetic waves (stars and light bulbs, for example) radiate in all
directions. A simple example of the electric field for a monochromatic electromagnetic wave produced by a spherical source is
$$E(r,\theta,\phi,t)=A\frac{\sin \theta}{r} \big(\cos...
< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >
A transverse wave on a string has an amplitude of 16cm, a wavenumber of 5.7m-1, and a frequency of 39Hz. What is the propagation speed of that wave?
(a) 6.84 m/s
(b) 39.2 m/s
(c) 43 m/s
(d) 6.24...
Homework Statement
http://i.imgur.com/sWZS9vQ.png
Homework Equations
P=½ √μF ω2 A2
The Attempt at a Solution
How is the equation related to the wavelength?
Thanks
For example, I am following the below proof:
Although the above derivation involves a projection on the position basis, it appears one can generalize this result by using any complete basis. So despite it not being explicitly mentioned here, are all wave functions with any continuum basis...
From the path integral approach, we know that ## \displaystyle \langle x,t|x_i,0\rangle \propto \int_{\xi(0)=x_i}^{\xi(t_f)=x} D\xi(t) \ e^{iS[\xi]}##. Now, using ## |x,t\rangle=e^{-iHt}|x,0\rangle ##, ## |y\rangle\equiv |y,0\rangle ## and ## \sum_b |\phi_b\rangle\langle \phi_b|=1 ## where ## \{...
I need to solve Cn for a wave function, and have reached the following integral:
Cn = -[√(1/a)](a/nπ)[cos(nπx/a)(ψ1(x)+ψ2(x))+∫cos(u)(dψ1(x)/dx)dx+∫cos(u)(dψ2(x)/dx)dx]This is a simplified version of the original equation, for
elaboration Cn is the constant for linear combinations of a wave...
Homework Statement
Alas, after a sybaritic festival, the cheap upright piano in your fraternity house is found upright at the bottom of the house swimming pool. You decide to play Handel's Water music but first test the sound of middle C (261.6 HZ). The speed of sound in water is...
Homework Statement
Homework EquationsThe Attempt at a Solution
So I was given the electromagnetic E field equation in phasor form and I converted it to sinusoidal form. Is it correct ?
Also will it be a reflected wave since we have (wt+Bz) and not (wt-Bz) ?
Also will it be circularly...
Homework Statement
A sound wave with intensity 2x10^(-3) W/m^2 is perceived to be modestly loud. Your eardrum is 6.0 mm in diameter. How much energy will be transferred to your eardrum while listening to this sound for 1.0 min?
Homework Equations
P=IA=(intensity)(area)
=2x10^(-3) * (pi...
Hi.
I'm a bit puzzled that the classical formula for the intensity of a monochromatic, linear EM wave
$$I=\frac{1}{2}\cdot c\cdot \varepsilon_0\cdot E_0 ^2$$
seems to be independent of frequency whereas I find for the energy of a mechanical wave (e.g. on a string with total mass ##M##)...
Homework Statement
Simple question we have to answer:
(Physics) How do I release the electrons from the cathode with a color filter? (The so called
Photoelectric effect)Homework Equations
none
The Attempt at a Solution[/B]
Here we have a conflict , the so called wave-particle duality, if...
How do you find the wave function Φα when given the Hamiltonian, and the equation:
aΦα(x) = αΦα(x)
Where I know the operator
a = 1/21/2((x/(ħ/mω)1/2) + i(p/(mħω)1/2))
And the Hamiltonian,
(p2/2m) + (mω2x2)/2
And α is a complex parameter.
I obviously don't want someone to do this question...
Homework Statement
The tension in the string is 90N; the string is 60cm long and has a weight of 34.44g. What is the speed of the wave on the string?
Answer: 396 m/s
Homework Equations
v = √ T / (m/L)
The Attempt at a Solution
v = √ 90N / (0.0344kg/0.6m)
v = 39.6 m/s
Huh? This looks like it...
Homework Statement
Assume a wave packet is has contributions from various frequencies, give by g(ω)=C for |ω|<ω0, and g(ω) =0 for elsewhere.
a)What is the signal strength as a function of time, i.e., V(t)=?
b) Sketch g(ω) and V(t); You can use fooplots.com, for example, or python.
c)...
Homework Statement
An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state.
Homework Equations
##\psi _{0} =\left(...
I have been trying to understand why two woodwind bore shapes behave so differently.
My understanding is that one end of a woodwind is an antinode (driven by the reed of the instrument) and the other end is a node (where the tube is open to the atmosphere).
a - - - - - - - - - - n
In the...
Homework Statement
A long rope with mass m = 10 kg is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope and the pulse travels up the rope.
(a) Explain why the speed of the wave pulse change as it moves up the rope; does it increase or...
As the universe expands and is per definition gravitationally decoupled on long distances and the overall metric therefore is "flat" and apparently no gravitational background exists, the question in some discussion arose:
Can GWs propagate in in a gravitational empty space at all?
If not, and...
It is hard not to hear that NASA has just published paper claiming confirmation of "impossible drive" - closed resonant chamber:
http://arc.aiaa.org/doi/full/10.2514/1.B36120
http://www.sciencealert.com/it-s-official-nasa-s-peer-reviewed-em-drive-paper-has-finally-been-published...
Hi, I wonder why we assume the matter wave of an electron is standing wave. Is there any reason why it has to be standing wave?Is it because standing wave is the right "wave equation solution" that satisfies integer multiple behaviour of bohr model?
Homework Statement
I don't see how the author normalizes ##u(r)=Asin(kr)##. From Griffiths, Introduction to Quantum Mechanics, 2nd edition, page 141-142:
http://imgur.com/a/bo8v6
Homework Equations
##\int_0^{\infty} \int_0^{\pi} \int_0^{2\pi}|A|^2 \sin^2(\frac{n\pi r}{a})r^2 \sin \theta...
Imagine that you have plucked a string and it is vibrating as a standing wave at its fundamental tone (frequency f1). You leave it there and later on come back with the intention of bringing it up to the second tone (frequency f2). What should you do? It seems obvious: apply a stimulous...
Does gravity affect waves such as gamma, xray, radio etc. and how does it interact with other wave forms considering gravity is a wave itself.
Respectfully,
Pat Hagar
I read through DeBroglie's original paper - and also a modern explanation on the same (attached).
The first contradiction that DeBroglie arrives at is simple enough - he considers the 'wave-particle' as observed from a stationary frame - and from a moving frame. The 'inner frequency' of the...
Hi,
what kind if integration used on equation 1 so it turned into equation 2? this does not look like integration by parts. and where (x-x0) appeared from instead of (k-k0) ?
thanks for your help.
Hello, is there a way to directly use a rectangular wave as input current without using an external circuit in ansoft maxwell? The instructions from ansoft that model a toyota motor just put the sine wave function directly into the winding's current settings, can I put a rectangular wave instead...
Hello.
I'm studying a course of the Quantum Field Theory and I got a question in a canonical quantization of a scalar field.
I don't write a full expression of the field quantization here but the textbook said terms with ei(p⋅x - Ept) are associated with an incoming particle and terms with...
As you can see from figure 4.4 from Griffiths book on QM, the radial wave function of the hydrogen atom has clear points where ## |R_{nl} (r)|^2 = 0 ##. My question is three fold:
First, how is the electron able to traverse this region? My intuition is that with the uncertainty principle, the...
Hello all,
First of all, I am aware that dissonance and consonance between pitches also depend to an extent by culture and musical origin but there also seems to be some degree of objective perception among people that can be explained scientifically. Also, I'm very new to this so I could be...
Hello all, I would like to know why an electron is accelerated in a linear accelerator because of the microwaves emitted by a magnetron?. Can someone tell me what are the relevant physics equations and what is the role of skin-effect here?
Thanks a lot.