Wave Superposition and Interference Drawing Urgent Help !

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#1
Hello, I have a few questions which I think are related to the superposition of waves. Although I have attempted to fully answer the question I am not sure if I have been able to draw the correct interference.

The question asks to draw the resulting wave for the situations 1 second later. I have attached the diagram provided in the question.

I understand that when two waves meet each will try to cause a wave displacement at the point of intersection according to its phase. The net effect is such that the overall displacement is the vector sum of the displacements caused by the individual waves. Following the encounter the waves will pass through each other as the energy progresses in the original direction of travel.
However, if this superposition occurs over an extended space as opposed to a single point a continuous wave is produced that is the sum of the displacements over the time in each location. If two waves are in phase, they constructively interfere producing a larger amplitude resultant wave, whereas if they are out-of -phase they destructively interfere, producing a zero-amplitude wave. The principle of adding displacements of overlapping waves is called the principle of superposition.
When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
I am having difficulty since the displacement axis is not labelled in the first two situations, so I do not know how to infer the displacements of the waves without this information?Although, maybe this is unnecessary as a plot of displacement vs distance is used to depict the physical scale of the oscillations and the movement of the energy of the waves.

1. I believe that the resultant displacement of the first situation will result in partial destructive interference. The question states to drawn the situation 1 second later, and as both waves are moving with a speed of 3ms^-1, then the first wave beginning at 0m will travel 3m to the right to a distance of 7m while the second wave will travel a distance of 3m to the left, to a distance of 4m. The waves appear to have the same amplitude but the waves are out of phase and have a displacement in the opposite directions. meaning they will destructively interfere to produce a zero amplitude wave between 4-7m. However, as the waves do not interfere between 3-4 m and 7-8m they will exhibit their typical displacements at these positions.

2. I believe the resultant wave is an example of constructive interference, as after 1 second the wave beginning at 0m will travel 3m to the right to a distance of 3m while the wave beginning at 7m will travel 3m to the left to a distance of 4m. The waves will interfere between 4-7m where they are in phase. Consequently, when the peaks and troughs of the pulses coincide, the amplitude of the resultant pulse is the sum of the amplitudes of the individual pulses, being twice the amplitude of the individual waves.

3. After 1 second the first wave will travel 2m to the left, to a distance of 4m while the second wave will travel a distance of 4m to the right, to a distance of 3m.
The since the displacement of the waves in the opposite directions they will destructively interfere. However, as shown here the two interfering waves do not need to have equal amplitudes in opposite directions for destructive interference to occur. The resulting displacement during the overlap between 3 and 4 m can be calculated by:
Amplitude of (A + B) = amplitude of A – amplitude of B
Amplitude of (A + B) = 0.4-0.2
Amplitude of (A + B) =0.2 m

I am not sure if I have correctly drawn the diagrams by exhibiting the waves continuing their individual displacements in areas where the waves do not overlap, i.e. in situation 3 between a distance of 4-5m.

Sorry, I know that I am a little confused,I just need to practise this topic to better become accustomed to it therefore I would be incredibly appreciate of any insight or help 👍
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1 year ago
#2
I may be able to help but if anyone else wants to input their suggestions I don't mind. Where is the image?

Edit - I see it now
Last edited by lauren.studies; 1 year ago
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1 year ago
#3
I'm going through it myself bit by bit so to me it looks like you got the first one right. Now I'll try the others
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1 year ago
#4
For the second one you are right , but it's not all constructive interference, can you see that?
Last edited by lauren.studies; 1 year ago
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1 year ago
#5
(Original post by Alexandramartis)
Hello, I have a few questions which I think are related to the superposition of waves. Although I have attempted to fully answer the question I am not sure if I have been able to draw the correct interference.

The question asks to draw the resulting wave for the situations 1 second later. I have attached the diagram provided in the question.

I understand that when two waves meet each will try to cause a wave displacement at the point of intersection according to its phase. The net effect is such that the overall displacement is the vector sum of the displacements caused by the individual waves. Following the encounter the waves will pass through each other as the energy progresses in the original direction of travel.
However, if this superposition occurs over an extended space as opposed to a single point a continuous wave is produced that is the sum of the displacements over the time in each location. If two waves are in phase, they constructively interfere producing a larger amplitude resultant wave, whereas if they are out-of -phase they destructively interfere, producing a zero-amplitude wave. The principle of adding displacements of overlapping waves is called the principle of superposition.
When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
I am having difficulty since the displacement axis is not labelled in the first two situations, so I do not know how to infer the displacements of the waves without this information?Although, maybe this is unnecessary as a plot of displacement vs distance is used to depict the physical scale of the oscillations and the movement of the energy of the waves.

1. I believe that the resultant displacement of the first situation will result in partial destructive interference. The question states to drawn the situation 1 second later, and as both waves are moving with a speed of 3ms^-1, then the first wave beginning at 0m will travel 3m to the right to a distance of 7m while the second wave will travel a distance of 3m to the left, to a distance of 4m. The waves appear to have the same amplitude but the waves are out of phase and have a displacement in the opposite directions. meaning they will destructively interfere to produce a zero amplitude wave between 4-7m. However, as the waves do not interfere between 3-4 m and 7-8m they will exhibit their typical displacements at these positions.

2. I believe the resultant wave is an example of constructive interference, as after 1 second the wave beginning at 0m will travel 3m to the right to a distance of 3m while the wave beginning at 7m will travel 3m to the left to a distance of 4m. The waves will interfere between 4-7m where they are in phase. Consequently, when the peaks and troughs of the pulses coincide, the amplitude of the resultant pulse is the sum of the amplitudes of the individual pulses, being twice the amplitude of the individual waves.

3. After 1 second the first wave will travel 2m to the left, to a distance of 4m while the second wave will travel a distance of 4m to the right, to a distance of 3m.
The since the displacement of the waves in the opposite directions they will destructively interfere. However, as shown here the two interfering waves do not need to have equal amplitudes in opposite directions for destructive interference to occur. The resulting displacement during the overlap between 3 and 4 m can be calculated by:
Amplitude of (A + B) = amplitude of A – amplitude of B
Amplitude of (A + B) = 0.4-0.2
Amplitude of (A + B) =0.2 m

I am not sure if I have correctly drawn the diagrams by exhibiting the waves continuing their individual displacements in areas where the waves do not overlap, i.e. in situation 3 between a distance of 4-5m.

Sorry, I know that I am a little confused,I just need to practise this topic to better become accustomed to it therefore I would be incredibly appreciate of any insight or help 👍
Right idea from the 3rd one. From the image I see that the wave moving at 4ms^-1 has an amplitude of -0.1m? if that is correct what would the superposed wave's amplitude be between the distance of 5-6m? You have the right idea though.
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#6
(Original post by lauren.studies)
Right idea from the 3rd one. From the image I see that the wave moving at 4ms^-1 has an amplitude of -0.1m? if that is correct what would the superposed wave's amplitude be between the distance of 5-6m? You have the right idea though.
Thank you very much for your replies.

1. Excellent thank you very much, do you think I can improve my diagram in anyway? In the sense that it is peculiar that the wave is not fully destructively interefering and there are still aspects which exhibit their individual displacements.

2. Oh, is there only constructive interference between a distance of 4-8m, while the first wave maintains its individual amplitide between a distance of 3-4m?

3. I was uncertain of the third situation, if the wave moving at 4ms^-1 had a displacement of -0.1m or -0.2m as it appears as if the labelling was slightly amiss on the displacement axis, where otherwise it had been increasing in increments of 0.2m?

If however, the wave travelling at 4ms^-1 had a displacement of -0.1m then;
Amplitude of (A + B) = amplitude of A – amplitude of B
Amplitude of (A + B) = 0.4-0.1
Amplitude of (A + B) =0.3 m

The resultant wave would have a displacement of 0.3m across a distance of 3-4m while the part of the wave travelling at 4ms^-1 which does not interfere with the wave travelling at 2ms^-1 would mainatin its original displacment of -0.1m acroass a distance of 4-5m. Would this be correct? I also noticed that I made a mistake in my original answer as I showed that the 2m^-1 wave travelled a distance of 1m not 2m in 1 second, so I have amended this diagram also. I have produced and attached diagrams of both scenarios.
Thank you very again for your responses 👍😁
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1 year ago
#7
(Original post by Alexandramartis)
Thank you very much for your replies.

1. Excellent thank you very much, do you think I can improve my diagram in anyway? In the sense that it is peculiar that the wave is not fully destructively interefering and there are still aspects which exhibit their individual displacements.

2. Oh, is there only constructive interference between a distance of 4-8m, while the first wave maintains its individual amplitide between a distance of 3-4m?

3. I was uncertain of the third situation, if the wave moving at 4ms^-1 had a displacement of -0.1m or -0.2m as it appears as if the labelling was slightly amiss on the displacement axis, where otherwise it had been increasing in increments of 0.2m?

If however, the wave travelling at 4ms^-1 had a displacement of -0.1m then;
Amplitude of (A + B) = amplitude of A – amplitude of B
Amplitude of (A + B) = 0.4-0.1
Amplitude of (A + B) =0.3 m

The resultant wave would have a displacement of 0.3m across a distance of 3-4m while the part of the wave travelling at 4ms^-1 which does not interfere with the wave travelling at 2ms^-1 would mainatin its original displacment of -0.1m acroass a distance of 4-5m. Would this be correct? I also noticed that I made a mistake in my original answer as I showed that the 2m^-1 wave travelled a distance of 1m not 2m in 1 second, so I have amended this diagram also. I have produced and attached diagrams of both scenarios.
Thank you very again for your responses 👍😁
You should draw the waves combined , so you need to show what the waves looks like when the waves have superposed each other not as separate waves. I hope that you understand what I'm trying to say
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#8
(Original post by lauren.studies)
You should draw the waves combined , so you need to show what the waves looks like when the waves have superposed each other not as separate waves. I hope that you understand what I'm trying to say
Thank you for your reply. Yes, I believe that I do understand, would this mean as the question is asking for the depiction of the resultant wave that for example in situation 1 I would only draw the destructive interference between a distance of 4-7m as the resultant wave?

For situation 2 the resultant wave would be limited to the constructive interference between a distance of 4-8m?

For sitauation 3 the resultant wave would be limited to a distance of 4-5m (I am still uncertain whether the original displcament of the 4ms^-1 wave is supposed to be; either -0.1m or -0.2m?) 😁
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1 year ago
#9
(Original post by Alexandramartis)
Thank you for your reply. Yes, I believe that I do understand, would this mean as the question is asking for the depiction of the resultant wave that for example in situation 1 I would only draw the destructive interference between a distance of 4-7m as the resultant wave?

For situation 2 the resultant wave would be limited to the constructive interference between a distance of 4-8m?

For sitauation 3 the resultant wave would be limited to a distance of 4-5m (I am still uncertain whether the original displcament of the 4ms^-1 wave is supposed to be; either -0.1m or -0.2m?) 😁
I think you are right, yes. For situation 3 , I wouldn't really worry - if you've got the idea. In the exam if a question came up like this (Which I'd doubt it will because it's a quite easy type of thing compared to other topics, probably worth 1/2 marks) the axis would be drawn out a lot more clearly. I think if something were to come up like this (I do AQA) I'd expect it to come into a multiple choice question.
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#10
(Original post by lauren.studies)
I think you are right, yes. For situation 3 , I wouldn't really worry - if you've got the idea. In the exam if a question came up like this (Which I'd doubt it will because it's a quite easy type of thing compared to other topics, probably worth 1/2 marks) the axis would be drawn out a lot more clearly. I think if something were to come up like this (I do AQA) I'd expect it to come into a multiple choice question.
Thank you for your reply and your help. Yes, I too suspect this would appear as a multiple choice question. Thank you again for all of your help I really appreciate it 👍😊
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