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Jetzt kostenlos anmeldenWhen two waves superimpose one over the other, their sum produces a different wave in terms of amplitude. This new wave has a different mathematical representation and results in a different shape.
The attributes of a wave are the amplitude ‘A’, the frequency ‘f’, and the phase ‘θ’. The amplitude indicates the excursion of the wave, the frequency is the number of oscillations per unit time (usually a second), and the phase is the position of the wave in space relative to a reference point.
To clarify the ideas and concepts behind amplitude, frequency, and phase, let’s examine an example where we have the sinusoidal functions \(\sin (x)\) and \(\sin{(x + \frac{\pi}{2})}\). Both have the same shape because the amplitude and frequency are the same. But let’s have a look at their graphs:
The phase is different, which causes a backward shift of the second wave (in black). We notice the shift because the point where the function passes from zero isn’t the origin anymore. This is very important because it changes the way the waves overlap.
We study phase differences with the help of a reference point. In the graph above, the reference point is taken as zero. The phase angle of the red wave sin (x) is zero and can be shown as sin (x+0). The starting point of the wave, therefore, is the same as the reference point with no phase difference.
For the black wave, however, the phase difference is positive (+ \(\frac{\pi}{2}\)), which means that the origin of the wave (its starting point) is said to be ‘before’. On the graph, it can be seen to the left of the reference point. When the phase difference is negative, the origin of the wave is said to be ‘after’ the reference point. On the graph, it would, therefore, be to the right of the reference point.
If we add up two identical waves, the resulting amplitude doubles:
\[\sin (x) + \sin (x) = 2 \sin (x)\]
While mathematically obvious, have a look at what it means visually, with two sinusoids one above the other, as in figure 2.
The points that have the same x coordinate also have the same amplitude. Applying the sum causes the wave to stretch. Where the amplitude was 1, it is now 2, and where it was -1, it is now -2. This is called constructive interference. An example from everyday life is two speakers playing the same track. The volume of the music perceived is maximum when the waves produced by the speakers are in phase, interfering constructively.
When the waves have different phases, the result of the superposition changes, especially if they are in phase opposition or counter-phase when every point is added to one of the opposite value, e.g., 1 + (-1), as in the graph below.
The sum of these waves is zero due to destructive interference. Notice how, in this case, the phase causes the same result as the negative sign before the function.
\(\sin (x - \frac{\pi}{2}) + sin (x + \frac{\pi}{2}) = 0\)
\(\sin (x - \frac{\pi}{2}) - \sin (x - \frac{\pi}{2}) = 0\)
We defined the two ends of the line. In between, there are all the combinations of the two waves. The phase of the resulting wave is shifted to somewhere between the phases of the interfering waves, depending on their amplitudes, and the value of its amplitude will be between zero and twice the amplitude of the interfering waves.
We talked about the interference between one-dimensional waves. The same phenomenon occurs when the propagation happens along two or more dimensions. In this case, two waves interfere and create an interference pattern.
When two stones are thrown into a lake, with one being thrown from a slightly different spot close to the one from which the first stone was thrown, a bi-dimensional wave forms on the surface of the water. In this scenario, the surface of the water gets corrugated but still exhibits a regularity, hence the name of this type of interference.
In the image, two circular waves propagate towards each other at an angle of \(\frac{\pi}{2}\). The wave fronts interfere almost orthogonally, giving the water a grid-shaped surface. The lines of the grid are points of destructive interference, while between them, there are points of constructive interference.
Destructive interference is the kind of interference that causes two waves to subtract each other.
Interference is the phenomenon that occurs when two waves collide with each other.
Interference is when two waves collide with each other. There are two types of interference: constructive and destructive interference.
Two waves collide, creating a wave that is the sum of the two.
If we add up two identical waves, which of the following will happen?
The resulting amplitude will double.
If two waves with the same amplitudes are in phase opposition, what will be their resulting amplitude?
Zero.
When two waves in phase opposition interfere with each other, what kind of interference occurs?
Destructive interference.
When the propagation happens along two or more dimensions, two waves interfere and create …
An interference pattern.
Which of the following is a definition for the frequency of a wave?
It is the number of oscillations per unit time.
When two or more waves overlap each other at one point, the total displacement caused at that point is the sum of individual displacements caused by the waves at that point.
What is the name of this phenomenon?
Superposition.
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