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superposition principle; maxima and minima
I'm baffled. Anyone care to explain this to me?
Where two or more waves meet at a point, the sum of the total displacement is the sum of the individual displacements of each wave at that point. Errrmmm, constructive interference occur where you have a maxima, destructive interference occurs where you have a minima. ERRRRMM in terms of light diffraction experiments, constructive interference occurs where path differences between coherent light waves are in phase with each other, despite being out by whole wavelengths. Destructive occurs where light sources are out of phases by an odd number of 1/2 wavelengths (if im not mistaken) This explains the dark/bright fringes... Dude there is absolutely loads of stuff in this topic. My fingers hurt now so somebody else can take over.
Here's one way to look at it.
Here's a water wave in profile:
Think of each black dot as a molecule of water.
Here they are again, without the background colour:
Each of these water molecules is seriously attracted to his neighbouring friends - he loves them so much that he will follow them up or down. It's as if they're all attached by a string.
Now, here's that wave 1s later (this is a VERY slow wave!
), along with white dots to represent the position of the molecules 1s earlier.
Can you see that, altought the wave has clearly moved on, the molecules have not? All they do is move up and down according to which way they are pulled?
Now, think about what will happen when two waves meet? Which way will the molecules go?
If they are "in phase", the molecules will be pulled in the same direction at the same time, twice. It's no different to me and an evenly matched friend friend both trying to pull you over.
So what will happen if they're "out of phase". This is where my friend and I stand on opposite sides of you - he pushes, and I pull. Provided neither of us cheats, you'll feel a bit mistreated, but you won't move from your spot.
So can you extend that analogy to waves that are only partially in phase?
Once you've got all this stuff nailed, you're almost all of the way into understanding it all. Everything else just simplifies down to the same thing.
I apologise for the naff quality of my drawings, they were all knocked up rather quickly in MS Paint
Here's a water wave in profile:
Think of each black dot as a molecule of water.
Here they are again, without the background colour:
Each of these water molecules is seriously attracted to his neighbouring friends - he loves them so much that he will follow them up or down. It's as if they're all attached by a string.
Now, here's that wave 1s later (this is a VERY slow wave!
), along with white dots to represent the position of the molecules 1s earlier.Can you see that, altought the wave has clearly moved on, the molecules have not? All they do is move up and down according to which way they are pulled?
Now, think about what will happen when two waves meet? Which way will the molecules go?
If they are "in phase", the molecules will be pulled in the same direction at the same time, twice. It's no different to me and an evenly matched friend friend both trying to pull you over.
So what will happen if they're "out of phase". This is where my friend and I stand on opposite sides of you - he pushes, and I pull. Provided neither of us cheats, you'll feel a bit mistreated, but you won't move from your spot.
So can you extend that analogy to waves that are only partially in phase?
Once you've got all this stuff nailed, you're almost all of the way into understanding it all. Everything else just simplifies down to the same thing.
I apologise for the naff quality of my drawings, they were all knocked up rather quickly in MS Paint
Hot diggity
thank you everyone for your help, and I apologise for the ambiguity of the thread. I have revised this area of the syllabus a lot in the past couple of days and feel a bit more confident.
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hmmm. I thought the whole principle of superposition was the vector addition of the amplitude of the two intercepting waves.
but what I originally found perplexing was the actual definition of 'maxima' and 'minima'. For example, I understand that constructive reinforcement of coherent and in-phase waves causes maxima, but does minima mean that the two waves are completely in anti-phase and have equal amplitudes so that the destructive interference causes complete cancellation (as apposed to different amplitudes that would just result in a reduced amplitude resultant wave)?
--------------
uk6458
wave superpostion means when two waves are in the same place at the same time, when they meet.
hmmm. I thought the whole principle of superposition was the vector addition of the amplitude of the two intercepting waves.
but what I originally found perplexing was the actual definition of 'maxima' and 'minima'. For example, I understand that constructive reinforcement of coherent and in-phase waves causes maxima, but does minima mean that the two waves are completely in anti-phase and have equal amplitudes so that the destructive interference causes complete cancellation (as apposed to different amplitudes that would just result in a reduced amplitude resultant wave)?
Yellowmellow
but what I originally found perplexing was the actual definition of 'maxima' and 'minima'. For example, I understand that constructive reinforcement of coherent and in-phase waves causes maxima, but does minima mean that the two waves are completely in anti-phase and have equal amplitudes so that the destructive interference causes complete cancellation (as apposed to different amplitudes that would just result in a reduced amplitude resultant wave)?
"Maxima" are where the amplitude of the resultant wave is greatest, "Minima" are where it's least. As you say, when both waves have the same amplitude, this results in complete cancellation at the minima. It's still a minimum regardless of whether this is the case, so long as they are anti-phase
ok here's a scenario.
When both waves that have the same positive amplitude, but moving in opposite directions meeting, would they cancel?
When both waves that have the same positive amplitude, but moving in same directions meeting, what would happen?
When both waves that have the same positive amplitude, but moving in opposite directions meeting, would they cancel?
When both waves that have the same positive amplitude, but moving in same directions meeting, what would happen?
When both waves that have the same positive amplitude, but moving in opposite directions meeting, would they cancel? No
When both waves that have the same positive amplitude, but moving in same directions meeting, what would happen? Again, no cancelation. The amplitude of the combined waves at that point would be twice their individual amplitude.
You've misunderstood. Look at what I put before, the example of a molecule being pushed up or down. A positive amplitude pushes it up, a negative amplitude pushes it down. Direction of travel is immaterial, because the things which make up the wave DON'T travel .
For complete cancelation, you need two waves which look like this at an instant:
Then you get no displacement at all.
When both waves that have the same positive amplitude, but moving in same directions meeting, what would happen? Again, no cancelation. The amplitude of the combined waves at that point would be twice their individual amplitude.
You've misunderstood. Look at what I put before, the example of a molecule being pushed up or down. A positive amplitude pushes it up, a negative amplitude pushes it down. Direction of travel is immaterial, because the things which make up the wave DON'T travel .
For complete cancelation, you need two waves which look like this at an instant:
Then you get no displacement at all.
Here's some crappy diagram i drew in 2 minutes.
Constructive:
Destructive:
If you have to draw the resultant wave here's an easy way to do it. Go along the x axis and add up the amplitudes at each point. So for the constructive wave, at the peak both amplitudes are 1 so the resultant is 2. At the trough both amplitudes are -1 so resultant is -2.
Then for destructive at the first peak the other wave is a trough. 1+-1=0 so amplitude is 0. This is true across the waves so the resultant is just 0.
--------------
In the first example the waves would change from in phase to out of phase repeatedly over time. You would hear a throbbing sound if you were in their path.
The second one sound like you are describing a constructive wave. It would sound twice as loud.
Constructive:
Destructive:
If you have to draw the resultant wave here's an easy way to do it. Go along the x axis and add up the amplitudes at each point. So for the constructive wave, at the peak both amplitudes are 1 so the resultant is 2. At the trough both amplitudes are -1 so resultant is -2.
Then for destructive at the first peak the other wave is a trough. 1+-1=0 so amplitude is 0. This is true across the waves so the resultant is just 0.
--------------
lookenneth
ok here's a scenario.
When both waves that have the same positive amplitude, but moving in opposite directions meeting, would they cancel?
When both waves that have the same positive amplitude, but moving in same directions meeting, what would happen?
When both waves that have the same positive amplitude, but moving in opposite directions meeting, would they cancel?
When both waves that have the same positive amplitude, but moving in same directions meeting, what would happen?
In the first example the waves would change from in phase to out of phase repeatedly over time. You would hear a throbbing sound if you were in their path.
The second one sound like you are describing a constructive wave. It would sound twice as loud.
Hey it really helped me out.. Thanks!!
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