Finding the max wavelength for two waves to interfere destructively

In summary, the time it takes for each wave to travel between two points with different refractive indices is calculated by dividing the distance by the speed of light in the respective medium. The maximum wavelength for destructive interference can be found using the equation for destructive interference, where the distance between the points is equal to the wavelength. In this case, the maximum wavelength in vacuum would be 4.7 x 10^-7 m.
  • #1
Sleve123
20
0

Homework Statement



i) Two waves travel between two points along paths that have the same length 4.7 x 10^-7 m, one travels in a medium having a refractive index of 3.5 while the other travels through a vacuum, how long does in take for each wave to travel between the points?

ii) If the two waves interfere destructively as the second point what is the max wavelength of the wave in the vacuum?


Homework Equations



i) Speed of Wave in Vacuum / Speed of Wave in Medium = Refractive Index

Time = Distance / Speed
ii) ASin(omega x time vacuum) + Asin(omega x time medium) = 0 ??

The Attempt at a Solution



i) time in vacuum = 4.7 x 10^-7 / 3 x10^8 = 1.57 fs

time in medium is 3.5 times longer therefore equals 5.49 fs

ii) This is where I get stuck, I've tried with that equation to find the points at which the amplitudes of the waves sum up to zero, I've done this in excel and I get the max wavelenght in a vacuum to be five times the distance between the points, but I'm not really sure how to go about htis question.
 
Physics news on Phys.org
  • #2

I would like to address your questions regarding the two waves traveling between two points with different refractive indices.

For the first question, your calculations for the time it takes for each wave to travel between the points are correct. The time in vacuum would indeed be 1.57 fs, and the time in the medium would be 5.49 fs. This is because the speed of light in a medium is slower than in vacuum, and the refractive index is a measure of how much slower it is.

For the second question, the equation you have written is not the correct one for finding the maximum wavelength. Instead, you can use the equation for destructive interference, which is given by:

2d = (m + 1/2)λ

Where d is the distance between the two points, m is the number of nodes (points where the waves cancel out) and λ is the wavelength. In this case, since the waves are traveling the same distance, the distance between the points is equal to the wavelength. So, for destructive interference to occur, the wavelength in vacuum must be equal to the distance between the points.

Therefore, the maximum wavelength in vacuum would be 4.7 x 10^-7 m. This would result in a destructive interference at the second point, as the wavelength in the medium would be 3.5 times longer.

I hope this helps clarify your understanding. Please let me know if you have any further questions.



Scientist
 

What is destructive interference between two waves?

Destructive interference occurs when two waves meet and their amplitudes cancel each other out. This results in a decrease or complete absence of the overall amplitude of the wave.

How do you calculate the maximum wavelength for two waves to interfere destructively?

The maximum wavelength for destructive interference is calculated by using the formula λ = 2d/n, where λ is the maximum wavelength, d is the distance between the two wave sources, and n is the number of nodes (points of destructive interference) between the sources.

What is the relationship between the distance between two wave sources and the maximum wavelength for destructive interference?

The distance between two wave sources and the maximum wavelength for destructive interference are inversely proportional. This means that as the distance between the sources increases, the maximum wavelength for destructive interference decreases, and vice versa.

Can the maximum wavelength for destructive interference ever be larger than the distance between the two wave sources?

No, the maximum wavelength for destructive interference can never be larger than the distance between the two wave sources. This is because the maximum wavelength is limited by the number of nodes between the sources, which cannot exceed the distance between the sources.

What happens if the maximum wavelength for destructive interference is equal to the distance between the two wave sources?

If the maximum wavelength for destructive interference is equal to the distance between the two wave sources, the waves will completely cancel each other out at all points between the sources. This is known as complete destructive interference.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
831
  • Introductory Physics Homework Help
Replies
5
Views
922
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
722
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
917
  • Introductory Physics Homework Help
Replies
1
Views
826
Replies
3
Views
2K
Replies
5
Views
912
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top