Waves A-level questions help pleasee xx

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Qxi.xli
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I'm really sorry in advance for the number of questions I have! if anyone could help me out with even one of these that would be really appreciated I've tried my best to google the answers

1. Does putting colour filters on two sources mean they're incoherent? What would the diffraction pattern look like? (if white light is shone on it)
2. Why are two independent sources incoherent: Google says is because light waves are emitted by billions of electron randomly and so it cannot be coherent. But if we go by same reasoning then light waves from a single source should also be incoherent? So how do we account for that?
3. In a video I watched, it says that the formula w=labdaD/n only works for small n as the screen doesnt curve? What does that mean?

4. In my notes it says that the properties of two particles between two nodes is that they have the same frequency and are in anti-phase. Why do they have the same frequency and are in antiphase? I was under the impression that they are in the same phase of a wavecycle?
5. In stationary waves, all the points between consecutive nodes are vibrating in phase. This means they all reach their max displacement at the same time, but each point will have a diff max displacement. Why does that mean that they are in phase though?
6. If stationary waves don’t transfer energy, then why is it that in instruments, eg. a guitar, after a while,the string stops moving and doesn't produce any sound? This goes against the definition and some energy must have been transferred.
I have like three more questions but I might ask them later. Thank youuu xx <3
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Callicious
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(Original post by Qxi.xli)
I'm really sorry in advance for the number of questions I have! if anyone could help me out with even one of these that would be really appreciated I've tried my best to google the answers

1. Does putting colour filters on two sources mean they're incoherent? What would the diffraction pattern look like? (if white light is shone on it)
2. Why are two independent sources incoherent: Google says is because light waves are emitted by billions of electron randomly and so it cannot be coherent. But if we go by same reasoning then light waves from a single source should also be incoherent? So how do we account for that?
3. In a video I watched, it says that the formula w=labdaD/n only works for small n as the screen doesnt curve? What does that mean?

4. In my notes it says that the properties of two particles between two nodes is that they have the same frequency and are in anti-phase. Why do they have the same frequency and are in antiphase? I was under the impression that they are in the same phase of a wavecycle?
5. In stationary waves, all the points between consecutive nodes are vibrating in phase. This means they all reach their max displacement at the same time, but each point will have a diff max displacement. Why does that mean that they are in phase though?
6. If stationary waves don’t transfer energy, then why is it that in instruments, eg. a guitar, after a while,the string stops moving and doesn't produce any sound? This goes against the definition and some energy must have been transferred.
I have like three more questions but I might ask them later. Thank youuu xx <3
1/2 (random photon production))
Coherent = Same phase relationship over time and identical waveform, i.e. same frequency. Even if a precise filter existed that was narrow enough to isolate one exact frequency (technically impossible) it would still not produce coherent light. Why? Because all you're doing is forcing the light into one frequency. Over a small enough/finite time period, that light will be coherent, but over time, it won't be. Photon production is random for such a source, and the superposition of all the waves produced will vary over time, and consequently this doesn't represent a spatially coherent wave: the waveform shape will vary wildly over time.

2 (Single slit coherence))
My explanation for diffraction is going to be a bit crude and frankly someone else might explain it better, but I'll try. You're going to need to keep in mind the "Huygens-Fresnel Principle," which states that each individual point on a wave front acts as a source of wavelets, i.e. can be modelled as the source for a new spherical wave. That's fancy speak for just saying you can model each point as a new source. This is covered in AQA, idk about OCR or the other boards, though.

Name:  1231241251.PNG
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Size:  80.8 KB
Consider your messy source of wave fronts (i.e. bottom part of the diagram I've given...)

By using a very thin slit, you're slicing off a very thin section of wave front from that messy curved mess of a wave fronts you get from superposition of lots of individual photons. Those curved fronts vary over time: they're spatially incoherent, due to the random nature of your source, but slicing off a very finite part of it will give you something flat to work with across the slit. That's the point of a thin slit. At any point in time, if the slit is thin enough, the wave front hitting it will be flat across the width of the slit.

In the diagram I've given, they're using a pinhole. The pinhole is just a thin slit with no height to it: let's just focus on the diffraction we're interested in occurring orthogonal to the length of the slit.

Now, what we've reduced the problem to is something like this:
Name:  123123123123.png
Views: 13
Size:  7.0 KB
a very thin slit, with a flat wave front hitting it. You model each point on that wave front as a source of wavelets (as I've drawn) and if you combine the effect of all the wavelets, you're going to get a wave front emanating from the slit, which is perfectly flat, and will spread out as a spherical wave with a smooth surface.

Note that this doesn't give temporal coherence, where each successive wave front is separated from the previous one by the same period. The slit just improves spatial coherence.

I've tried to make the explanation work for AS/A... hopefully that helps a bit? The only other way I know is more math-y... ;-;

As for the bit about two sources... same argument. They're not spatially coherent, because ultimately the random nature of photon production involved will yield a time-varying phase relationship between the two, which doesn't abide our definition of coherence. That's the short of it. I've covered the single source above.

3)
Can't read the formula, but likely worth considering any derivations. A lot of these formulae ignore sines/cosines involved, which a curved screen can rectify the errors associated with, if I recall the things Poon was saying back in our labs.

4)
Standing waves I'm guessing. Should be in phase if I recall... bit concerning they're not. If not standing waves, idk. Opposite side of node = antiphase.

5)
Moving in phase. Same frequency, same phase relationship between them all, they reach max displacements at same time.

6)
Drag, attenuation, whatever else. I never did acoustic physics but if we're just talking the string stopping it's motion, it dissipates energy naturally. The waves aren't ideal, and nothing is perfect as in theory: drag exists, etc.
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Qxi.xli
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(Original post by Callicious)
1/2 (random photon production))
Coherent = Same phase relationship over time and identical waveform, i.e. same frequency. Even if a precise filter existed that was narrow enough to isolate one exact frequency (technically impossible) it would still not produce coherent light. Why? Because all you're doing is forcing the light into one frequency. Over a small enough/finite time period, that light will be coherent, but over time, it won't be. Photon production is random for such a source, and the superposition of all the waves produced will vary over time, and consequently this doesn't represent a spatially coherent wave: the waveform shape will vary wildly over time.

2 (Single slit coherence))
My explanation for diffraction is going to be a bit crude and frankly someone else might explain it better, but I'll try. You're going to need to keep in mind the "Huygens-Fresnel Principle," which states that each individual point on a wave front acts as a source of wavelets, i.e. can be modelled as the source for a new spherical wave. That's fancy speak for just saying you can model each point as a new source. This is covered in AQA, idk about OCR or the other boards, though.

Name:  1231241251.PNG
Views: 16
Size:  80.8 KB
Consider your messy source of wave fronts (i.e. bottom part of the diagram I've given...)

By using a very thin slit, you're slicing off a very thin section of wave front from that messy curved mess of a wave fronts you get from superposition of lots of individual photons. Those curved fronts vary over time: they're spatially incoherent, due to the random nature of your source, but slicing off a very finite part of it will give you something flat to work with across the slit. That's the point of a thin slit. At any point in time, if the slit is thin enough, the wave front hitting it will be flat across the width of the slit.

In the diagram I've given, they're using a pinhole. The pinhole is just a thin slit with no height to it: let's just focus on the diffraction we're interested in occurring orthogonal to the length of the slit.

Now, what we've reduced the problem to is something like this:
Name:  123123123123.png
Views: 13
Size:  7.0 KB
a very thin slit, with a flat wave front hitting it. You model each point on that wave front as a source of wavelets (as I've drawn) and if you combine the effect of all the wavelets, you're going to get a wave front emanating from the slit, which is perfectly flat, and will spread out as a spherical wave with a smooth surface.

Note that this doesn't give temporal coherence, where each successive wave front is separated from the previous one by the same period. The slit just improves spatial coherence.

I've tried to make the explanation work for AS/A... hopefully that helps a bit? The only other way I know is more math-y... ;-;

As for the bit about two sources... same argument. They're not spatially coherent, because ultimately the random nature of photon production involved will yield a time-varying phase relationship between the two, which doesn't abide our definition of coherence. That's the short of it. I've covered the single source above.

3)
Can't read the formula, but likely worth considering any derivations. A lot of these formulae ignore sines/cosines involved, which a curved screen can rectify the errors associated with, if I recall the things Poon was saying back in our labs.

4)
Standing waves I'm guessing. Should be in phase if I recall... bit concerning they're not. If not standing waves, idk. Opposite side of node = antiphase.

5)
Moving in phase. Same frequency, same phase relationship between them all, they reach max displacements at same time.

6)
Drag, attenuation, whatever else. I never did acoustic physics but if we're just talking the string stopping it's motion, it dissipates energy naturally. The waves aren't ideal, and nothing is perfect as in theory: drag exists, etc.
tysmmm xxx
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