Two-point source interference pattern

In summary, the conversation is about calculating the angles of the nodal lines in a pattern that is located far from the sources. The question asks for the calculation of θ' and the number of nodal lines to be solved for. The frequency is provided but it is unclear why. The person suggests using the formula dsinθn= (n - 0.5)λ to calculate the first two nodal lines, but encountered a domain error when trying to calculate the third nodal line. They also mention doing some web research for more information. The reason for providing the frequency is still unknown. The conversation ends with a suggestion to calculate sinθ3 to see what value is obtained.
  • #1
19
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Homework Statement
A two-point source operates at a frequency of 1.0 Hz to produce an interference pattern in a ripple tank. The sources are 2.5 cm apart and the wavelength of the waves is 1.2 cm.

Calculate the angles at which the nodal lines in the pattern are located far from the sources. (Assume the angles are measured from the central line of the pattern.)
Relevant Equations
λ = (xn/L)[d/(n - 0.5)]
dsinθn= (n - 0.5)λ
xn = perpendicular distance from the right bisector t o the point Pn on the nodal line
L = distance from midpoint between the two sources to the point Pn
n = number of the nodal line
d= separation of the sources
I'm having trouble understanding what it's asking me. "Calculate the angles at which the nodal lines in the pattern are located far from the sources." I assume they are very far away, making lines PnS1 and PnC parallel. Is the question asking me to calculate θ' in the example?

"nodal lines" should I solve for several different values of n? I was thinking of using dsinθn= (n - 0.5)λ to solve for θn since θn = θ' If that's right, for how many nodal lines do I do this? Also why would they provide the frequency? Attached in a diagram from a previous example.

20191116_130741.jpg
 
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  • #2
RippleNodes.png

Do some web research. There is a lot of useful stuff out there.
 
  • #3
So I used dsinθn= (n - 0.5)λ to solve for the first two nodal lines and got 13.8° for the first and 46° for the second. When I tried to to input 3 for n I got a domain error. Does that mean the third nodal line is greater than 90° and didn't strike the screen?

I also still don't know the reason why frequency is provided.
 
Last edited:
  • #4
benca said:
Does that mean the third nodal line is greater than 90° and didn't strike the screen?
What do you think? Calculate sinθ3 and see what you get.
benca said:
I also still don't know the reason why frequency is provided.
I don't know either.
 

1. What is a two-point source interference pattern?

A two-point source interference pattern occurs when two coherent waves, such as light or sound waves, interfere with each other. This results in a pattern of alternating bright and dark spots, known as interference fringes, which can be observed on a screen or detector.

2. How does the distance between the two sources affect the interference pattern?

The distance between the two sources, also known as the path difference, determines the spacing of the interference fringes. If the path difference is an integer multiple of the wavelength of the waves, the interference will be constructive and result in bright fringes. If the path difference is a half-integer multiple, the interference will be destructive and result in dark fringes.

3. What is the difference between constructive and destructive interference in a two-point source pattern?

Constructive interference occurs when the peaks of the two waves align and reinforce each other, resulting in a bright fringe. Destructive interference occurs when the peaks of one wave align with the troughs of the other wave, resulting in cancellation and a dark fringe.

4. How does changing the wavelength affect the interference pattern?

Changing the wavelength of the waves will change the spacing of the interference fringes. A shorter wavelength will result in fringes that are closer together, while a longer wavelength will result in fringes that are further apart.

5. What is the practical application of studying two-point source interference patterns?

Two-point source interference patterns have many practical applications, such as in the field of optics for creating diffraction gratings and in acoustics for studying sound waves. They are also used in interferometers, devices that measure small changes in distance or wavelength, and in the study of quantum mechanics.

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