13 votes

Sound waves adding up

Since the phases are random, the waves do not add coherently... but neither do they cancel coherently. Furthermore, loudness is really a measure of the intensity of the sound. Thus, if we consider a ...
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4 votes

Double slit experiment: how to derive the figure of interference?

I think the most straightforward way to get the pattern is to first consider an isotropic point source of particles with momentum $k$. Here I consider the $d=2$ case. The wave function for the ...
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  • 1,075
2 votes

Sound waves adding up

You can compare this to taking the mean of a random sample of mean zero random variables. Some observations will be positive, and some will be negative, and so there will be a lot of canceling. ...
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2 votes
Accepted

How can we derive an equation for double slit interference without the approximations made?

For near-field effects, it may be better to think about the full field rather than just path differences. Based on you wording of "point sources" and the fact that you are using speakers, I ...
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1 vote

Phase difference and path difference relation confusion

$\delta$ is the phase-difference $\theta_2 - \theta_1$ at the meeting point, where $\Delta x$ is the path-difference (difference in path lengths) $\ell_2 - \ell_1$ between the two paths from the ...
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1 vote
Accepted

Path Integral QM and Destructive Interference

Pay attention to the word crudely. The value $\pi$ is not a precise estimate, just a typical value for phases out of phase. Shankar is implying that when the path integral sum up a neighborhood of ...
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  • 169k
1 vote
Accepted

Law of conservation of momentum and interference

On screen 4 you will still see "interference", as with photons each particle/wave will determine its own path (per Dirac, Feynman and QM) and all electrons going to the right have the option ...
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1 vote

Intensity of Diffraction and inteferance

We will assume that the distance between centres of slits is several times greater than the width of each slit. The intensity of the interference pattern will then be 'modulated' by that of the ...
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1 vote

Why is the width of a dark fringe in an interference pattern much less than the width of a bright fringe?

The range of intensities from bright to dark is very large and you will see from the photograph of some fringes (not on the same horizontal scale as the graph) that the dark look wider than the bright....
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