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.
For this question I want to clarify that 5k which is the electric field component perpendicular to the incident plane ( the xy plane) will be continuous for reflection and refraction ,
For which none of the options seems correct ,am I right??
The component of magnetic field perpendicular to...
Would not any real measurement taken on a complex state logically require that the results of the measurement have less information than the state? Although I’m just beginning in QM, it appears to me unsurpring that a real measurement on the complex wave function seems to collapse the wave...
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...
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...
Hello,
I'm trying to write a wave function for a perturbed system. The original (unperturbed) wave function has two solutions for even and odd n-values, for example ##sin(n \pi x)## for even-n and ##cos(n\pi x)## for odd-n. Then, the perturbed wave function also has an even and odd solutions...
Homework Statement
*I cannot place the original image due to copyright reasons, but the image above is a good alternative.
"Wave crests spread out behind a boat as shown above. What do the wave crests indicate about the boat's speed?"
It is increasing.
It is less than the speed of the water...
I was studying Feynman Lectures on Physics Volume 1 chapter 29. In there he proves that electric field propagates like a wave. Here is my attempt (in image), please tell me my mistake.
Thank you
Is it a fair prediction to state that in the next several years or so, globally, there will be major investments into gravitational wave research, and many more ‘LIGOs’ being developed?
Is it a good idea to venture into that area of physics?
Hello all again,
I was just thinking again about another aspect of electromagnetic waves: Assume we have a planar wave. How "broad" is it or how far does the electric field of it reach? For instance if we have a single planar wave, assume the k-vector in the direction of propagation and then the...
Just like a concave mirror concentrates light, it can also concentrate sound waves. Ray diagrams like the following look as if all waves converge to a single point of INFINITE power density which of course is not true, probably because of the wave nature of light or sound. What is the correct...
If someone wanted to pursue a career in gravitational wave physics, and work at places like LIGO, studying astrophysical objects such as black holes and neutron stars, etc.
What are some key courses/skills that person should take/learn as an undergraduate, and graduate student?
Homework Statement
A generic state represented by the wave function ##\psi (\vec(x)## can be expanded in the eigenstates with defined angular momentum. Write such an expansion for a plane wave traveling along the z direction with momentum ##p = \hbar k## in terms of unknown coefficients ##c ( k...
Homework Statement
For a region where the potential V=0, the wave function is given by ψ(x)=2αsin(3πx/a). Calculate the energy expectation value of this system. Note that α and a are two different constants.
Homework Equations
ψ(x)=2αsin(3πx/a)
E=K+V=K
K=p^2/2m
∫ψ*Pψdx=Expected momentum...
Hello Forum,
A sound wave intensity (pure frequency) is proportional to the square of the wave pressure amplitude, i.e. ##I \approx p_0^2##, where ##p_0## is the pressure wave amplitude: ##p_0 sin(\omega t \pm kx)##. This means that the (gauge) pressure value goes larger (positive) and lower...
...at the same speed in all directions?
Suppose we are an observer floating "stationary" above a body of water moving in a straight line .
We drop a weight vertically into the water and cause a wave to propagate out from the point where it meets the water.
If we have two additional...
Homework Statement
Derive the energy of the standing wave.
Homework Equations
Standing wave equation: $$y(x,t)=2Asin(kx)cos(ωt)$$
The Attempt at a Solution
I am trying to derive the energy of the standing wave. But I am kind of stuck at the approach.
Standing wave has no translational...
To start of, I'm new to physics Forums.
My thoughts this evening are directed to a physics question. "How to calculate a direction of a wave".
The things i believe i need is three sensors that indicates When the wave passes the equipment.
I will measure each specific time and compare them...
Homework Statement
Consider a particle which is confined in a one-dimensional box of size L, so that the position space wave function ψ(x) has to vanish at x = 0 and x = L. The energy operator is H = p2/2m + V (x), where the potential is V (x) = 0 for 0 < x < L, and V (x) = ∞ otherwise.
Find...
Homework Statement
A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.381m. The maximum transverse acceleration of a point at the middle of the segment is 8600 m/s and the max. transverse velocity is...
The question is;
In an experimental small universe, a photon is released from a source. It continues its path as a probabilistic wave function. if it interacted with mass, we could say the wave function collapsed and observe a particle photon hitting an object.
But what happens when the photon...
As I understand space time fabric is exclusively the Gravitational field according to Einstein.So every field wave or interaction is contained in the Gravitational Field.This fabric of spacetime(gravitational field) is having properties of inertia and elasticity that is why gravitational waves...
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.
Homework Statement
This is Rankine-Hugoniot conditions at a hydrodynamic shock front. Where P2=0 v2=0.
The problem is attached. I need to solve a system of equations. I thought it would be relatively straight forward solving for the three unknowns but I'm struggling. I know it's possible to...
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...
Homework Statement
In the attached file.
Homework Equations
No equations needed.
The Attempt at a Solution
I answered it B. Not sure,though. If it is a thick rope the frequency decreses; therefore, the speed decreases.
(1)What is the real cause of refraction?
Light wave cannot possible have a change of speed in going onto diffrent medium hence what is going on inside actually that we say its a change of speed.
(2) I am notable to comprehend how a change in wavelength not always means a change in frequency. If...
Homework Statement
What will be the wave velocity, if a string of 100 cm length is in a 10 kg-wt tension forms 9 nodes when vibrated and becomes symphonic to a 50 Hz tuning fork. Given, Cross sectional area of string, $$A=4.95 mm^2$$ & density, $$d = 0.25 g/cc$$?
Homework Equations
$$...
Homework Statement
the question asks at which point is the string moving upward at the instant shown?
Homework Equations
No equations needed
The Attempt at a Solution
I am not sure how I should approach this type of questions.
A) will move downward
B) downward then upward
C) upward then...
Homework Statement
A long, heavy rope hangs straight down from a high balcony on an apartment building. The lower end of the rope hangs about 1.0 m above the ground. If you grab onto the lower end and waggle it back and forth with constant frequency f, a wave travels up the rope. What would...
For the half harmonic oscillator the ground state wave function is of the form x*exp(-x^2/2)
But sir how to check it's parity and with respect to with point
As this function is valid for positive x only
Thank you
I am currently reading through 'Optics' by Eugene Hecht chp 2 page 20, he talks about the function of the wave and the direction of travel of the wave i.e ##\psi(x)=f(x-t)## and right at the bottom of the page he say this:
Equation (2.5) is often expressed equivalently as some function of ##t -...
There are some things that confuse me about electromagnetic waves, and I haven't found good answers anywhere.
Consider the following equation: E=E0 e i(wt-kx) (here E and E0 are vectors, I couldn't find the right symbols).
The things that confuse me are the following:
1° We say that the power...
I have seen few examples on Doppler effect and i am confused about one such.
We are standing on ground.
If the source of sound S moves and Object O is stationary. We would presume the frequency as well as wavelength of sound be changed to the obeject O.
But if O moves towards or away from S...
Homework Statement
$$\Psi = Ae^{\frac{i}{\hbar}(px-\frac{p^2}{2m}t)}$$
where ##p = \hbar k## and ##E = \hbar \omega = \frac{p^2}{2m}## for a nonrelativistic particle.
Find ##\Psi'(x',t')##, E' and p', under a galilean tranformation.
Homework Equations
$$\Psi'(x',t') = f(x,t)\Psi(x,t)$$
where...
Homework Statement
The wavefunction at t = 0 is given by
$$\Psi = N*e^{-\frac{r}{a_0}}$$
where ##r = |\mathbf{x}|##. ##a_0## is a constant with units of length. The electron is in 3 dimensions.
Find the approximate probability that the electron is found inside a tiny sphere centered at the...
Homework Statement
A beam of light of vacuum wavelength λ = 550nm passes from water (refractive index 1.33) into air (refractive index 1.00).
(a) What is the critical angle?
(b) Suppose the beam is totally internally reflected. At what angle of incidence would the decay length of the...
When a non-polarized electromagnetic wave cross a polarizer filter, its intensity drops to a half. Then this now polarized wave cross a polarizer such that it has 90 degree compared to the other. The wave is completely vanished. But if we put another polarizer with, let's say 45 degree in...
Homework Statement
Homework Equations
See above in the question
The Attempt at a Solution
I know that I need to be using a summing amp with the sinusoidal terms but I am struggling to calculate the input values that I need, also I think I need a capacitor in place of R6 but I'm not...
Hello! (Wave)
I want to show for the initial value problem of the wave equation
$$u_{tt}=u_{xx}+f(x,t), x \in \mathbb{R}, 0<t<\infty$$
that if the data (i.e. the initial data and the non-homogeneous term $f$) have compact support, then, at each time, the solution has also compact support.
I...
Homework Statement
The sound source of a ship’s sonar system operates at
a frequency of 18.0 kHz. The speed of sound in water (assumed
to be at a uniform 20°C) is 1482 m/s. What is the difference
in frequency between the directly radiated waves and the waves
reflected from a whale traveling...
How can we prove that ##k^\mu=(\frac{\omega}{c}, \vec{k})## is a four-vector?
One way is to consider the invariance of light velocity. If we postulate ##k^\mu## to be a four-vector then the scalar product of ##k^\mu\,x_\mu=\vec{k}\cdot\vec{r}-\frac{\omega}{c}\,t## is invariant, if it constant...
I don't really know where my brain is taking me on this one. I was wondering a couple things..
You set up everything for a Slit Experiment. You shoot an atom and observed it before the slit, then somehow collected the particle. It loops back and shoots it out again, this time with the particle...
Interference pattern made by light shows the wave nature of light and photoelectric effect shows
particle nature of light. So, what is light?
According to the photoelectric effect, light consists of photons with energy E and momentum ## \vec
p##.
According to the interference pattern, we...
Hi. I'm reading a paper "Transmission of light through a single rectangular hole in a real metal" and the author refers to the incident light shown below as "p-polarized" without further specification.
Note that ax > ay. Is there any convention in regarding a certain polarization as...
I'm trying to get a sense of the current state of knowledge regarding the relationship between gravity and quantum phenomena. For example, if you had a super-sensitive gravity detector, would that count as a "measurement" in the double-slit experiment in the same way that a particle detector...
I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet.
First I'm decomposing a Gaussian wave packet
$$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...
In this article, researchers have used electrons to image light as both particle and wave at the same time.
https://phys.org/news/2015-03-particle.html