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 👍