Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Can $A \sin (kx - \omega t)$ be used for longitudinal wave?
Question: One particle in the medium has its equilibrium position at $x = 1.00 \ m $. Show that the speed of this particle at $t=0.882 \ s$ is $4.9 \ m/s$.
I attempted at using the formula
$$y=A \sin(kx- \omega t)$$
and then I tried to use
$$\frac{dy}{dt}=\... | You can use $y(x,t)=A\sin(kx-\omega t+\phi)$ for longitudinal waves. But understand its meaning: $y$ denotes the longitudinal displacement of the particle whose equilibrium position is $x$, at time $t$.
The problem wants you to evaluate the speed of the particle whose equilibrium position is $x=1$ (let's label the part... | {
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Could speed of light be variable and time be absolute? I get my "demonstration" of time dilation from the textbook thought experiment.
A laser is mounted on a cart with a reflective ceiling. At $t=0$ the cart starts moving and the laser is fired. When the laser is reflected back at the starting point the (thought) expe... | There is a physics where time is constant and the speed of light is not: Newtonian with an ether.
Galilean transformations in Newtonian physics have time as a fixed parameter that ticks away uniformly for all points and states of motion.
For the speed of light to be frame dependent, one needs the ether in which it prop... | {
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Is Griffiths simply wrong here? (Electrostatic Boundary Conditions)
In the above illustration, shouldn't $E_{above}$ and $E_{below}$ be in opposite directions? If not, how did Griffiths end up the following equation? From the above directions, shouldn't the flux add up?
| Griffiths in correct. The flux through the top portion of the box is not just $E_{\small{top}}^\top$ but actually $\vec E\cdot (A\vec n) $ where $\hat n$ is perpendicular to the surface and points out: in your diagram, $\hat n$ would be along $+{\hat z}$ for the top portion of the flux calculation.
For the bottom of t... | {
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What causes a black hole ringdown and why can it prove the no-hair theorem? When two black holes merge, they will produce the so-called ringdown before forming a new black hole, even the newly created black hole produces some sort of tones due to the force of the impact, but it is barely audible for LIGO and other inst... | The ringdown is simply the black hole formed in the merger settling down to a final stationary form. According to the no-hair theorem, this stationary form has to be described by the Kerr family of metrics described by the mass and angular momentum of the final black hole (since the intitial system is assumed to be ele... | {
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Conservation of Angular Momentum for Rigid Bodies I have question about Conservation of Angular Momentum of Rigid Bodies. I've been doing some examples from Hibbeler's book, and noticed that in this chapter about Conservation of Angular Momentum of Rigid Bodies, there are some examples where we sum all the angular mome... | As long as point A isn't moving, you can do it either way. In vector form, angular momentum about A is
$$ \boldsymbol{H}_A = \mathbf{I}_G \boldsymbol{\omega} + \boldsymbol{c} \times \boldsymbol{p} = \mathbf{I}_G \boldsymbol{\omega} + \boldsymbol{c} \times ( m \,\boldsymbol{v}_G ) = \mathbf{I}_G \boldsymbol{\omega} - m... | {
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String Landscape, De Sitter vacua and Broken Supersymmetry If we assume that the swampland conjectures, etc. regarding de sitter vacuas existence in the string / F-theory landscape turn out to be incorrect (and therefore we can assume the problem is well-posed), would all such solutions have broken supersymmetry?
Ther... | You're right. Realistic string compactifications require four macroscopic dimensions. For supersymmetry to exist in a given background a non zero globally defined Killing spinor is required. In the d=4 case such a spinor should be (locally) the generator of the $Spin(4,1)$ group, the problem is that $Spin(4,1)$ has no ... | {
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Postulate of constancy of speed of light in vacuum I'm not of course questioning the constancy of the speed of light, just the way the postulate about it is worded. It is often stated that the speed of light is independent of the motion of the source. Einstein himself said "and also introduce another postulate, which i... | There is no medium. The equations stand alone. The possibility that empty space may itself be a stationary medium for somebody has been disproved by experiment.
Hence, any electromagnetic propagation in empty space always seems to any inertial observer to proceed at the universal constant speed irrespective of where ... | {
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Do colliding black holes violate time reversal symmetry? Two black holes can collide and merge into one bigger black hole, but not split into two. Does this mean colliding black holes violate time reversal symmetry?
Related: Do black holes violate T-symmetry? Based on the answer to that question, time-reversing a black... | Yes, to the same extent as falling egg violates time reversal symmetry (have you seen a broken egg spontaneously jump from the floor to your cup?).
This is called "second law of thermodynamics" and it is not time-symmetric.
| {
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Connection between Poisson bracket and Anti-commutator? Canonical quantization promotes Poisson brackets in classical mechanics to commutators in quantum mechanics. Is there any classical counterpart similar to the Poisson bracket for the anticommutator?
| FWIW, in classical Hamiltonian formalism, the phase space is a supermanifold with a super-Poisson bracket $\{\cdot,\cdot\}_{SPB}$. The super-Poisson bracket corresponds to a super-commutator $\frac{1}{i\hbar}[\cdot,\cdot]_{SC}$ upon quantization. The super-commutator is a commutator (an anticommutator) in the Grassmann... | {
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How gravity time dilation affect radio wave communication? I'm not in any way an expert so sorry if my question is silly.
So i was wondering about a hypothetical situation. I'm orbiting a black hole and I'm trying to contact via radio with someone outside the gravitational effect of that black hole. As far I understand... | First of all let's make the situation more concrete. The effect of gravity extends to infinity, although it drops off as a factor of $(\sim \frac{1}{r^2})$ according to Newtonian mechanics(which suffices in terms of building our intuition here). When you are just outside the event horizon of the black hole, all the sig... | {
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Are the muon/tau neutrinos produced in the Sun? If not, then where? I was reading about Solar Neutrinos, and apparently they are all Electron Neutrinos.
However, there are two other types of neutrinos, the Muon and Tau Neutrinos. Does the Sun produce them? If not, are they produced naturally anywhere in the universe?
| There can also be blackbody (thermal) antineutrino and neutrinos of all flavors, which are emitted during type-II supernovae core collapse.
Here is a figure from H.-Thomas Janka, Neutrinos from type-II supernovae and the neutrino-driven supernova mechanism (reprint from: Conference Proceedings Vol. 40: "Frontier Object... | {
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What happens to matter when it is converted into energy? According to Einstein’s equation
$$E=mc^2$$
Matter can be converted into Energy. An example of this is a nuclear reaction. What happens to the matter in the process? Do the atoms/subatomic particles just vanish? Any insights into this process are appreciated.
| To start with the $m$ in $E=mc^2$ is the relativistic mass, and in particle physics this is out of use it causes confusion. One uses four vectors , where the "length" of the four vector is the invariant mass, uniquely identified with elementary particles, and with systems of elementary particles.
Four vectors are good... | {
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Maximum speed in a spring-mass system I am studying energy right now and I can use only gravitational potential energy, elastic energy and kinetic energy to solve some problems. My doubt is how can I prove that the maximum speed in a mass hanging on a spring is reached at the middle of the elongation of the spring.
The... | Maximum speed occurs at the mean position of spring mass system as Diffrentiation of velocity, acceleration is 0 there.
| {
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Time in Lorentz transformation While doing Lorentz transformation for position
$$x'=\gamma(x-ut)$$
Here I understand that instead of just length contraction we also use the term
$$ut$$
To include the distances between the frames of reference.
But while doing Lorentz transformation for time that is
$$t'=\... | To show how the term in question accounts for synchronization, consider Einstein's famous train thought experiment. The station observer sees the light that strikes the front of the frame moving toward the observer in the middle of the train car with relative speed (c+u) and for the light from the back of the train it'... | {
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Eigenvalue corresponding to the stationary state If $M$ denotes the transition matrix of a Markov chain, then the vector $x$ that satisfies $Mx=x$ is the stationary distribution or stationary state. However, this paper seems to use the term stationary state in a different sense, wherein the stationary state satisfies $... | I am going to answer my own question since I was able to find the answer very shortly, after bit of searching on Google.
If $x$ is the stationary state, then the usual Markov matrix or transition matrix satisfies $Mx=x$. In other words, $M_{ij}$ is just the transition probability from state $i$ to $j$.
There is another... | {
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Does work expend a permanent magnet? My understanding of a permanent magnet is that it has the potential to do work. This would seem to me to imply it has a kind of magnetic charge similar to how a battery is charged with energy. Does this imply that that using the magnet to do work will expend this charge causing th... | The magnet may perform work while attracting another magnet or a piece of iron, but all that work is reversed when you take the two magnets and pry them loose from one another and separate them again. Energy is conserved in this process.
To make a chunk of iron into a permanent magnet requires you to perform work upon ... | {
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What is the Eigenvalue of $T^2$ ($SU(3)$ Casimir)? For example, in $SU(2)$, $\hat{S}^2|s,m_s>=\bar{h}^2 s(s+1)|s,m_s>$.
What about in $SU(3)$, $\hat{T}^2|T,m_3,m_8>=?|T,m_3,m_8>$ where $\hat{T}^2=\sum_i^8 T_iT_i $, $T_i = \frac{\lambda_i}{2} $, $\lambda_i$ is $SU(3)$ generator.
| Like for $SU(2)$ the Casimirs of $SU(3)$ provide extra labels to the irreducible representations that can be useful in distinguishing irreps. that have the same dimension. Note I talk in the plural because for $SU(3)$ one can construct two Casimirs:
$$\hat{C}_{1} = \sum_{k= 1}^{8}T^{k}T^{k} \qquad \textrm{ and } \qquad... | {
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Origin of terms in the Nernst-Planck equation We know the Nernst Planck equation is
$$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \mathbf A}{\partial t}\right) \right] $$ $$\iff\frac{\partial c}{\partial t} = ... | I see now that for Chemical Systems of non-ideal solutions/mixtures Ficks First Law is:
$$ J_i = - \frac{D c_i}{RT} \frac{\partial \mu_i}{\partial x}$$
This is a restatement of the First Law as $$ J_i = - \frac{D c_i}{RT} \frac{\partial \mu_i}{\partial x}= - \frac{D c_i}{RT} \frac{RT\partial \ln C}{\partial x} \implies... | {
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Confused about what a wave is When a wave of something, let's say light or some electromagnetic wave is given, I am confused because I do not understand if shape of a wave represents projectile of it or some value that possess at certain positions. I researched a lot but I have no idea what a wave really is.
My questi... | You are asking whether the shape of the EM wave represents a projectile (projection) of it, or some value that the EM wave posesses at certain points.
You are confused because you see these images of EM waves.
In reality, it is the value of the EM field at any given point in space that these diagrams represent for th... | {
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Does $Δs^2 = - Δ\tau^2$ imply two distinct metrics for spacelike and timelike displacements? Reading Misner-Thorne-Wheeler concerning the metric for spacelike and timelike displacements it seems to me that two different metrics must be distinguished, one metric for spacelike and one for timelike displacements - is this... | Yes, you can talk about there being two metrics, which are coincident for a proper relativistic spacetime - but whose distinction becomes important when considering the classical limit. This is similar to the case for quantum mechanics, where the classical limit requires us to bifurcate the wave function to separate po... | {
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Help Understanding this Free Body Diagram (Eotvos Experiment) I am reading through Hartle's "Introduction to Einstein's General Relativity" and it discusses the Eotvos Experiment in Chapter 6. The free-body diagram (shown below) has me a little puzzled.
This experiment was designed to see if there's any difference in i... | This isn’t a proper free body diagram, because the $ma$ line doesn’t represent a force. Only $T$ and $mg$ are forces. Only forces should be in a free body diagram.
Their resulting net force has to equal that $ma$ line because the Earth is rotating.
Now that you see that, note that $T$, the hanging direction, isn’t al... | {
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Are matter particles really excitations of fields? So it is said that particles are excitations of fields. We are given examples like photons for electromagnetic field, gravitons for gravity, etc. We are also told that normal matter is an excitation. However the former are all virtual particles that can never be detect... | You are confused because of the difference between static EM fields and EM radiation.
An electromagnetic field (also EM field) is a classical (i.e. non-quantum) field produced by moving electric charges.[1] It is the field described by classical electrodynamics and is the classical counterpart to the quantized electro... | {
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Do silicon solar cells act like an LED when you flip the voltage, or are we just seeing black body radiation? In science communicator Steve Mould's Youtube video Why all solar panels are secretly LEDs, he supplies a voltage across a solar cell. Using an IR camera, we see IR emission coming from the solar cell, and he c... | Indeed, silicon does not act as an infrared LED. That is because the band gap is indirect, the maximum of the valence band and the minimum of the conduction band are not at the same point in $k$-space. Momentum must be conserved in recombination, and this is impossible because the infrared photon has negligible momentu... | {
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What makes a wheel spin? I don't fully grasp what makes a wheel much easier to move than to push a solid block.
The pressure at the point of contact between a wheel and the ground must be pretty enormous compared to the pressure created by a block of same material and mass as the wheel.
Friction is defined as the pro... | Let's see if we can answer your question by drawing a free body diagram for these two objects.
From the picture we can see, that in order for body to move, external force must be greater than friction force. If objects have the same mass and are in identical surroundings, they will be equally hard to move. (iff torque... | {
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If a ball is thrown to a person standing on a frictionless surface, is the impulse of the thrower equal to that of the catcher? If a person throws a ball, exerting a given impulse does the person that catches the ball receive the same impulse assuming that the catcher moves. Is the impulse that the catcher receives les... | Momentum is conserved in any inertial frame. You choose an inertial frame to write the equations for momentum conservation. In the catcher's frame obviously the ball's momentum is less than that in thrower's frame due to relatively slow motion.
| {
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Is the Four-gradient of a Scalar Field a Four-Vector? Consider a scalar field $\phi$ as a function of spacetime coordinates $x^\mu$. The four-gradient of $\phi$ is given by
\begin{equation}
\frac{\partial \phi}{\partial x^\mu} = \left( \frac{\partial \phi}{\partial t}, \frac{\partial \phi}{\partial x}, \frac{\partial \... | The four gradient is a four vector but it transforms covariantly, rather than contravariantly. This makes it a "covector".
It also has a contravariant form, obtained by multiplying it by the metric, which transforms like 4 four position or four momentum.
| {
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What does the arbitrary constant in cosine equation of displacement in S.H.M say? The phase and phase constant in a displacement time equation show from where the particle has started.
In my school textbook, first the displacement equation was given as :-
$$x= A\sin(\omega t+\phi)$$
where $\phi$ i... | It depends on the initial conditions. If its at maximum displacement at $t=0$ then the equation is $x=A\cos{\omega t}$. If it is at equilibrium position and maximum velocity at $t=0$ then $x=A\sin{\omega t}$. In general, the solution is $x=a\cos{\omega t} + b\sin{\omega t}$ which simplifies to either $A\cos{(\omega t +... | {
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On the "spectrum" of an operator in quantum mechanics Very simple question, I'm new to this. I'm reading Griffiths book on QM and have a question about the "spectrum" of an observable operator. Does the spectrum of an operator require specification of a particular system? Or is the spectrum of an operator just every po... | In general, the spectrum of an operator depends on the Hilbert space (= space of possible wavefunctions) on which it is defined. For example, the Hamiltonian for a free particle in one dimension $H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2}$ has eigenvalues that depend on the boundary conditions for the wave... | {
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Is the coefficient of drag the same on two similar objects? if I had two objects, scaled perfectly to each other so that one is $5$ times the size of another while keeping the shape the same, would their coefficients of drag, $C_d$, be the same in the formula $D = \frac12 \rho C_d S V^2$?
| Not necessarily.
If we take the fluid dynamical system under consideration to be only a function of fluid density $\rho$, some characteristic speed $V$, fluid viscosity $\mu$, and some characteristic length $R$, then it has to be the case from dimensional analysis that the drag coefficient is only a function of the Rey... | {
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$V$-$I$ characteristic of a solar cell please explain the VI characteristics of a solar cell. The characteristics is given in my book without any explanation. How can the Voltage decrease on increasing current shouldn't it be opposite.
Solar Cell I-V characteristics
(Image from Electrical 4 U - Characteristics of a S... | VI characteristic graph of diode with and without illumination (breakdown not shown):
When light falls on the depletion region of the diode, electron-hole pairs are generated that try to reach their parent nuclei. The electrons move towards the n-side and the holes to the p-side. This leads to a photovoltage that trie... | {
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How does the current remain the same in a circuit? I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.
Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the ... | The question
The charges obviously lose energy in the lamp and so become SLOWER, which should mean current decreases, right?
shows that you have a misconception about the motion of the conduction electrons.
If you were correct then to maintain the same current around a circuit by a miracle more conduction electr... | {
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2-D water jet on oblique plane We have a 2-D water jet on oblique plane. We are ignoring gravity and want to calculate the force on the plane. The explanation I have been given goes as follows. We assume inviscid flow. Image is attached.
Using Bernoulli's theorem on the free surface streamline:
$$\frac{1}{2}V^2+\frac... | The pressure doesn't figure in the parallel component because it is acting perpendicular to the wall (and, moreover, at the inlet and outlet, the pressure is atmospheric).
| {
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To what extent is standard quantum mechanics actually non-relativistic? I often hear that while QFT is a relativistic theory, standard quantum mechanics is not. But fields aren't inherently relativistic, you can easily construct non-relativistic QFTs, a relativistic QFT is one with a Lorentz invariant Lagrangian.
In t... |
the actual non-relativistic part is the Schrödinger equation
Indeed. Hence, people tried to come up with a Lorentz-invariant evolution equation for the wave function such as the Klein-Gordan and Dirac equations (as mentioned by anna v). However, interpretation of solutions of these equations as probability densities ... | {
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Normalization of the action in Special Relativity The action for a massive point particle in Special Relativity is given as
$$A =-mc^2\int d\tau,$$
Where $\tau$ represents the proper time, and $m$ represents the (rest) mass. From what I could understand, the Action must not change with respect to the reference frame, a... | I prefer to think like this. Inertial observer ($X$) is at rest in his/hers reference frame. The world-line of $X$ is the longest possible route between any two events. This follows since, in its frame, $X$ is moving fully along the temporal axis, therefore $ds=cd\tau$ (displacement in time; $c$ is the speed of light),... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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If magnetic field lines don't exist, what are these iron filings doing around a magnet? Obviously the iron filings can be seen aligning themselves along the virtual magnetic field lines produced by the permanent magnet, the virtual magnetic field line is made of electromagnetic field due to the alignment of electrons i... | The iron filings themselves repel each other and create a pattern that can be observed visually as lines.
Liquid metals create mountains that end with peaks as the active forces dissipate, so you can see the concentration is highest nearest the origin.
| {
"language": "en",
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"source": "stackexchange",
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Heisenberg's principle in classical world I have a ball with me and I have been observing it's position which remains constant at a place only, hence it must be largely localised, further as it remains on the same place from so long, it's velocity must be largely localised to 0 only.
Now with both momentum and position... | First, while the amount of uncertainty required by the Principle is significant at quantum mechanical scales, it's tiny on macroscopic scales. Are you certain where the ball is, down to an atom's radius?
Second, the uncertainty is regarding the object's momentum, not its velocity. If you have an object that's 10,000 ti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530120",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Explicit calculation of spin connection through Cartan's first structure equation Given the metric
$$
ds^2 = F(r)^2dr^2 + r^2d\theta^2 + r^2 \sin^2(\theta)\, d\phi^2,
$$
I'm trying to find the corresponding spin connections $\omega^a_{\ b}$ using the first structure equation:
$$
de + \omega e = 0.
$$
I found the vi... | As you have, the first step is to identify $e^r = F(r)\mathrm{d}r, e^\theta = r\mathrm{d}\theta$ and $e^\phi = r\sin \theta \mathrm{d}\phi$. The trick is to then take the derivatives but re-express them in terms of $e$ again. Thus,
$$\mathrm{d}e^r = 0, \quad \mathrm{d}e^\theta = -\mathrm{d\theta} \wedge \mathrm{d}r = -... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530257",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Gravitational Wave - What is waving? Two kinds of wave transmission are:
*
*Light waves, where a substance (photon) travels as a wave.
*An attached rope, like at the gym, that is "waved" up and down. Here, no substance travels to a new spot, but adjacent parts transmit the energy to others.
QUESTION: Which method d... | A gravitational wave is a wave in a tensor field called the “metric of spacetime”. This metric determines the geometry of spacetime by specifying how far apart spacetime events are. The wave just consists of changes at each point in the values of the components of this field.
It is very similar to a classical electrom... | {
"language": "en",
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"source": "stackexchange",
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How to find expectation value from probability density? How to find expectation value from a given probability density?
E.g. given to find expectation value of $x^2$ from probability density $\rho(x)= 1/(2(hx)^{1/2}) $.
This is not a homework question, I just want to understand how to solve questions like this, you may... | According to expected value basic properties:
$$ {\displaystyle \operatorname {E} [g(X)]=\int _{\mathbb {R} }g(x)f(x)\,dx.} $$
it should be :
$$
E[x^2] = \int x^2\,\frac{1}{{{2}{\sqrt{{h}{x}}}}}\,dx
$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530493",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Wave function of $s$-band with odd parity How does a wave function of a $s$-band state with odd parity looks like (in real space)? To keep it simple, the restriction to a linear chain and a state at the $\vec{k}=0$-point might be useful.
My understanding is somehow like described in https://www.ensc-rennes.fr/wp-conten... | While my picture of band creation and the spatial extend of the corresponding wave functions was right, the assumption that the origin/center for inversion symmetry is always on an atom CAN be wrong. While considering a linear chain, the choice of the inversion center can be on an atom or halfway between two atoms. For... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530707",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If sound passes through material, vibration is produced. So are electromagnetic waves produced too? Sound means vibration of molecules and vibration produces electromagnetic waves. So, this means that sound produces electromagnetic waves directly.
Is this possible?
| A sound wave passing through a medium (e.g. air) indeed displaces molecules by a distance of a few nanometers. It seems reasonable that it should also displace the atoms, and thus electrons and protons in the process, which are charged particles and should radiate by Larmor's equation when undergoing acceleration.
Let ... | {
"language": "en",
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"source": "stackexchange",
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Observing from a true stationary point in space is there a "True time" we can observe? Aren't all points on planets, in solar systems, in galaxies moving through space subject to different amounts of time dilation due to gravity and velocity when observed from a stationary point in space? Do we generally have a mathema... | As trula's answer reveals there is no place in the universe and never has been that allows a static observer. Think of it like we're all under water floating around and nobody is excluded.
We can't have an objective "point" from which to measure all others. All measurements are relative.
20 meters floating in strong ... | {
"language": "en",
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Why is it that lampblack repels water but graphite doesn't? I have been playing around with lampblack recently, and one property that I particularly like in them is their Hydrophobicity. It's interesting to watch water drops just bouncing off the surface.
I reasoned that this was because lampblack was carbon, which ... | the lampblack contains partially-burned hydrocarbons which are strongly hydrophobic.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531117",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Torque and force Does the force due to torque on the edge of a wheel depend on the mass of the the wheel or is it always $\tau / R$?
| A car engine puts effort into producing a torque about the wheel's axle. This torque makes the wheel turn.
If the wheel is heavy (large mass, thus large moment of inertia), then it is harder for the engine to produce this torque.
But if the engine succeeds in producing the torque, then that torque causes a force at th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531249",
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The motion of an electron accelerating in a uniform magnetic field As far as I know, when electrons travel perpendicular to a uniform magnetic field, the Lorentz force makes the electron undergo circular motion. As this electron undergoes circular motion, it emits EM radiation, so it goes through a spiral trajectory wi... | The constant speed of electron is by assuming electron does not emit EM radiation.You just mixed up with it.
| {
"language": "en",
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Why does the same proportion of a radioactive substance decay per time period? (half life) Just wondering, if decay is random, why does the activity half every half life, as in, why does it have to reduce by the same proportion in the same time period?
| The word random in this context does not mean totally without order.
What it means is that one cannot predict exactly when a particular unstable nucleus will decay although there is an underlying probability of decay of an unstable nucleus in a specified interval of time.
An interval of time which is often used for a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531441",
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"source": "stackexchange",
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Would connecting two pressurized gas tanks together exchange gases? While the answer to the title is inevitably "Yes", allow me to clarify. I have no background in physics, so please bare with me and I'll be happy to add any clarifications requested in the comments.
If I have 2 tanks:
*
*rated for 100,000 kPa, curre... | Note that two gas in cylinder will diffuse with each other and come to same pressure and temperature. Also will occupy whole volume of two container.
Mathematically finding pressure
$$P(V_1+V_2)=(n_1+n_2)RT$$(for final combination).
Now for final temperature $$n_1C_1(T-T_1)=n_2C_1(T_2-T)$$
Finally solving these
$$P=(R... | {
"language": "en",
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Double slit for electrons (two beams or one)? I understand the double slit for waves but for electrons do we have a beam for each slit so each beam is responsible le to shoot electrons through its own slit.
Or do we have just one beam? Which slit do we place the beam to? If it’s in the middle, wouldn’t all the electro... | There is only one source or one beam of electrons. They are directed toward the slits, with some hitting the middle and some making contact with the edges of the openings.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is it possible to reduce the speed and frequency of a light wave to zero in a liquid medium? Assume that two mirrors are located in a huge liquid medium – say, deep down on an ocean floor – with a refractive index of $n'$ as measured by an observer $A$ standing on the beach platform at rest WRT the liquid. One of the m... | In other words, does speed of light (after reflection) depend on speed of mirrors as well as speed of water or not? Clearly the answer is NO.
Let's redo this experiment, but this time in space not water. Simply enough we can see that speed of light will be c no matter what. Wavelength is the only thing which is affect... | {
"language": "en",
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Fringing of electric field I have read that in a capacitor with charged parallel plates the electric field lines are parallel in the middle, but they tend to bend outwards (causing a "fringe") towards the ends of the parallel plates. Can someone explain why this really happens? Does it happen due to the lack of symmetr... | How is the field produced? By charges on the surface. If you go to the quantum frame, it is excess electrons on one plate and excess positive charge (holes) on the other plate. Think of the electric field generated by an electron. It goes radially out. In an infinite plate capacitor the addition of the fields, because... | {
"language": "en",
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Age of Universe from Friedmann Equation - How to actually solve the integral? The Friedmann equation for a flat universe can be written as
$$
H(t)=\frac{\dot{a}}{a}=H_0\sqrt{\Omega_{m,0}\cdot a^{-3}+\Omega_{\Lambda,0}}=H(a)
$$
To calculate the age of the universe, many books jump directly to the result. But there shoul... | In a flat universe where $\Omega_m+\Omega_{\Lambda}=1$ you can first simplify to
$$H=\frac{\dot{a}}{a}=H_0\sqrt{(1-\Omega_{\Lambda}) a^{-3}+\Omega_{\Lambda}}$$
then you solve for $a$ and get ⁽¹⁾
$$a=\sqrt[3]{\frac{1}{\Omega \Lambda }-1} \ \sinh ^{\frac{2}{3}}\left(\frac{3}{2} H_0 \ t \ \sqrt{\Omega \Lambda }\right)$$
w... | {
"language": "en",
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"source": "stackexchange",
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Why does the galvanometer read 0 at a certain point?
We are studying potentiometers in class, and our teacher wasn't able to explain why the galvanometer would read 0 at a certain point along the wire. I think I'm not quite understanding how the current is flowing through the circuit because of the orientation of the ... | The driver cell in the OP's figure is connected to the potentiometer wire AB which is acting as a voltage divider with the output at the jockey. It may help to rotate the figure. (It may also help to set the bottom potential to zero, ground.) Then that part of the figure looks like this:
Now, if the output voltage $V_... | {
"language": "en",
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Ionizing radiation in thermal radiation According to the black-body radiation equation, the spectrum extends to infinitely high frequency (although its intensity gets small quickly towards high frequency).
(1) How do you roughly estimate the ionizing radiation power in common high power thermal sources like a 2KW heate... | for 1) In this link there is the black body formula of Planck's law that gives the
the power per unit solid angle and per unit of area normal to the propagation
So for a given temperature of the body one can calculate the power, in your case for high enough frequencies, take a $Δ(ν)$ .
Once you have the power you ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533166",
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"source": "stackexchange",
"question_score": "13",
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How to properly calibrate phase axis to represent an optical interferometric stability curve? Assume we want to measure how stable an interferometer is.
We send two ultrashort pulses (left figure), delayed by the fixed time $\Delta t=T$ relative to each other, into a spectrometer to observe an interference pattern (mi... | This is really an engineering problem, not a physics problem. Nevertheless there are probably half a dozen if not more ways to skin the cat.
The way I would do it is capture the initial spectrum as a baseline. Then at regular intervals, seconds, minutes hours (you should decide based on the expected spectrum of your in... | {
"language": "en",
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Stability of plum pudding model My textbook says that the plum pudding model(Thomson's model) should be electrostatically unstable. Why is that so?
| No system can be electrostatically stable. As Wikipedia explains,
Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges.
It can be understood intuitively as a consequence that electrosta... | {
"language": "en",
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What determines how transparent a material is? Every time light hits a material, both reflection and refraction occurs. How does a material determine how much light gets reflected/ refracted e.g. glass vs silver? So far what I could find is light gets scattered by atoms in the material in all directions, but they all c... | Classical light is the super position of zillions of photons with the energy of $hν$, mathematically this means their wave functions are added to create light and the images carried by its variations.
Lets take glass:
In order for the material to be transparent, it means that the image information carried by the superp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533552",
"timestamp": "2023-03-29T00:00:00",
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Why in quantum hall effect longitudinal resistance and conductivity can be simultaneously zero? Why in quantum hall effect longitudinal resistance and conductivity can be simultaneously zero? I am puzzled about it. What's the physics meaning of it?
| The resistivity and conductivity are tensors
\begin{align}
\rho &= \begin{pmatrix}\rho_{xx} & \rho_{xy}\\\rho_{yx} & \rho_{yy}\end{pmatrix}\\
\sigma &= \begin{pmatrix}\sigma_{xx} & \sigma_{xy}\\\sigma_{yx} & \sigma_{yy}\end{pmatrix}
\end{align}
linearly relating the electric field and current density:
\begin{align}
E_a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Clarification of the concept "less resistance means less heating" in a wire So my textbook says that the reason cables that are suppose to carry high currents, are thicker that those that are meant to carry lesser current, is that "less resistance (of the wire) means less heating..."? Is this even true?
Isn't CURRENT ... | The rate of heating of a wire is the power dissipated in the wire which is
$$P=I^{2}R$$
The resistance of wiring is much less than the resistance of the loads that the wiring supplies current to. Therefore the size of the wire has little effect on the current supplied to the loads (within reason). In other words, we ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533927",
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"source": "stackexchange",
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Do black holes move through space? I know it was already asked here:
Does a black hole move through space? What happens to other things around it?
And it might be a very stupid question, but here it is:
From a relativistic perspective, do black holes move through space, or is it the space around them that is curved in... | Yes. Here is a geometric perspective.
Take e.g. the Schwarzschild metric in coordinates $x^\mu=(t,r,\phi,\theta)$:
$$
g_{\mu\nu}dx^\mu dx^\nu=-(1-r_S/r) dt^2 + (1-r_S/r)^{-1}dr^2 + r^2 (d\theta^2+ \sin^2\theta d\phi^2) \qquad \text{(Schwarzschild)}
$$
where $r_S$ is the Schwarzschild radius. The geometry as $r\to +\in... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dumping hot liquid water in sink When I make pasta or potatoes, I dispose of the hot water (around 80-100°C) in a metal sink.
Am I justified to first pour regular hot tap water on the sink to reduce the amount of steam generated, or is this pure superstition ?
If it's not, what is the physical explanation ?
| Steam is water in the gaseous phase and is invisible. It occurs when water boils which, at one atmosphere, is a temperature of 100 C.
What you are seeing coming up from your sink is not steam, but water vapor that is condensing into liquid water droplets. You can see the same thing above a hot, but not boiling, cup of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534114",
"timestamp": "2023-03-29T00:00:00",
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How should I treat background radiation in an experiment? I am performing an experiment to verify the inverse-square law for the intensity of a beam of $\gamma$ rays emitted by a sample of $^{60}\text{Co}$. The set-up is as follows:
*
*A Geiger-Müller tube connected to an electronic counter is set up.
*A background... | If you think of the problem in terms of random variables, it becomes easy. You have two random variables: The first one $X_1$ for the background noise, and the second one $X_2$ for the radioactive decay. Both follow a Poisson distribution.
\begin{align}
X_1 &\sim Pois(\lambda_1) \\
X_2 &\sim Pois(\lambda_2)
\end{align... | {
"language": "en",
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Do eigenfunctions of the position and momentum operators vary from one problem to another? Now the eigenfunctions of the Hamiltonian clearly differ from one problem to another since the Hamiltonian depends on the potential and hence for a different potential we get a different eigenvalue equation for the Hamiltonian he... | Yes they do vary. Say you're doing quantum mechanics on a circle. $\hat p\equiv -i\hbar \partial_x$ where $x\sim x+2\pi R$ is the coordinate along the circle, will then have discrete eigenvalues $k$ and complex exponential eigenfunctions: we have
$$
\hat p e^{ikx/\hbar}=k e^{ikx/\hbar}\,,
$$
but $e^{ikx/\hbar}$ will b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534375",
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The Enigma of Universal Gravitation Forces This is taken from a book called "Physical Paradoxes and Sophisms" by V. N. Lange.
1.22. The Enigma of Universal Gravitation Forces
The law of gravitation can be written $F=\gamma\frac{m_1m_2}{R^2}$.
By analyzing this relationship we can easily arrive at some interesting ... | Consider the gravitational acceleration $g$ at a surface point $p$ of a massive compact body $M$ whose density $\rho$ is assumed to be bounded from above. Then $g$ is finite rather than infinite.
*
*If $M$ is a spherically symmetric ball, this is true due to Newton's shell theorem. The effective distance $r>0$ in Ne... | {
"language": "en",
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What does Heisenberg's uncertainty principle tell about nature? I agree with the fact that the principle points out to the inaccuracy in the measurement of the two quantities of the particles (momentum and position).
But measurements apart, does it explain anything about how nature works, in general? As in, I think the... | The HUP is what tells us that the world is fundamentally QM in nature. All the elementary particles that you see defined in the SM are behaving in a way that will obey this simple rule, and it is not just about momentum and position (though that is a pair of observables or physical quantities that is commonly used in e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534614",
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"source": "stackexchange",
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Time period of piston performing SHM Suppose I have a closed piston-cylinder system which contains an ideal gas,and it is being compressed adiabatically by the piston which has a vertical orientation,and in doing so,the piston is actually undergoing SHM. Now if I use a similar piston in a horizontal orientation (keepin... | The equilibrium position of the piston would change due to the weight of piston. However it would not interfere with time period or frequency as it is acting throughout the process. In the second position equilibrium position would be different. For more accuracy you could also take into account the change in external ... | {
"language": "en",
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In Rotational Dynamics do we have to consider the torque of pseudo force in Instantaneous Axis of Rotation frame? In the attached image have I done everything right? If yes then why there is no torque of Pseudo Force?
| There will be a pseudo force acting on the COM of that body. How ever this will not provide any torque because, the instantaneous acceleration of the Point of contact will be $\frac{v^2}{R}$ acting upwards. So when the pseudo force is applied on the centre of mass, it will be pointed downwards passing through the IAOR.... | {
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Raising and Lowering Indices of Basis Tensors? Can you raise and lower the indices of basis vectors and dual basis vectors? I know I can write
$$V^\mu = g^{\mu\nu} V_\nu $$
but can I also write
$$\vec{V} = V^\alpha \hat{e}_\alpha = V_\beta \hat{e}^\beta?$$
| The equation $$\vec{V} = V^\alpha \hat{e}_\alpha = V_\beta \hat{e}^\beta$$ does not make sense, you are equating two different objects, a vector and a covector. If you take a finite dimensional vector space, $V$, the dual space $V^*$ is the set of all linear functions that map elements of $V$ to the field over which it... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535142",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If we ignore energy and talk about force, Why do objects bounce lower when they hit a softer surface? If an object hits a soft surface it will bounce lower compared to the object hitting a hard surface, isn't the impulse in the first case equal to the impulse in the second case, so why does the object bounce lower when... | No, the final speed is lower with a softer surface, so the impulse is lower.
If you throw a ball at a hard surface, the ball will not stop instantly. It will compress as it slows down. The energy of that compression will then be released, pushing the ball back in the direction opposite of the original motion. In the th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535442",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Is there an analogy for Wilson loops/lines in statistical mechanics? When reformulated in Euclidean space, quantum field theory bears some strong resemblance to statistical mechanics: for example a scalar field $\phi$ can be seen as a spin $s$ in Landau theory, and the source $J$ in path integral formalism can be seen ... | Gauge theories often appear in condensed matter. For introduction I recommend read brilliant introduction article by professor Wen Topological order: from long-range entangled quantum matter to an unification of light and electrons.
In gauge theory, observables are gauge-invariant operators (because gauge symmetry is n... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Minimal coupling to electric dipole form When deriving the electric dipole form of the semiclassical hamiltonian from the minimal coupling form, we define a new state vector as:
$$\psi_{old}=e^{i\textbf{A}\cdot\textbf{x}/\hbar}\psi_{new}=\textit{u}(\textbf{x},t)\psi_{new}$$
we now put this into the SE:
$$i\hbar\frac{\p... | Here you work in the Schrödinger representation, where the time dependence is encoded in the wave function. (This is opposed to the Heisenberg representation, where the time evolution is shifted to the operators.) Thus the derivative of any operator in respect to time is zero, unless it contains explicit time dependenc... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is a simple argument to prove that the stars in the sky are further away from the Earth than the Moon? How do we know, without using modern equipment, that the stars are further away than the moon in the night sky? Further, is there a simple and actionable argument to prove that this is indeed the case? Additional... | If you take it as a given that the Earth is revolving around its axis once per day than you could make the argument that anything that does not move (after subtracting the apparent movement due to the Earth's rotation) must be far away, or it would fall down.
Satellites have a short orbital period, the Moon a longer o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536244",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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"answer_id": 5
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Confusion about cells in parallel I cant understand why cells in parallel will last longer. Could someone please explain?
| A battery is like a store in which you shop for electrons. If two are in parallel you have more stuff you can buy simultaneously; that is you can have two guys shopping at the same time, then get on the road and go home. If they are connected in series first you have to visit one store and then you may go to the next a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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If work is a scalar measurement, why do we sometimes represent it as the product of force (a vector) and distance (scalar)? Consider an object being pushed 3/4 of the distance around a circular track. The work done on the object would be the distance of 3/4 the track’s circumference times the force applied to the objec... | The reason for this is that your understanding of the definition of work contains an error:
"product of ... distance (scalar)"
Work is not defined using a product of force and a "distance", but a displacement. A displacement is the difference of two positions, which are points, and displacements are vectors. So it is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536688",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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How does amplitude affect photon's intensity as a particle? Considering the scenario were a photon acts as a particle, how does amplitude affect the photon?
Does it increase its intensity? How do you visualise this?
| For a higher amplitude, just visualize more photons per unit volume (i.e., a higher number density and a higher energy density). But each individual photon has an energy that depends only on the frequency, not on the amplitude. Having lots of low-energy photons around doesn’t tend to ionize atoms if none of them have e... | {
"language": "en",
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What does "up to a total derivative" really mean and how should I know when to use it? I am a mathematician who is taking a quantum field theory course without much prior pyhsics. We have had the term "up to a total derivative" a few times, yet every time I asked what it meant I didn't really grasp it.
As an example, f... | *
*The Euler-Lagrange (EL) equations are not affected by total derivative terms, cf. e.g. this Phys.SE post.
*In OP's concrete example the Lagrangian density (2) is preferred as it is manifestly real. See also this related Phys.SE post.
| {
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Conservation of energy of 2 identical Rolling Disks with and without friction My physics book claims that if two identical disks moving at the same velocity travel up nearly identical hills, with the second hill not having friction, then the disk rolling up the first hill will travel to a greater height. Given that the... | Your second disk cannot convert its rotational energy to gravitational potential energy.
If I understand you correctly, both disks start out with some forward motion, and some rotation.
Disk 1 will slow down as it travels uphill, converting both kinetic energy from its forward motion and kinetic energy from its rotatio... | {
"language": "en",
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Confusion regarding properties of Poisson Brackets I have just started learning about Poisson Brackets, and came across the following property
$$\{q_i,q_j\}=0$$
And
$$\{p_i,p_j\}=0.$$
Where $p$ and $q$ are respectively the momentum and position coordinates i.e. phase space coordinates.
Now Poisson Brackets are defined ... | As $p$ and $q$ do not depend functionally on one another
$$ \frac{\partial q_i}{\partial p_j} = 0$$ and also $$ \frac{\partial p_i}{\partial q_j} = 0$$ for all $i,j$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can vector components not be resolved by Laws of Vector Addition? A vector at any angle can be thought of as resultant of two vector components (namely sin and cos).
But a vector can also be thought of resultant or sum of two vectors following Triangle Law of Addition or Parallelogram Law of Addition, as a vector ... | Indeed, any vector can be resolved in terms of two components (in $n$-dimensional space in terms of $n$ components). For this being possible the components should be linearly independent, i.e. in your case they should not be parallel. The advantage of using two orthogonal/perpendicular components is that their scalar p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537550",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Difference between projection and component of a vector in product? This is a very basic question about dot products or scalar products:-
If I want to move a block and I apply a force parallel to displacement, the block will move and some work will be done. So in the formula will be $W= F\cdot S$, here we won't calcula... | Projection and component mean the same thing in this context.
Let me however note that a force is a part of the physical reality, existing in the world (at least for the purposes of mechanics), whereas a projection is a mathematical object/construct. From this point of view the work is done by the force (or by its com... | {
"language": "en",
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Experiment for jammers I'm going to grade 11 and I have to write an essay in physics. One requirement is to do an experiment which - in the best case - also includes measurements.
I would like to write about jammers, which cut connections by interference signals. Since it is not legal, I will not build or use a real ja... | Do you have access to a laboratory with a water wave channel?
If yes, you could reproduce this soliton experiment . Solitons are wavepackets, and one could use them sequentially to carry information, a Morse code for example, dependent on the distance between them.
Jamming could be a water sprout , disturbing the flow... | {
"language": "en",
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What is the meaning of a "permutation -invariant " MHV amplitude? When reading my notes, I read that the difference between 4 points colour-ordered MHV amplitude and gravitational MHV amplitude is that the gravitational MHV amplitude is permutation-invariant, unlike the latter.
I don't understand what this means. Is it... | By little group scaling, the three-particle MHV amplitude for three massless spin-1 particles is given by
$$ \mathcal{M}^{--+} =\frac{\langle 12 \rangle^3}{\langle 13 \rangle\langle 32 \rangle}~.$$
This is not permutation invariant in the sense that if I exchange legs one and two I pick up a minus sign. The equivalent ... | {
"language": "en",
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What is *physical meaning*? What do we mean when we talk about physical meaning of a quantity, an equation, theory, etc.? Should the physical meaning touch on the relation between the math and the real world? Or does it have more to do with how the equation/theory is used by physicists?
Background
For the immediate bac... | Let me first ask you a question; what do you think I mean by
$$\mathbf{F} = m \mathbf a$$
?
From a mathematical point of view, the equation expresses the relationship between two vectors.
However, a physicist, when using mathematics to understand nature, makes mapping between physical concepts and mathematical objects... | {
"language": "en",
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Why the imaginary constant on the spin-connection? I have been studying the spin-connection for the Dirac equation. The covariant derivative is defined as:
$$D_\mu \psi = (\partial_\mu - {i \over 4} {\omega_\mu}^{ab} \sigma_{ab}) \psi$$
where $\sigma_{ab} = i[\gamma^a,\gamma^b]$ and ${\omega_\mu}^{ab}$ is the spin-conn... | The $i$ is necessary.
In order to derive the Dirac equations in curved spacetime, the approach is the following: We know how Lorentz vectors can be transported in a generic curved spacetime using covariant derivatives. We use the fact that bilinears of $\psi$(a spinor) should transform like a vector. This then gives ri... | {
"language": "en",
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"source": "stackexchange",
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The electric field should be in circular coil. But why do current flows in whole circuit? We know changing magnetic flux induces electric field which makes current to flow .here in the below picture the flux is changing through only circular coil bout not through the rectangular part.so what induces electric field in r... | By moving a magnet, voltage will be induced in the circular part of the coil (which is in the range of magnetic field). This voltage will drive the current in rest of the part of wire.
| {
"language": "en",
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Energy conservation in reflection of light from a perfect mirror I came across a question where a light source is shined on a mirror attached to a spring which is attached to a rigid support. The question goes:
A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular f... | I'm not totally sure, but this sounds like a problem concerning the frame of reference. In the center of mass frame there should be no energy transfer for an elastic collision. But as the mass of the mirror is not given, the center of mass frame may not even be approximately the lab frame where the mirror is at rest in... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is De Broglie's formula $\textbf{p}=\hbar \textbf{k}$ applicable to a discrete wave number system? I don't know if my question has sense at all but while doing my homework there appeared in my mind this question.
Say, for a particle in a box, the confinement makes that the wave number k is discrete, depending on integ... | No. You can't use the De Broglie formula here because De Broglie's formula is true only for a free particle $(V(x)=0$ everywhere$)$.
For the infinite square well, we can write down the energy eigenvalue equation as:
$$\frac{-\hbar^2}{2m}\frac{\partial^{2}\psi(x)}{\partial x^2}+V(x)\psi(x)=E\psi(x)$$ such that $V(x)=0 $... | {
"language": "en",
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Why are there no even harmonics in a closed pipe? I have seen a diagram on sites such as hyperphysics.com that show that there is a missing bit every time so that it makes every harmonic odd. I was hoping I could get a more intuitive explanation. We recently got introduced to harmonics and standing waves in class and ... | Musical notes are made by strings and by pipes. Standard discussion of harmonics and standing waves focusses on strings, but pipes are just a little more subtle.
For a wave on a string you plot the displacement and get sine waves and that's obvious as the plot looks like the excited string.
For a wave in a pipe the dis... | {
"language": "en",
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How do we know that a non-rechargeable battery obeys the law of conservation of energy? For a rechargeable battery, I can show that energy is conserved by
*
*Discharging the battery.
*Measuring the energy required to charge the battery.
*Measuring the energy I get out from a second discharge.
For a non-rechargeab... | This will provide an upper bound:
*
*Measure the mass of the battery.
*Count all the atoms in the battery (good luck!).
*Compute the mass of all the atoms under the assumption of the atoms are non-interacting.
*Since E=mc^2, the difference between the actual mass and the computed mass is an upper bound on the pote... | {
"language": "en",
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How can a red light photon be different from a blue light photon? How can photons have different energies if they have the same rest mass (zero) and same speed (speed of light)?
| Let me add a few things.
*
*A photon is an elementary particle, and as long as it propagates, it is in a superposition of states, meaning it is in a superposition of frequencies, and does not have a well defined frequency. You cannot know its frequency until you interact with it or absorb it.
As a quantum mechani... | {
"language": "en",
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"source": "stackexchange",
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Moment of inertia tensor and symmetry of the object What information does the moment of inertia tensor give on the structure of an item.
I was told that its eigenvectors give the principal axes of the object.
Do you know more about this?
| Using the inertia tensor $I_{jk}$ of an object, you can construct an ellipsoid satisfying the equation $$1=x_{j}I_{jk}x_{k} .$$ As you said, the eigenvectors of $I_{jk}$ are the principal axis $\vec{r}_{j}$ of your object with the respective moment of inertia $\theta_{j}$ as eigenvalue. Thus, changing coordinates to th... | {
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Why does frequency remain the same when waves travel from one medium to another? I was reading about reflection and refraction on BBC Bitesize and I can't understand why frequency is a constant in the wave speed equation. I can't visualise the idea of it. I know that wave speed and wavelength are proportional to each o... | Imagine a rope attached to the bottom of a swimming pool. You, above the surface, grab it and shake it back and forth to create waves along the rope. The part of the rope just above the surface has to be moving back and forth at the same frequency as the part of the rope just below the surface. Otherwise the rope would... | {
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Why does the dielectric field not cancel out the capacitor's field? When a conductor is in a region with electric field, free charges will move until they balance out the external electric field. However in dielectrics this does not happen. I know that charges are bounded to the atoms, and there is only a small portion... |
why does not the dielectric field cancel out the capacitor's field?
The polarization of the dielectric in the capacitor does reduce the effective electric field of the capacitor, but doesn't completely cancel it out. The reason is the molecules of the dielectric material are not perfectly polarized by the capacitor's... | {
"language": "en",
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Why atmospheric pressure on a liquid and not on a solid? An open cylindrical container (radius = 0.5 m) has 100 kg of water.
a) Find the water pressure at the bottom of the container.
b) Find the pressure exerted by the container on the floor (ignore the mass of the container)
What confuses me, in a) We simply use p ... | In my opinion, it should have been explicitly mentioned in part (b) that the value of excess pressure is being asked. By excess pressure, I mean the difference between the pressure on the ground below the container and the pressure on the ground elsewhere. This way, the answer $\rho g h$ is justified.
| {
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Why a ball doesn't stop when it collides with a wall? If a ball collides with a ball of same mass the first ball stops and the second ball gets the velocity of first ball.The first ball stops due to the reaction force acting on it. But when a ball collides with a wall why doesn't it stop due to the reaction force?
| Because the reaction force is larger.
The force needed to make an object reach a certain speed is the same as the force needed to slow it down from that speed to zero over the same time. This is Newton's 2nd law.
So, when two equal and movable objects collide, the (action) force that is required to make one object spee... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If an observer changes their velocity, is it equivalent to a momentum shift? Suppose we have a world with one massive free particle and one observer. If the observer changes their velocity with respect to the particle, will this have the same effect on $\lvert\Psi(r,t)\rvert^2$ as if $\langle p\rangle$ was changed loca... | The relation between the two cases is given by a unitary transformation. This means that $|\psi(x,t)|^2$ is necessarily preserved.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Newton 3rd law of motion If I took both hands and hold as I am greeting someonei.e.namaste. Now, I push both hands with same force say 10N , there is no change in position.But Newton 3rd law has said,equal and opposite forces are on different bodies and they never cancel each other (action reaction). So, why they don't... | When you push on your right hand with your left you feel a force back on your right hand.
This is the 'equal and opposite' force that comes from Newton's third law. However, at the same time you are pushing with your right hand you are also pushing with your left and feel a force back on your left hand, again due to Ne... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to prove the Jackson-Feenberg identity in quantum mechanics? The Jackson-Feenberg identity for evaluating the expectation of kinetic energy is frequently used in the theory of quantum liquids and is given by:
$$<\hat{T}>=-\frac{\hbar^2}{8m}\int d^3r[(\nabla^2\psi^*)\psi+\psi^*(\nabla^2\psi)-2(\nabla\psi)\cdot\nabla... | Just integrate by parts a few times to get it in the desired form. For the first term in the identity,
$$\int d\mathbf{r} \, (\nabla^2 \psi^*) \psi = - \int d\mathbf{r} \, (\nabla \psi^*) \cdot (\nabla \psi) = \int d\mathbf{r} \, \psi^* \nabla^2 \psi.$$
For the third term in the identity,
$$- 2 \int d \mathbf{r} (\nab... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "2",
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Why entropy in ideal BEC is independent of density I am confused about one statement from the book Bose-Einstein Condensation in Dilute Gases.
In the chapter discussing superfluid, the auther claims:
The pressure and the entropy density $\frac{S}{V}$ of ideal Bose-Einstein condensed gas depend on temperature but not on... | For an homogeneous ideal gas in 3D below $T_c$ we get
\begin{align}
p &= \zeta(5/2) \left(
\frac{m}{2\pi \hbar^2}\right)^{3/2} \;
(k_B T)^{5/2}\propto T^{5/2}
\\
\frac{S}{N} &= k_B \frac{5}{2}
\frac{\zeta(5/2)}{\zeta(3/2)}
\left(\frac{T}{T_c}\right)^{3/2}
\propto \left(\frac{T}{T_c}\right)^{3/2}
\propto \left(\frac... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is energy density of two $P$ W lamps the same for one $2P$ W lamp? Do two lamps of power $P$ produce the same energy output as single lamp of power $2P$, assuming ideal environment? E.g. lamps do not occlude each other, distance between lamps is negligible, no monochromatic interference, same input energy to output ene... | Radiant flux does add linearly - two lamps with radiant flux P will sum to a total flux of 2P and match the single lamp with 2P.
With lamps, we should all be careful to separate electrical power from radiant power. Different lamps will have a different conversion rate of electrical power to radiant power (especially i... | {
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How can we calculate the change in entropy of a block and its surroundings, when the block is placed in a heath bath? Let's say we have a block of lead (of heat capacity $C$) at temperature $T$, and a heat bath of temperature $T_0$. The block is placed in the bath and it cools to $T_0$ (a clearly irreversible process).... | Just calculate $\Delta S=mc \ln(T_2/T_1)$ for the block, assuming it's an incompressible solid (we'll derive this below). Entropy is a state function so the process of how you aquired this change doesn't matter. Now to answer your questions:
*
*This is true because the path/process determines $Q$, which changes the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542146",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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