Questions tagged [waves]
Waves are disturbances that propagate through space and time. Classically, they travelled through a medium, disturbing the particles but not changing their mean position. Electromagnetic waves/particle-waves need no medium; they are disturbances in their respective fields.
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Calculation of the reflected wave amplitude in a string [closed]
I have a problem to calculate the reflection amplitude of the wave when a wave passed to another medium with different density.
To obtain the amplitude of the reflected and transmitted wave, I ...
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Why the Electrical field is that way? [duplicate]
So, I asked my teacher to draw the incident and reflected wave in the case of the incidence onto a perfect electric conductor. The thing I Don’t undersand is why the reflected field is that way. The ...
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How can we derive the polarization of reflected electric field? [closed]
Simply out: How can we derive the polarization of a reflected electric fields in the case of parallel polarization, where the electrical field lays on the incidence plane
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Why do airplanes sound louder when its cloudier?
I am from India, and now its monsoon season. Typically, during this time, the sky is filled with dark rain clouds. Me, along with several of my friends, have observed from childhood that the planes ...
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Formal description of an electron absorbing a photon
This question is about how the electromagnetic field interacts with matter.
Suppose we have an electromagnetic wave, let us say it is planar but not monochromatic. So the wave is described by an $L^1$ ...
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Can taut membranes and strings that are clamped at both ends propagate non-standing waves?
I'm going through an introductory course in acoustics and I'm struggling with the intuition behind standing waves.
When deriving solutions to the various wave equations we usually impose a boundary ...
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Steady-state wave equation
I know that for the heat equation $u_t=\nabla^2u$, the steady-state condition $u_t=0$ suggests we need to solve $\nabla^2u=0$ (i.e. Laplace's equation), which yields the equilibrium temperature ...
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How to "rectify" this wave-equation derivation for Longitudinal waves?
To derive the differential equation for longitudinal waves, my professor proceeded like this:
We are using the concept of $N$-coupled oscillators. Consider a slab of length $l$ and cross sectional ...
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How to show the ratio (spin angular momentum density)/(energy density) for circularly-polarized gravitational plane wave = $\pm 2/\omega$?
It is well understood that an infinite monochromatic, circularly-polarized electromagnetic plane wave has no angular momentum density. However, a finite monochromatic, circularly-polarized ...
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When a taut string is plucked, what will be the direction of the transverse wave's propagation?
Intuitively, I'd guess that the direction of propagation depends on where you pluck the string, namely which half of the string.
In the case of a stringed instrument, this guess of mine would ...
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How was the speed of colored light measured in a vacuum? [closed]
Light is affected by the change in the speed of the source as the frequency of light changes. This is called the Doppler effect, where the red shift can be observed in galaxies moving away from us.
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Showing the following wave equation solution vanishes for $||\vec{x}||>|t|$
For $(t,\vec{x}) \in \mathbb{R}\times\mathbb{R}^n$ we put
$$
f(t,\vec{x}) = \frac{1}{(2\pi)^n} \int_{\vec{k}\in\mathbb{R}^n}
e^{i(\vec{k}\cdot\vec{x} - ||\vec{k}||t)} d^n k \,.
$$
Then $f(t,\vec{...
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How was this equation for the stability of a finite difference model Wave Equation derived? Von Neumann analysis?
Wave Equation
In this paper, the following equation is given for a wave equation:
Stability Equation
They then go on to state the stability of such a wave equation in sample based solutions (in terms ...
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Waves, energy and matter
What is the physical reason why a wave (mechanical or electromagnetic) can transport only energy and not matter?
Is it perhaps because if a wave could transport matter, then a larger amount of energy (...
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Linear-array diffraction beam splitter
This question is composed of two parts. The first is about the grating equation. The second is about a particular software used for diffraction gratings.
The grating equation is
$$
\sin(\theta_m) = \...
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Refracted Spherical Wavefront
Consider an optical wavefront propagating in a homogeneous medium with refractive index n.
Said wavefront encounters a spherical lens with radius of curvature R and refractive index n'.
At the ...
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Do prisms disperse light by frequency but don't disperse magenetic waves or electric waves on their own in Maxwells Equations?
In a class about EM fields based on Maxwells equations, we learned that when electric field lines cross from medium 1 to medium 2 they obey:
$$\frac{\tan \alpha_1}{\tan \alpha_2} = \frac{\varepsilon_1}...
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Proof that the solution to a time dependent wave equation is (anti-)symmetric given (anti-)symmetric boundary conditions
I am unable to prove the following statement (which is numerically motivated).
For a function $F(t_1,t_2)$ fulfilling the following ODE
$$\partial_{t_1}^2F(t_1,t_2) + E(t_1)^2F(t_1,t_2)=0$$
for $(t_1,...
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Lamb wave derivation: Elastic wave propagation in a thin sheet
I am trying to follow the derivation for the phase velocity for elastic waves with large wavelengths compared to sheet thickness, propagating in a floating ice sheet, as described in Propagation of ...
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Is the Doppler Effect for sound waves with a moving source due to the fact that the wave speed is independent of the source?
The Doppler Effect is typically formulated as follows:
$$f' = \dfrac{v \pm v_o}{v \mp v_s} \cdot f$$
The reason for the frequency increasing for observer moving towards source seems clear enough. It ...
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An echo that sounds for years?
How exactly should I understand United Airlines Flight 2860's description and English Wikipedia? Namely, last sentence of the fourth chapter of the summary:
The "echo" of the crash could be ...
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Physical basis of "forced harmonics" on a violin
I have recently learnt of a somewhat novel violin technique, sometimes known as "forced harmonics", where, in a physicist's terms, instead of the normal N=1 stationary wave (fundamental mode)...
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Constructing wave equation for known dispersion relation
Hello,
I am wondering how to construct differential wave equation for a given dispersion relation.
Simplest wave equation (constant wave velocity for all frequencies) is as follows:$$\frac{\partial^2u}...
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TEM Waves in conductors
I am having some trouble understanding ohmic losses in conductors. Suppose I have copper cable and run some high frequency sinusoidal current throught it. The skin effect should be very noticable and ...
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Can refraction change a wave's frequency?
Can refraction change a wave's frequency under any circumstances ?
If yes, what conditions must apply for this to occur ?
Is this a common phenomenon or only happening in extreme circumstances (such ...
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Conceptual confusion about how a string gives rise to a quantum field in spacetime
In bosonic string theory, looking at the Polyakov action in the appropriate gauge, we find that the solution to the classical string is the (constrained) free scalar field (see http://www.damtp.cam.ac....
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How can sound travel as a transverse wave?
We know that sound travels by each previous particle transferring its energy to the next successive particle.
We also know that transverse waves are those waves in which particles move about their ...
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Since waves are abstractions, does it even make sense to ask whether light is a wave? [closed]
All waves transmit energy.
Water Waves
Let's say you're in the middle of a calm pond and you start moving your hand up and down. Transverse "waves" are generated, and they propagate ...
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Does Voltage of solar cell depends on Intensity of light?
On measuring voltage across the two terminal of solar panel (made of semiconductor material) ,the Voltage (V) increases with increase in intensity (I) of sunlight in open circuit. But it should be ...
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Could someone explain to me why my approach here is wrong? [closed]
The area of the central maximum produced by a circular aperture is $8.25*10^{-6}$ m$^{2}$. If the aperture is 1.2 mm in diameter and the screen is 3 m away from the slit, what is the wavelength of the ...
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Physical Interpretation of equality in 1+1D wave equation
I was re-reading Eugene Hecht's textbook on Optics, and he derived the one-dimensional differential wave equation:
$$\frac{\partial^2 \psi}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 \psi}{\...
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Interpreting the magnitude of vectorial phasors
In fields of physics such as acoustics and electromagnetism, we often deal with physical quantities that are both vectorial and oscillating. These can be represented as vectorial phasors,
$$
\vec{b}(t)...
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Interface excess free energy using spherical harmonics
I am a bit struggling to calculate a quantity involving spherical harmonics $Y_{lm}(\theta,\varphi)$. We parameterize as surface in spherical coordinates as:
\begin{equation}
\xi(\theta,\varphi) = R \...
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Can we equate energy of photons to energy of EM waves by volumes?
I am trying to connect the wave model with the particle model of a beam of light through energy of a fixed volume in space.
By definition, the intensity is equal to power density $\left(\frac{J}{s \...
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Relation between four-wave vector $k^\mu = (k_0, \bf{k})$ and velocity four-vector
Question: how is a (subluminal) wave's wave-vector related to the 4-velocity (phase velocity)?
Wikipedia says that $$k^\mu \propto v^\mu \quad\quad\quad (1)$$
as stated in https://en.wikipedia.org/...
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Absorption in solarcells / External Quantum Efficiency (EQE)
How can I calculate total EQE when I have the absorption of the first two modes of the system and their S parameters?
Do I need to use S parameters at all?
(I'm using CST Microwave Studio for ...
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Calculating the amplitude of a vibration based on the sound intensity
I am stuck on this problem.
Assume I have a speaker generating a single frequency tone, $f_s = 100$ Hz, and I want to calculate the amplitude of the speaker vibration $A_s$. I measure the sound ...
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Confusion about sound intensity
I think there is something fundamental I'm not understanding about sound intensity.
I have a small speaker at home, roughly 10cm square and the specs state it has 3 W output. That equates to 300 W/m^2 ...
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What is the frequency of a standing wave? [closed]
I understand that constructive interference of waves results in standing waves. And for a wire with both ends fixed the frequency should match the fundamental frequency of the wire to produce standing ...
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Galilean invariance of the wave equation
Given the wave equation for a material wave:
$$\frac{\partial^2 \phi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2},$$
we can apply the Galilean transformation $x'=x-Vt$ and $t'= ...
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Why the frequency component is not included when the energy of a wave is described?
Energy of a wave is directly proportional to its Amplitude squared. There is no inclusion of frequency in it. But by intuition if one thinks about it, isn't it obvious that a wave with higher ...
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Connection between dispersion relation and symmetries of the Hamiltonian
I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
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What is the mathematical support for the formula $f_n = n f_1$, used to calculate the frequency of a standing wave? [closed]
could someone explain to me the mathematical support for the formula $f_n = n f_1$. This formula refers to the fact that the frequency of a standing wave is equal to the number of antinodes times the ...
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Why does the pet's water bowl overflow?
So when i give the pet fresh water in a stainless steel bowl that i place on a mat according to the attached picture, from $t=0$ the bowl is at rest, the water normally oscillates in the bowl like a ...
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Diffraction when the wavefront is not parallel to the plane
I am studying Feynman's chapter on the origin of the index of the refractive index (see this link).
If I am not mistaken, what he does is to prove that when a wave enters a medium (modelled as a ...
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The "small amplitude" assumption in the derivation of the wave equation for the string
I am reading about the wave equation for transverse waves in a string from the book Mathematics of wave propagation (2000) by J. Davis. On page 10, just before the derivation of the (one-dimensional) ...
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Directionality of EM Waves in Double Slit Experiment
In the experiment of any wave through the double slit we see and model the interference pattern as shown.
In this depiction that means the wave propagates in/out of the page. ie we are seeing a sin ...
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Phase Slope Distance Calcuation
After trying to implement IFFT algorithms for phase-based ranging, as outlined in this very interesting and descriptive blog post; I've been getting horrendous results (orders of magnitude inaccurate),...
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What actually happens when light goes into a waveguide?
I have only dealt with a rudimentary theoretical treatment of how light propagates inside a waveguide, such as those available in Griffiths.
One thing bugging me is that I still do not know how ...
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Wave interference and fluid dynamics question
I'm curious to find an answer to this question:
In the college canteen I would often slide my Styrofoam cup of milky coffee across the melamine table top. (unlike paper or plastic, Styrofoam is a ...
