Twin Source Interference - Radio Towers

[elemis]

Homework Statement

http://www.mediafire.com/view/?09c89b8986u5zls

The above is a question from my problem sheet. I've got no idea how to attack this since its been very poorly explained in my lecture handouts.

Can someone please help me ?

 

[Simon Bridge]

The problem is basically Young's interference - you can look it up online.

 

[elemis]

The problem is basically Young's interference - you can look it up online.

Could you please just give me a quick run down of the theory or how to approach the question ?

 

[Simon Bridge]

Two waves will add together
sometimes the addition will make the wave bigger, sometimes smaller, sometimes it will make the wave disappear completely ... the first is "constructive interference" and the last is "destructive interference".

in 2D, if the wave sources are in-phase, then the maxima will occur at locations of constructive interference - i.e. 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

The approach to the question is by analogy with 2-slit interference.
The radio towers are the slits.

 

[elemis]

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

dsinθ=mλ

2λsinθ=mλ

sinθ ≈ θ ≈ 0, 0.5, 1, 1.5, 2 etc.

Theta is in radians correct ?

For destructive :

θ≈m/2 where m = 1,3,5,7 etc.

a)Moving the sources closer together means a wider gap between each fringe ?

b)Higher λ means wider fringe spacing ?

c)The central fringe which is normally a maxima will be a minima... What else would happen ?

Also, how could I calculate the positions of the maxima and minima if the sources have a phase difference of pi ?

 

[Simon Bridge]

dsinθ=mλ

2λsinθ=mλ

sinθ ≈ θ ≈ 0, 0.5, 1, 1.5, 2 etc.

Theta is in radians correct ?

Yep - unless otherwise specified, theta is [ialways[/i] in radians.

For destructive :

θ≈m/2 where m = 1,3,5,7 etc.

You should show your reasoning - why those numbers?
Didn't you include some of those numbers in your previous answer for the maxima angles?

a)Moving the sources closer together means a wider gap between each fringe ?
b)Higher λ means wider fringe spacing ?

Again - show your reasoning.

c)The central fringe which is normally a maxima will be a minima... What else would happen ?

hat about the angles for the maxima and minima?

Also, how could I calculate the positions of the maxima and minima if the sources have a phase difference of pi ?

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?

 

[elemis]

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?

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.

Again - show your reasoning.

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

hat about the angles for the maxima and minima?

I'm not really sure :s Please help me !

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?

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 ?

 

[Simon Bridge]

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.

but aren't 1,3,5... etc integers too?

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

That works ... you could also have used the angle formula since you don't have a screen in this case.

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 ?

You need to go back to the derivation of the formulae and rework them for the phase difference.
That is the break-down for you: it's geometry.
The point of the exercise is to get you to do this so you will understand the phenomena: physics is not about memorizing and applying equations.