New answers tagged waves
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What is the frequency of a standing wave?
A harmonic is a wave pattern formed by a standing wave. The first harmonic is the one with the longest wavelength(and lowest frequency), which decreases with higher harmonics. All harmonics have ...
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Galilean invariance of the wave equation
You derived the wave equation assuming the material was stationary, and that is the only case for which that equation is valid. When you transform reference frames you no longer have a stationary ...
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Galilean invariance of the wave equation
A simple derivation of the wave equation from Newton’s second law is to consider harmonic oscillators in series:
$$
\ddot u_n = (u_{n+1}+u_{n-1}-2u_n)
$$
with $u$ the displacement and normalized mass ...
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Is it possible to "pull" sound waves using only an object?
A receiver dialed in to a specific frequency band, and headphones to perceive the initial vibration of the medium that generated said frequency.
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Diffraction when the wavefront is not parallel to the plane
So even if your wave fronts are "parallel" to the plane, if they have a phase that varies over one dimension of the plane, they are in effect incoming or outgoing at an angle. So this is ...
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Why does the pet's water bowl overflow?
The reason may be simple, because your container not only has angular movement, initially T-2 tilts forward, then T-1 tilts backward, but also horizontal movement from right to left during this ...
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Why does the pet's water bowl overflow?
If you check the tide chart for your local area you will find that the bowl overflows only during the incoming tide and is directly proportionate to what stage the tide is at when you set the bowl ...
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Why the frequency component is not included when the energy of a wave is described?
According to particle theory, the energy of a photon depends on frequency which makes sense. But in classical theory, how is it included? I am not seeing it.
Energy density vs. energy flux
One has to ...
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Why the frequency component is not included when the energy of a wave is described?
This really depends on the wave. If it's a wave in rope, there is kinetic energy associated with the velocity of the rope moving up and down, and in the linear limit:
$$ v \propto A\omega $$
which has ...
- 35.4k
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Diffraction when the wavefront is not parallel to the plane
This is how you derive Snell's law: https://ocw.mit.edu/courses/3-024-electronic-optical-and-magnetic-properties-of-materials-spring-2013/480e12b984eb21a5e88b8ee5cc051ef8_MIT3_024S13_2012lec22.pdf
...
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Accepted
What is the mathematical support for the formula $f_n = n f_1$, used to calculate the frequency of a standing wave?
Let's start with a quick answer: the boundary conditions fix the frequencies of the harmonics. It's worth emphasizing that boundary conditions come from physics, not mathematics. Below, I'll consider ...
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Why does the pet's water bowl overflow?
The two horizontal sloshing modes could have slightly different frequencies (e.g. if the rotational symmetry is not perfect).
If you then start with the combination of both, but out of phase, which is ...
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Why does the pet's water bowl overflow?
If the mat is thick and soft enough to be compliant, then it will couple with the moving mass of the dish and water and allow the dish to tip back and forth, causing the spillage.
This can be directly ...
- 95.5k
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Why does the pet's water bowl overflow?
A guess. Perhaps there are multiple modes present. It takes a while for them to have an interference maximum at the edge of the bowl.
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The "small amplitude" assumption in the derivation of the wave equation for the string
Following the most recent comment, I am going to try and prove that the “vertical displacement force law” assumption implies the small-amplitude assumption. The small-amplitude assumption is ...
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The "small amplitude" assumption in the derivation of the wave equation for the string
A propos "the restoring force being proportional to the displacement," a textbook that does not use the small-amplitude assumption in the derivation of the wave equation for the string is ...
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Directionality of EM Waves in Double Slit Experiment
The diagram on the left is in the xy-plane and you can liken it to a contour map taken at an instant of time, like a photograph.
Initially let me assume that the incoming light is plane polarised in y-...
- 97.9k
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Human error in wave experiment
However, because it is done just by looking it means that there is some subjectivity which could lead to human error, so do not look at the frequency display whilst altering the frequency and take ...
- 97.9k
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Human error in wave experiment
To get a high degree of accuracy in this kind of mechanical experiment you need patience on the order of humans who existed before the digital age. Run the driving for a long time and use video ...
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Why does radiation of small wavelength interact with small objects?
Your bullet analogy applies in the sense that the bullet is analogous to the macroscopic thermal "damage" caused by lower frequency, longer wavelength microwave radiation, while the higher ...
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Is there a relation between phase plane and complex plane?
Given a configuration space $M$, the phase space $T^*M$ is a cotangent bundle on $M$. Any cotangent bundle has a canonical symplectic structure, and any symplectic manifold with a Riemann metric has a ...
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Huygens' principle and the laws of reflection/refraction
The points shown as yellow blobs on your diagram are in phase, even though they are not on the same wavefront. The hemispheres drawn in the lower medium do seem like Huygens secondary wavelets. But ...
- 36.1k
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Accepted
Huygens' principle and the laws of reflection/refraction
The construction you link to shows the same wavefront at multiple points in time, not a snapshot of a light wave at one point in time. The yellow dots constituting the point sources at the interface ...
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How to visualize the angular frequency in SHM?
For your first question regarding how to "visualize" $\omega$, I understand what your asking is, "can we draw an intuitive understanding of the angular frequency $\omega$ in much the ...
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Weird looking sine wave behavior in an electric circuit
I suspect that the signal generator is struggling to produce the lower frequencies you used in your tests and is not driving your circuit with a true sine wave, but with something looking like a ...
- 95.5k
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Understanding Loop Formation in a Plucked String
One simple way to get some intuition is to think of it like this: After plucking, the string would like to relax into a sinusoidal wave which is zero at the edges and has a maximum amplitude (antinode)...
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Weird looking sine wave behavior in an electric circuit
With competent values that you have given and assuming that the voltage source has little or no resistance then $Q=10$ and the resonant frequency is $\approx 36\,\rm kHz$.
As the $Q$ value is ...
- 97.9k
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Is it possible for a double slit experiment to create an interference pattern at 90 degrees?
Yes, it is possible. In the Fraunhofer approximation you have
$$
I(\theta)
\propto \cos^2 \left [{\frac {\pi d \sin \theta}{\lambda}}\right]~\mathrm{sinc}^2 \left [ \frac {\pi b \sin \theta}{\lambda} ...
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Is it possible for a double slit experiment to create an interference pattern at 90 degrees?
No but Its possible to stretch the 5 interference bars into(at least approaching ) a superposition wave packet by angle offset of the laser source but slits are very restrictive overall. Free ...
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Accepted
Where did the energy created go if there are no non conservative forces like friction acting in my scenario?
I don't think that you can have a wave in a massless string. So I will ignore that bit.
If half wave with positive amplitude is sent through the string with some speed. ... another half wave with ...
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Where did the energy created go if there are no non conservative forces like friction acting in my scenario?
If the "+ wave" and "– wave" are traveling in opposite directions, there will be a moment when the string is flat as they pass through each other and cancel, but then they will ...
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Decoupling Linearly Coupled Wave Equations with Potentials
Since $V$ is space dependent, you will need to diagonalise $\Delta+V$. This is like solving for the stationary solutions of the Schrödinger equation with internal degrees of freedom (like the Pauli ...
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