Vectors, superposition and interference of waves

In summary, the difference in the magnitudes of two vectors, r2 and r1, that share the same horizontal displacement is due to the directional factor and the fact that they lay along different paths. This difference becomes apparent when taking the square root of the squared magnitudes of r2 and r1.
  • #1
Gear300
1,213
9
I ran into this problem while working on superposition and interference of waves...its bugging the crap out of me...mind hasn't been working well lately...

A horizontal line intersects a vertical line to form a quadrant with the intersection being the origin. There are 2 vectors, r1 and r2, that extend from the same point on the horizontal line to 2 different points, y1 and y2, on the vertical line (r2 being higher than r1). Breaking each vector into their components, one would notice that both share the same horizontal displacement. Therefore, deltar = r2 - r1 = (y2 - y1)j, j being the vertical unit vector. However, when taking r2 = sqr(x^2 + y2^2) and r1 = sqr(x^2 + y1^2) (sqr being a square root function), r2 - r1 is equal to something different from r2 - r1. Why does this difference exist?
 
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  • #2


ಠ_ಠ??
 
  • #3


Gear300 said:
I ran into this problem while working on superposition and interference of waves...its bugging the crap out of me...mind hasn't been working well lately...

A horizontal line intersects a vertical line to form a quadrant with the intersection being the origin. There are 2 vectors, r1 and r2, that extend from the same point on the horizontal line to 2 different points, y1 and y2, on the vertical line (r2 being higher than r1). Breaking each vector into their components, one would notice that both share the same horizontal displacement. Therefore, deltar = r2 - r1 = (y2 - y1)j, j being the vertical unit vector. However, when taking r2 = sqr(x^2 + y2^2) and r1 = sqr(x^2 + y1^2) (sqr being a square root function), r2 - r1 is equal to something different from r2 - r1. Why does this difference exist?

Because you are comparing the magnitudes of two vectors, that by definition lay along different paths. The Vector subtraction yields the vector of magnitude Y2 - Y1. The difference in the hypotenuses don't apply.
 
  • #4


I see...its due to the directional factor...
 

1. What is a vector in regards to waves?

A vector in regards to waves is a quantity that has both magnitude and direction. It is often used to represent the displacement or direction of a wave's movement.

2. What is superposition of waves?

Superposition of waves is the principle that states when two or more waves meet, the resulting wave is the sum of the individual waves. This can lead to constructive or destructive interference depending on the waves' amplitudes and phases.

3. How does interference of waves occur?

Interference of waves occurs when two or more waves meet and overlap in space. The resulting wave is determined by the superposition of the individual waves and can either amplify or cancel out the individual waves' amplitudes.

4. What is the difference between constructive and destructive interference?

Constructive interference occurs when two waves meet and their amplitudes combine to create a larger amplitude. Destructive interference occurs when two waves meet and their amplitudes cancel out, resulting in a smaller or zero amplitude.

5. How are vectors used to represent the interference of waves?

Vectors are used to represent the displacement and direction of a wave's movement, which is essential in calculating the resulting wave from interference. By understanding the direction and magnitude of each wave, the resulting wave can be accurately determined using vector addition.

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