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.
I'm trying to find the wavelength. However, I don't understand why the wavelength is different if the wave is moving in the +z direction.
I have
##\Psi(z=15cm,t) = \hat{x} 6 cos (\frac{\pi}{3}t)##
##\Psi(z=12cm,t + 2s) = \Psi(z=18cm,t)##
For a wave moving on the -z direction
I know that the...
The final wave function solutions for a particle trapped in an infinite square well is written as:
$$\Psi(x,t) = \Sigma_{n=1}^{\infty} C_n\sqrt{\frac{2}{L_x}}sin(\frac{n\pi}{L_x}x)e^{-\frac{in^2{\pi}^2\hbar t}{2m{L_x}^2}}$$
The square of the coefficient ##C_n## i.e. ##{|C_n|}^2## is...
https://www.nature.com/articles/s41561-021-00843-9
Popular science version:
https://scitechdaily.com/uncovering-the-surprising-secrets-behind-Earth's-first-major-mass-extinction/
Nature paper discusses causes of the second "wave" of mass extinction at the end of the Ordovician (~445mya)
Really...
##-w1## and ##-w2## are to shift the cosine graph to the right, and ##\frac{2pi}{\lambda}## is to stretch the graph. But I can't seem to draw an appropriate ##y1+y2## graph (quite irregular) and I struggle to find the resultant frequency and wavelength. Also, why is there angular frequency in a...
Summary:: We are currently studying basics of quantum mechanics. I'm getting the theory part but it's hard to visualise everything and understand. We are given this question to plot the function so if someone could help me in this.
Plot the following function and the corresponding g²(x)
g(x)...
Hi,
First of all, I'm wondering if a beaded string is the right term?
I have to find the amplitude of the modes 2 and 3 for a string with 5 beads.
In my book I have $$A_n = sin(\kappa p)$$ or $$A_n = cos(\kappa p) $$ it depends if the string is fixed or not I guess. where $$\kappa = \frac{n\pi...
If ##\hat{T} = -\frac{\hbar}{2m}\frac{\mathrm{d^2} }{\mathrm{d} x^2}##, then the expectation value of the kinetic energy should be given as:
$$\begin{align*}
\left \langle T \right \rangle &= \int_{0}^{L} \sqrt{\frac{2}{L}} \sin{\left(\frac{\pi x}{L}\right)}...
I need an equation to graph a sine wave that act like a unit circle but only positive numbers.
so I need it to be 0 at 0, A at 90 , 0 at 180, A at 270, 0 at 360, and A at 450 and so on and so on...
Now I know sin(0) is 0 in degrees and sin(90) 1
and I know if you Square a number is...
I understand the part where there will be more nodes produced because number of wave produced will increase (let say from half wave to one wave). But I don't understand the part where the amplitude will be less. How can number of nodes (or frequency) affect the amplitude of standing wave...
Good day.
We know how simple objects, such as 1D wires behave when a simple harmonic wave travels along a wire, or two wires knotted togethe.We also know what happens if you excite a circular thin disc with a single frequency.
Are there some material I can read on, that considers the effect...
Consider the situation where an observer at rest on the ground measures the frequency of a siren which is moving away from the observer at speed ##v_{Ex}##. Let ##v_w## be the speed of the sound wave. Let ##\lambda_0##, ##f_0##, ##\lambda_D##, and ##f_D## be the wavelengths and frequencies...
But in the notes from teacher, the equation is ##y=A \sin (kx - \omega t)## for wave traveling to the right and ##y=A \sin (-kx - \omega t)## for wave traveling to the left
When I transform the equation of the wave traveling to the left using trigonometry:
$$y=A \sin (-kx - \omega t)$$
$$y=-A...
How does the photoelectric effect prove the wave-particle wrong? Higher intensity does not mean higher energy. If we were to assume the wave-particle model, an increase in intensity means an increase in the amplitude of the wave right? The energy of light is never dependent on amplitude, it is...
I am trying to create a two phase type setup where I have a square wave in the multi-gigahertz frequency. However, I want the second wave to start once the first one reaches 90 degrees. How can the circuit be configured to do this? Will a phase shifter do or can a square wave be phase shifted at...
I imagine a particle traveling across 1 wave cycle. The total vertical distance traveled across the wave cycle is 4 x the amplitude of the wave. The total vertical distance traveled in 1 minute:
5 cycles in 1 second, thus 5x60 cycles in a minute
then 4 x amplitudes effectively traveled per...
Hello everyone, I would really appreciate some help on the following problem on plane waves and propagation. Not too sure if my attempt at writing the propagation wave expressions are correct, and how to handle the arbitrary function f(u). For the velocity, the wavelength is not specified, so is...
The full title of the publication is:
Rare Events Detected with a Bulk Acoustic Wave High Frequency Gravitational Wave Antenna
It is published in Physics Review Letters and reported in Phys Org.
They have created a small piezo-electric device (< 2cm, though it gets bigger once you create an...
Hi, I am 16 year old and I am very interested in Physics.
This summer I solved Schrödinger equation using griffiths' introduction to quantum physics and other sources. I achieved to get an exact solution of the wave function but I would like to plot it in a programm in order to get the 3d...
What is the difference between an absolutely continuously differentiable function and a wave? Are all absolutely continuously differentiable equations waves?
From hyperphysics, "The unique point in the case of the traveling wave in the string is the element of the string that is at the maximum displacement as the wave passes. That element has a zero instantaneous velocity perpendicular to the straight string configuration, and as the wave goes "over...
Hello!
Let's say we have a wave function. Maybe it's in a potential well, maybe not, I think it's arbitrary here. This wave function is one-dimensional for now to keep things simple. Then, we use a device, maybe a photon emitter and detector system where the photon crosses paths with the wave...
I would like to know if any of you think there's any sort of connection, analogy, or common features between, sets in set theory and wave functions in QT?
Wave functions lack trajectories, so do sets. Wave functions also distribute over areas, as sets can do. To my understanding, wave...
Hello,
Regarding the wave oblique angle propagation and based on Balanis "Advanced engineering Electromagnetic" book on page 136 ( it has been attached) I need to know why the phase velocity in x direction is not important to keep in step with a constant phase plane( Just equation 4-23).
I...
Hi,
I have created a sine wave with the following options:
1.) - changing the period/length in days of the sine wave (Cycle Length in Days)
2.) - calculating the start value of the "dummy" so that the sine wave always starts with -1 (Dummy Start at Cycle Trough) when the phase shift is set...
Regarding wave equation we are faced with this form
$$\nabla^2 \vec{E}=j\omega \mu \sigma \vec{E}-j\omega \mu\varepsilon \vec{E}=\gamma ^2\vec{E}$$
where
$$\gamma ^2=j\omega \mu \sigma -j\omega \mu\varepsilon $$
$$\gamma =\alpha +j\beta $$
where alpha and beta are attenuation and phase...
This is a fluid dynamic simulation.
The top area has 100 degrees Celsius.
The bottom area has 0 degrees Celsius.
And both are filled with an ideal gas which is 1-atmosphere pressure.
Two areas are connected through the left small line. Another part is blocked.
So heat transfer can only happen...
A wavefront is defined as a surface in space where the argument of the cosine has a constant value. So I set the argument of the cosine to an arbitrary constant s.
## k(\hat{u} \cdot r - c t) + \phi = s ##
The positional information is is in r, so I rearrange the equation to be
## \hat{u}...
I recall some time ago seeing a GR equation describing the rate of orbital energy loss from the moving objects in orbit generating gravitational waves. I can no longer find this equation again. I am hoping someone can help me.
I have a question, say a wave of light is emitted, and it passes through water, changing it's wave length to 380nm inside the water, once it comes out of the water, to vacuum will the wavelength remain at 380nm or will it change?
Hey Everyone,
I am trying to gain a level of fundamental understanding of an RC circuit sine wave response through the mathematics and was wondering if someone could help me work it out.
Fundamentally a sine wave is represented by the equation y=-ky'' . When a sine wave is used as the input...
It can be shown mathematically that the scalar massless wave equation is conformally invariant. However, doing so is rather tedious and muted in terms of physical understanding. As such, is there a physically intuitive explanation as to why the scalar massless wave equation is conformally invariant?
I have calculated the wave length of a 36 kHz acoustic wave in 20 °C water to be around 41.16mm.
Suppose I have a transducer that produces a 36 kHz acoustic wave and a small water container with a length of 41.6 mm. How will the standing acoustic wave look like, which is produced by the...
I need help with part (a)... I know that the root-mean-square voltage is the dc-equivalent voltage for an AC waveform and what my book labels "##V_{dc}## is actually the average voltage. Hence I am assuming the question is asking me to find ##V_{rms}## ...
Is my assumption that the...
Hi,
If I build a machine that its sole purpose is to radiate xx Hz of electromagnetic wave, how do I calculate the intensity of the waves? Let's say I put it in the room of 30 sq meters.
Thank you.
That is part of the article. I want to ask about step 4. I know the basic theory of how stationary wave is formed (superposition of incoming and reflected wave) and also basic concept about stationary wave in open and closed tube, something like this:
But I don't know the reason why in step 4...
Can a continuous wave laser weapon be converted to a Ultrashort Pulsed Laser like the one mentioned in this article?:
https://www.forbes.com/sites/davidhambling/2021/03/11/us-army-develops-laser-machinegun-firing-light-bullets/?sh=6555843768a3
Israel is also developing laser weapon for...
I am trying to find the $$\nabla_{\mu}\nabla^{\mu} \Phi$$ for $$ds^2 = (1 - \frac{2M}{r})dt^2 + (1 - \frac{2M}{r})^{-1}dr^2 + r^2d\Omega^2$$
I have did some calculations by using
$$\nabla_{\mu}\nabla^{\mu}\Phi = \frac{1}{\sqrt{-g}}\partial_{\mu}(\sqrt{-g}g^{\mu \nu}\partial_{\nu}\Phi)$$...
I understand how waves undergo superposition. However, for a standing wave, the reflected wave is a mirror opposite of the incoming wave. By the superposition principle, won’t the 2 waves add up to 0, at all points?
qn iv.
I understand that when 1.5 periods pass, every compression will become rarefaction, and every rarefaction will become compression(someone please correct if wrong) but the answer key shows something else.
I'm interpreting the answer key drawing to be 1 compression and 4 rarefactions...
A massless scalar field in a curved spacetime propagates as $$(-g)^{-1/2}\partial_\mu(-g)^{1/2}g^{\mu\nu}\partial_\nu \psi=0 .$$
Suppose the gravitational field is weak, and ##g_{\mu\nu}=\eta_{\mu\nu}+\epsilon \gamma_{\mu\nu}## where ##\epsilon## is the perturbation parameter. And let the field...