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.
Hi,
i am looking for a general form of a wave equation in a medium. i am not looking for a concrete physical equation but rather a generalized form (preferably in n dimension) of such under the simplest assumptions (it's of course a little equivocal what 'simplest' means but, well).
so for a...
Homework Statement
y1(x,t) = 5.00sin(2.00x - 10.0t)
y2(x,t) = 10.0cos(2.00x - 10.0t)
a) Prove that the wave that is the result of the superposition is a function of sin.
b) What's the phase angle and amplitude of said wave?
Homework Equations
y = y1 + y2
The Attempt at a Solution...
Note: added to the title should be "and a particle description". ## \\ ## The intensity (energy density) of an electromagnetic wave is proportional to the second power of the electric field amplitude, i.e. intensity ## I=n \, E^2 ##, apart from proportionality constants. Meanwhile the energy...
A body is reentering the Earth's atmosphere at a Mach number of 20. In front of the body is a shock
wave. Opposite the nose of the body, the shock can be seen to be normal to the flow direction. Determine the stagnation pressure and temperature to which the nose is subjected. Assume that the air...
Homework Statement
There's a string with tension T & mass density μ that has a transverse wave with ψ(x,t) = f(x±vt). f(x) is an even function & goes to zero as x→±∞
Show that the total energy in the string is given by ∫dw*T*((f'(w))2; limits of integration are ±∞
Homework Equations
The...
So I am just working with a synth and I am having it create a single sine wave. I am then looking at the output on a db vs frequency graph and I would expect the db to only be reading at the frequency of that sine wave, but there are readings from 20 Hz all the way to 2k Hz sometimes(althought...
Homework Statement
A ship floats across the coat, at a distance d = 600 m from it. The radio of the ship receives simultaneously signals of the same frequency from RadioTowers A & B, which are L = 800 m apart. At Point G (Γ), the two waves confluent in a strengthening way, where G's (Γ)...
Homework Statement
Two identical speakers, 10.0 m apart from each other, are stimulated by the same oscillator, with a frequency f, of 21.5 Hz, at a place where the speed of sound is 344 m/s.
a) Show that a receiver at A will receive the minimum intensity of sound (Amin) due to the...
Hi,
I'm recently reading something which briefly introduces C symmetry. So the thing that confuses me is that how does the spatial wave function contribute the (-1)^L factor?
Thanks!
Homework Statement
A transverse wave that is propagated through a wire, is described through this function: y(x,t) = 0.350sin(1.25x + 99.6t) SI
Consider the point of the wire that is found at x= 0:
a) What's the time difference between the two first arrivals of x = 0 at the height y =...
We know that a wave is represented by f(x - vt) and it follows the differential wave equation. e^(x - vt) satisfies both the condition. But is it really a wave? Because to sustain the wave we need infinite energy which is not possible. So what's happening here?
Homework Statement
A mass of 120 g rolls down a frictionless hill, reaching a speed of 4.2 m/s. This mass collides with another mass of 300 g that is at rest and attached to a spring with constant 30 N/m. The two masses stick together and enter into periodic motion. What is the equation for the...
Homework Statement
given: A wire loop with a circumference of L has a bead that moves freely around it. The momentum state function for the bead is ## \psi(x) = \sqrt{\frac{2}{L}} \sin \left (\frac{4\pi}{L}x \right ) ##
find: The probability of finding the bead between ## \textstyle...
I am a beginner in quantum mechanics. I started out with D. J. Griffiths' book in quantum mechanics.
I'm having a problem in understanding the wave function. What is the physical meaning of the wave function? I searched on the net but didn't get any good explanation. I understand that the...
Homework Statement
A guitar string with 0.60 m and 0.012 of mass vibrates with frequencies that are multiples of 109 Hz. Approaching to the string a tuning fork of 440 Hz we verify beats between the sound signals of the string and the tuning fork. Calculate the time interval between consecutive...
If you know where to look for an electron (e.g. in an atom or an experimental setup) it is quite understandable that, until you know exactly where it is, there is a calculable probability of where it might be. However, if we take the case of an un-associated electron in space, it would seem that...
Homework Statement
Suppose a tube is filled with helium gas at a pressure of 0.11MPa and a temperature of 297K. If a piston of area of 400mm2 at one end of the tube creates sound by moving sinusoidally with a frequency of 60Hz, creating a wave with amplitude of 3.8mm,
what power goes into (I'm...
Hello! I am reading some introductory stuff on Klein-Gordon equation and I see that the author mentions sometimes that in a certain context the K-G equation "is a classical field equation, not a quantum mechanical field equation". I am not sure I understand. What is the difference between the...
Hi!
1. Homework Statement
From the website http://www1.uprh.edu/rbaretti/MomentumspaceIntegration8feb2010.htm
we can see the Fourier transform of the ground state hydrogenic wave function :
Φ(p) = ∫ ∫ ∫ exp(-i p r) (Z3/π )1/2 exp(-Zr) sin(θ) dθ dφ r² dr (1.1)
After intregation...
Homework Statement
In Griffiths' book "Introduction to Quantum Mechanics", Section 2.3, Chapter 2, the Fig. 2.7 gives the plots of the wave function (##\psi_{n}##) and its modulus of the harmonics oscillator, see the Appendix. With the order (##n##) increasing, they become both higher. However...
This animation demonstrates a longitudinal wave by means of moving bars.
I realized that if we increase the amplitude of the wave, the bars will eventually start passing through each other, which sounds (no pun intended) like an unphysical scenario.
Does this mean that there is a cap, a...
In the 1930s, John von Neumann consolidated ideas from Bohr, Heisenberg and Schrodinger and placed the new quantum theory in Hilbert space.
In Hilbert space, a vector represents the Schrodinger wave function.
I know they are equivalent..
But can we say it is more natural and intuitive to say...
Homework Statement
A wave is shown below. The dots represent the particles of the wave at a time t = 0 s, and the vertical lines represent the positions of the particles before the wave arrives. Find the amplitude and wavelength of the wave
Homework Equations
Not sure
The Attempt at a...
In the Great Courses lecture series "Oceanography", Prof. Tobin says that the general direction of beach sand movement ("sediment transport") along both the east and west coasts of the USA is from north to south. On the east coast, this is because the prevailing direction of waves is from the...
https://www.nature.com/search?journal=nphys&q=wave%20particle%20duality&page=1
When people come to this forum enquiring about the concept of wave particle duality the usual advice seems to be based on the idea that the concept is outdated and has historical interest only.
The problem is that...
For using Galilean transformation, I have to assume that speed of light w.r.t. ether frame is c.
W.r.t. ether frame,
E = E0 eik(x-ct)
W.r.t. S' frame which is moving with speed v along the direction of propagation of light,
E' = E0 eik(x'-c't')
Under Galilean transformation,
x' = x-vt,
t' = t...
Hi PF! Suppose we have a water wave with mean depth ##H## with disturbance ##\zeta## above/below ##H## propagating through a channel of thickness ##b##. The book parenthetically remarks that the continuity equation becomes $$\partial_t(b(H+\zeta))+\partial_x(bHu)=0.$$ However, when I try...
A system of |1> and |2>, in the beggining has a function |Ψ(0)>= cosa|1> + sina|2>.
The energy of the system is;
https://i.imgur.com/I0C7BFg.png
a, ε,n are known. Find the |Ψ(t)>
The solution is;
https://i.imgur.com/urWs6XW.png
It is known that; |Ψ(t)>= e^(-iHt/ħ) * |Ψ(0)>
but I don't...
The speed of light (in the vacuum) is a function of the permeability and permittivity of the vacuum. In other mediums the phase velocity will be different. It is assumed (by me) that the speed of a gravitational wave does not change depending on the medium i.e. a gravitational wave would not...
This latest observation of gravity waves has brought up a question with me..
Since gravity is a mass-caused distortion in space-time aren't these waves wave distortions of the space-time?
I know there is no such thing as ether but for this analogy and my simple mind I'll use it to illustrate...
It is required to be continuous in the following text:
The book's reason why wave functions are continuous (for finite V) is as follows. But for infinite V, ##\frac{\partial P}{\partial t}=\infty-\infty=## undefined, and so the reason that wave functions must be continuous is invalid...
Numerically, speed of wave propagation(defined as wave velocity) = ω/k = phase velocity
But, conceptually is there any difference between phase velocity and wave velocity?
Speed of a wave in a string is given by √(τ/μ) .
But this speed is with respect to which reference frame?
Since, the speed depends on τ and μ( which are independent of reference frame ), I can consider speed of wave independent of reference frame.
But this is not so. From experiment, we know...
Sinusoidal wave form ?
I am asking:
We know that if a coil rotates in a transverse magnetic field a sinusoidal voltage is induced between its terminals.
.
My question now is:
Why it is exactly sinusoidal in the shape and not any other wave shape??
.
The equation below (2.9) is also a linear differential equation.
This equation also describes the wave phenomena.
So, why is this equation not considered as wave equation?
I have taken it from the optics book by Chapter two Eugene Hecht,5th edition ,Pearson.
Hello! (Wave)
Let $$u_{tt}-c^2 u_{xx}=0, x \in \mathbb{R}, t>0 \\ u(x,0)=0, u_t(x,0)=g(x)$$
where $g \in C^1(\mathbb{R})$ with $g(x)>0$ for $x \in (0,1)$, $g(x)=0$ for $x \geq 1$ and $g(x)=-g(-x)$ for $x \leq 0$. I want to find the sets of $\{ (x,t): x \in \mathbb{R}, t \geq 0 \}$ where $u=0...
How can I calculate the capacitor needed for my wave energy collector?
I have have build a wave energy collector. It consists of multiple coils in series with magnets moving up and down, following the waves underneath the unit.
My multi-meter measures anywhere between 60 and 250 milli volts...
Hi,
My teacher tasked me with a complex waveform question, i have looked for some time to find out how to tackle these, but i still do not know where to begin.
Any help would be greatly appreciated, not look for an answer just a method.
i=12sin(40*\pi t) + 4sin(120* \pi t - /3\pi) + 2sin(200...
In the wave equation## \frac {\partial^2 \psi} {\partial x^2}=\frac{1}{v^2}\frac{\partial^2 \psi}{\partial t^2}\tag{1}##, v is the speed of the wave propagation.
With respect to which reference frame is this speed measured( in general)?
A clever new paper explores the notion that the reduced Planck's constant in the quantum analogy to Newton's constant for macroscopic quantities though a hybrid quantity that generalized the Compton wavelength and the Schwarzschild radius. This allows for a linkage between the Einstein equations...
How come a+a- ψn = nψn ? This is eq. 2.65 of Griffith, Introduction to Quantum Mechanics, 2e. I followed the previous operation from the following analysis but I cannot get anywhere with this statement. Kindly help me with it. Thank you for your time.
In a recent article by BBM in Physical Review Letters highlights another approach to link QM to Zeta to Prove R.H. There approach proved unsuccessful. I want to ask professional Physicists if the following new approach have merit in connecting the Zeta function to QM? This new line of attack...
Homework Statement
A flute player hears four beats per second when she compares her note to a 587 Hz tuning fork (the note D). She can match the frequency of the tuning fork by pulling out the "tuning joint" to lengthen her flute slightly. What was her initial frequency?
Homework Equations
Not...
I have the following program that moves a wave on a string with fixed ends. The program solves the wave equation given a initial condition wave. The initial condition is a triangle wave splitting into two pulses.
Here is the code written in Python:
from numpy import *
from matplotlib.pyplot...
Homework Statement
The wave function of a particle is known to have the form $$u(r,\theta,\phi)=AR(r)f(\theta)\cos(2\phi)$$ where ##f## is an unknown function of ##\theta##. What can be predicted about the results of measuring
(a) the z-component of angular momentum;
(b) the square of the...