Twin Source Interference - Radio Towers

In summary, the conversation is about Young's interference and the approach to solving a problem related to it. Two waves can add together in different ways, leading to constructive or destructive interference. The maxima and minima occur at specific angles, and the distance between sources and wavelength can affect the interference pattern. The conversation also discusses the role of phase difference in interference. The listener is seeking clarification and guidance in understanding the concept.
  • #1
elemis
163
1

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 ?
 
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  • #2
The problem is basically Young's interference - you can look it up online.
 
  • #3
Simon Bridge said:
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 ?
 
  • #4
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.
 
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  • #5
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

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 ?
 
  • #6
elemis said:
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?
 
  • #7
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?

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.

Simon Bridge said:
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

Simon Bridge said:
hat about the angles for the maxima and minima?

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

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?

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 ?
 
  • #8
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.
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.
 

FAQ: Twin Source Interference - Radio Towers

1. What is Twin Source Interference?

Twin Source Interference is a phenomenon that occurs when two radio towers, broadcasting on the same frequency, are located close to each other. The overlapping signals from the two towers create interference, resulting in poor reception for listeners.

2. How does Twin Source Interference affect radio reception?

Twin Source Interference can cause distortion, static, and even complete loss of signal for listeners. The overlapping signals create a "dead zone" where the two towers' signals cancel each other out, leading to poor reception in that area.

3. What causes Twin Source Interference?

Twin Source Interference is caused by the overlapping of radio signals from two towers broadcasting on the same frequency. This can occur when the towers are too close to each other, or when the signals are not properly synchronized.

4. How can Twin Source Interference be reduced?

To reduce Twin Source Interference, the two towers need to be spaced further apart or their signals need to be synchronized. Other solutions include using different frequencies for each tower or adjusting the power of the signals to minimize overlap.

5. Is Twin Source Interference a common problem?

Yes, Twin Source Interference is a common issue in areas with multiple radio towers broadcasting on the same frequency. It can also occur in areas with tall buildings or structures that can reflect or block the radio signals, causing interference. However, advancements in technology have allowed for better synchronization and signal management, reducing the impact of Twin Source Interference in modern times.

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