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theneedtoknow
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Homework Statement
2 sources emitting radio waves of the same frequency are placed at x=0 meters and x = 1.2 meters. There are nodes at x= 0.344m, x= 0.719m, and x=1.094m. What is the frequency of the 2 sources and the difference in their phase constant
Homework Equations
The Attempt at a Solution
Well i know that maximum destructive interference occurs for every 2pi increase in the difference in phase of the waves
The difference in phase is:
dФ = 2Pi (dr)/wavelength + dФ0
where dr is r2 - r1 = difference in radial distance between each source and the point in question
now here is my problem:
since dФ0 stays the same, it means that there will be a node for every increase in dr equal to one wavelength
however, if i use those points mentioned above to find the radial difference for each point, i get
dr1 = 0.512
dr2 = 0.238
dr3 = 0.988
so each one of these nodes has an increase in phase difference of 2Pi from the previous
so taking the 2 with lower drs :
dФ1 = 2Pi (0.238)/wavelength + dФ0
dФ2 = 2Pi (0.512)/wavelength + dФ0 = dФо+ 2Pi
dФ2 - dФ1 = 2 pi = 2pi (0.512)/wavelength - 2Pi (0.238)/wavelength
wavelength = 0.512 - 0.238
so the difference between 2 consecutive nodes should give me the wavelength
...but these are not evenly spaced, so if i use the 2nd set of points instead i get a different result (0.988 - 0.512 = 0.476) so I don't get it, where is my thinking going wrong?