Phase difference in a two slit interference problem

In summary, the problem involves two sources emitting long-range radio waves with a wavelength of 390 m. Source A is ahead of source B by 90° in phase. The distance from source A to detector D is 130 m greater than the distance from source B. The goal is to find the phase difference at point D. To solve this problem, we can apply the double slit equation and consider the path difference between the two sources. Starting with the assumption that the two waves started off in phase, we can work out the phase difference at point D.
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DODGEVIPER13
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Homework Statement


In the figure below, sources A and B emit long-range radio waves of wavelength λ = 390 m, with the phase of the emission from A ahead of that from source B by 90°. The distance rA from A to detector D is greater than the corresponding distance rB by 130 m. What is the phase difference at D? The image is at : http://www.webassign.net/hrw/hrw7_35-38.gif


Homework Equations


Δphase = 2∏L/λ(n2 - n1)
dsin(theta) = mλ

The Attempt at a Solution


Not really sure what to do I plugged 130m into L and used the given lamda and ignored n2-n1 this did not work, help me. I assume I need to use the above two slit equation but I am not sure.
 
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  • #2
DODGEVIPER13 said:

Homework Statement


In the figure below, sources A and B emit long-range radio waves of wavelength λ = 390 m, with the phase of the emission from A ahead of that from source B by 90°. The distance rA from A to detector D is greater than the corresponding distance rB by 130 m. What is the phase difference at D? The image is at : http://www.webassign.net/hrw/hrw7_35-38.gif

Homework Equations


Δphase = 2∏L/λ(n2 - n1)
dsin(theta) = mλ

The Attempt at a Solution


Not really sure what to do I plugged 130m into L and used the given lamda and ignored n2-n1 this did not work, help me. I assume I need to use the above two slit equation but I am not sure.

It is not generally a good strategy to ignore part of an equation in the hopes that the rest of it will be relevant to you but that part will not. Instead, think about how the double slit equation is derived: the idea is that you get a maximum brightness if the path difference to the screen from points A and B is some multiple of a full wavelength (assuming the two sources start off in phase). This problem relates to the same physical principle too. First start by answering the following: if the two waves started off in phase, would they end up in phase at point D given the information you have? Then, work out the slightly more complicated case of not starting out in phase.
 

FAQ: Phase difference in a two slit interference problem

What is phase difference in a two slit interference problem?

Phase difference refers to the difference in the phase of two waves at a particular point in space. In the case of a two slit interference problem, it is the difference in the phase of the waves passing through two parallel slits and interfering with each other.

How is phase difference calculated in a two slit interference problem?

Phase difference is calculated by taking the difference between the path lengths of the two waves. This can be done by measuring the distance between the two slits and the point of interference, as well as the wavelength of the waves.

What is the significance of phase difference in a two slit interference problem?

Phase difference determines whether the waves will interfere constructively or destructively. If the phase difference is an integer multiple of the wavelength, the waves will interfere constructively and create bright fringes. If the phase difference is a half-integer multiple, the waves will interfere destructively and create dark fringes.

How does the distance between the slits affect the phase difference in a two slit interference problem?

The distance between the slits affects the path length difference and therefore the phase difference. As the distance between the slits increases, the path length difference and phase difference also increase, resulting in a wider interference pattern.

Can the phase difference be manipulated in a two slit interference problem?

Yes, the phase difference can be manipulated by changing the distance between the slits, the wavelength of the waves, or the angle of incidence. This can be used to control the interference pattern and create different fringes.

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