The discussion revolves around a problem related to interference patterns produced by twin radio towers, drawing parallels to Young's double-slit experiment. Participants express confusion regarding the theoretical background and mathematical treatment of the problem, which involves concepts of constructive and destructive interference.
There is an ongoing exploration of the problem, with participants seeking clarification on various aspects of the theory and its application. Some guidance has been offered regarding the use of formulas and the importance of understanding the underlying physics, but no consensus has been reached on the specific calculations or interpretations.
Participants note that the problem has been poorly explained in lecture materials, leading to uncertainty about the correct approach. There is also mention of the need to revisit foundational concepts related to interference and wave behavior.
Simon Bridge said:The problem is basically Young's interference - you can look it up online.
Simon Bridge said:Two waves will add together
sometimes the addition will make the wave bigger, sometimes smaller, sometimes it will make thre wave disappear completely ... the first is "constructive interference" and the second is "destructive interference".
in 2D, if the sources are in-phase, then the maxima will occur when the path-difference from each source is an integer number of whole wavelengths.
Have a look at:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html
Yep - unless otherwise specified, theta is [ialways[/i] in radians.elemis said:dsinθ=mλ
2λsinθ=mλ
sinθ ≈ θ ≈ 0, 0.5, 1, 1.5, 2 etc.
Theta is in radians correct ?
You should show your reasoning - why those numbers?For destructive :
θ≈m/2 where m = 1,3,5,7 etc.
Again - show your reasoning.a)Moving the sources closer together means a wider gap between each fringe ?
b)Higher λ means wider fringe spacing ?
hat about the angles for the maxima and minima?c)The central fringe which is normally a maxima will be a minima... What else would happen ?
From the physics ... the angle for a maxima is normally where the path difference is an integer number of whole wavelengths - what does the phase difference do to this condition?Also, how could I calculate the positions of the maxima and minima if the sources have a phase difference of pi ?
Simon Bridge said:Yep - unless otherwise specified, theta is [ialways[/i] in radians.You should show your reasoning - why those numbers?
Didn't you include some of those numbers in your previous answer for the maxima angles?
I've applied the formula x=λD/a where D is the distance from the screen and a is separation between the slits i.e. towersSimon Bridge said:Again - show your reasoning.
Simon Bridge said:hat about the angles for the maxima and minima?
Simon Bridge said:From the physics ... the angle for a maxima is normally where the path difference is an integer number of whole wavelengths - what does the phase difference do to this condition?
but aren't 1,3,5... etc integers too?elemis said:If m is allowed to take those values then we have a non-integer number of wavelengths and hence this meets the primary condition for destructive interference.
That works ... you could also have used the angle formula since you don't have a screen in this case.I've applied the formula x=λD/a where D is the distance from the screen and a is separation between the slits i.e. towers
You need to go back to the derivation of the formulae and rework them for the phase difference.I really don't know. I'm a FIrst year chemistry student who's been plunged back into all the interference stuff from school... stuff I never really enjoyed. Could you please break it down for me ?