Understanding Waves: Questions on Phase Differences and Interference Patterns

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Homework Help Overview

The discussion revolves around understanding wave phenomena, specifically phase differences and interference patterns in the context of radio waves and a double-slit experiment. The original poster presents two distinct problems related to these topics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the phase difference at a detector based on given distances and phase shifts. They also explore the separation of bright fringes in a double-slit experiment with two different wavelengths. Some participants question the validity of the original poster's approach and reasoning regarding the interference of different wavelengths.

Discussion Status

The discussion includes attempts to clarify the original poster's calculations and reasoning. Some participants provide tips to guide the original poster in their approach to the problems, indicating a collaborative effort to explore the concepts without reaching a definitive solution.

Contextual Notes

The original poster mentions that the first question is part of an online test, which may impose constraints on the type of assistance they can receive. There is also a suggestion that the two wavelengths may not produce interference due to their differences, which is under consideration.

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1.
Sources A and B emit long-range radio waves of wavelength 320 m, with the phase of the emission from A ahead of that from source B by 90°. The distance rA from A to a detector is greater than the corresponding distance rB from B by 82 m. What is the magnitude of the phase difference at the detector?


2.
In a double-slit experiment the distance between slits is 5.2 mm and the slits are 0.82 m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 450 nm, and the other due to light of wavelength 580 nm. What is the separation in meters on the screen between the m = 4 bright fringes of the two interference patterns?



The first one is actually an online-test question. I have tried 3 times using the method from the textbook, but i still haven't got the right answer. Can anyone help me? THANKS!
 
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You understand, don't you, that you have to show what you have done yourself?
 
HallsofIvy said:
You understand, don't you, that you have to show what you have done yourself?

Hello! What i have done for the first question is:
devide the wave length 320m by 4, since A is 90° ahead (a quarter of a cycle)
then I take 82m away from it, since the wave from source A goes 82m further
finally i just take the ratio of the phase difference with the wavelength and multiply the result by 2π in order to convert the unit to radian.

is it correct?
 
i can't do the second one. i thought the 2 lights will not have any bright fringes, because the wavelengths are different, double-slit interference will not occur...
do you think so?
 
Tips:
1. How much is A in front of B? (90 deg)
How big is the phase difference between A and B just because wave A has to travel longer?

2. For both 450 nm and 580 nm a double-slit interference will occur. What distance for m=4 at 450 nm and what distance for the 580 nm wave?
 
I've got the answers now! thanks!
 

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