Phase Difference Homework: Find Magnitude of Phase Difference at Detector

AI Thread Summary
The problem involves two radio wave sources, A and B, with a 90° phase difference and a distance discrepancy of 140 m. The initial phase difference from source A is equivalent to 0.25 wavelengths, while the distance difference translates to approximately 0.2545 wavelengths. The calculated net phase difference at the detector was initially reported as -0.732 radians, but this was identified as incorrect due to an oversight in the calculations. After consulting a friend, the error was recognized as a simple mistake, leading to a corrected understanding of the problem. Accurate calculations are essential for determining the phase difference in wave interference scenarios.
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Homework Statement


Sources A and B emit long-range radio waves of wavelength 550 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 140 m. What is the magnitude of the phase difference at the detector?


Homework Equations





The Attempt at a Solution




Initially, source A leads source B by 90°, which is equivalent to \frac{1}{4} wavelength.
However, source A also lags behind source B since rA is longer than rB by 140 m, which is \frac{140}{550}=0.2545 wavelength. So the net phase difference between A and B at the
detector is -0.732 Rad.

This is wrong though, can someone help me =D
 
Last edited:
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How'd you come up with -0.732 rad? It looks like you completely ignored one of the terms.
 
To be honest I'm not sure.
I have tried everything I can think off but all my answers are wrong.
 
Thank you for your time but I asked a friend and he showed me. It was just a stupid mistake that I missed thank yiu
 

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