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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 ...
DinoS's user avatar
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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-...
Farcher's user avatar
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1 vote

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 ...
Farcher's user avatar
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2 votes
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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 ...
mike1994's user avatar
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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 ...
Bob D's user avatar
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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 ...
Godfly666's user avatar
3 votes

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 ...
Philip Wood's user avatar
6 votes
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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 ...
hijit's user avatar
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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 ...
hijit's user avatar
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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 ...
niels nielsen's user avatar
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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)...
Codename 47's user avatar
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1 vote

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 ...
Farcher's user avatar
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1 vote

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} ...
my2cts's user avatar
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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 ...
Kev Andrews's user avatar
1 vote
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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 ...
Dale's user avatar
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1 vote

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 ...
RC_23's user avatar
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2 votes

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 ...
LPZ's user avatar
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