Path length differences/ interference problem

So, for minimum disturbance, the path length difference should be a half wavelength. Therefore, the only possible answer is III. In summary, the correct answer is III. The path length difference of 1.5λ will result in a minimum disturbance at a particular point P on the surface of the water.
  • #1
YMMMA
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Homework Statement


In the figure below, Two wave sources, M and N, are vibrating in phase on the surface of water and generate waves of wavelength λ. Which of the following values for the distances MP and NP will result in minimum disturbance at a particular point P on the surface of the water?

MP NP
I 5λ 5λ
II 5λ 6λ
III 5λ 6.5λ

Homework Equations


ΔL= mλ
ΔL= (m+½)λ

Where L is path length and m is an integer.

The Attempt at a Solution



[/B]I am not really sure if minimum disturbance means arriving out of phase (destructive interference).
If so, then the only possible answer is III. ΔL=1.5λ. Is that correct?
 

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  • #2
YMMMA said:
I am not really sure if minimum disturbance means arriving out of phase (destructive interference).
If so, then the only possible answer is III. ΔL=1.5λ. Is that correct?
Yes, sounds good to me. Minimum disturbance means the lowest amplitude of a wave at that point, which would be when they destructively interfere.
 
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FAQ: Path length differences/ interference problem

1. What is the concept of path length differences in interference?

Path length differences refer to the difference in distance traveled by two or more waves in an interference pattern. This difference can affect the phase of the waves and result in constructive or destructive interference.

2. How does path length differences affect the visibility of interference fringes?

When the path length difference between two waves is a multiple of the wavelength, the waves will be in phase and produce constructive interference, resulting in visible interference fringes. On the other hand, if the path length difference is not a multiple of the wavelength, the waves will be out of phase and produce destructive interference, making the fringes less visible or even invisible.

3. What factors can cause path length differences in interference?

Path length differences can be caused by various factors such as the angle of incidence, the medium through which the waves are traveling, and any obstacles or barriers in the path of the waves. These factors can alter the distance traveled by the waves, resulting in a difference in path length.

4. How can path length differences be minimized in interference experiments?

To minimize path length differences, careful alignment of the sources and the experimental setup is necessary. The use of a monochromatic light source can also help reduce variations in path length as all the waves will have the same wavelength. Additionally, using a vacuum or an optically dense medium can also minimize the impact of path length differences.

5. What are some real-life applications of path length differences in interference?

Path length differences and interference phenomena have applications in various fields such as optics, acoustics, and telecommunications. For example, in fiber optic communication, path length differences are carefully controlled to ensure efficient signal transmission. In optics, path length differences are used in interferometers to measure small changes in distance, and in acoustics, they are utilized in noise-canceling technology.

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