Two radio antennae radiating in phase

In summary, you'll want to set r_2 = Y+X and r_1=X, in order to get r_2 - r_1 > 0 (otherwise you'll get a negative wavelenght).
  • #1
sghaussi
33
0
hii guys! I'm having trouble with a homework and I was wondering if you could explain something to me. Here's the problem:


Two radio antennas A and B radiate in phase. Antenna B is a distance of X meters to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of Y meters to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.

What is the longest wavelength for which there will be destructive interference at point Q?



I know I want to use the formula: (r2 - r1) = (m + 1/2)lamda

my r2 is the distance from B to Q which is Y meters
my r1 is the distance from A to Q which is Y + X meters

I'm trying to solve for lamda, but I don't know what m is. I know m has to do with "the longest wavelength" but I'm not sure how to calculate it. Or is it 0? I was guessing it would be 0 or 1. The book isn't clear. I hope you can help me!
 
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  • #2
sghaussi said:
hii guys! I'm having trouble with a homework and I was wondering if you could explain something to me. Here's the problem:


Two radio antennas A and B radiate in phase. Antenna B is a distance of X meters to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of Y meters to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.

What is the longest wavelength for which there will be destructive interference at point Q?



I know I want to use the formula: (r2 - r1) = (m + 1/2)lamda

my r2 is the distance from B to Q which is Y meters
my r1 is the distance from A to Q which is Y + X meters

I'm trying to solve for lamda, but I don't know what m is. I know m has to do with "the longest wavelength" but I'm not sure how to calculate it. Or is it 0? I was guessing it would be 0 or 1. The book isn't clear. I hope you can help me!

You'll want to set r_2 = Y+X and r_1=X, in order to get r_2 - r_1 > 0 (otherwise you'll get a negative wavelenght).

Ok, where does the formula (r2 - r1) = (m + 1/2)lamda for destructive interference comes from? Let's try to understand it. It says that if the difference of the distances r_2 and r_1 is 1/2, 3/2, 5/2, etc. of the wavelenght, then we'll have destructive interference. Why? Because then the waves will arrive at point Q completely out of phase (completely = phase difference of pi), like illustrated here: http://scienceworld.wolfram.com/physics/DestructiveInterference.html

Ok, that explanation sucked. But the formula says that we have destructive interference at point Q whenever [itex]r_2-r_1 = (m+1/2)\lambda[/itex] where [itex]m=0,1,2,3,...[/itex]. Here, r_2 - r_1 = X, so the formula tells us that we have destructive interference whenever

[tex]X = (m+1/2)\lambda \Leftrightarrow \lambda = \frac{X}{m+1/2}[/tex]

For which m between 0,1,2,3,... is lambda the biggest?
 
Last edited:
  • #3
Thanks, that really clears things up, however I'm still confused a little. So by looking at the formula that equals lambda, I would assume that when m = 0, is when lambda is the greatest right? however the answer i am getting is still incorrect. Am i not understanding you correctly?
 
  • #4
sghaussi said:
Thanks, that really clears things up, however I'm still confused a little. So by looking at the formula that equals lambda, I would assume that when m = 0, is when lambda is the greatest right?
That's what I'd say too.


sghaussi said:
however the answer i am getting is still incorrect. Am i not understanding you correctly?
The answer is not 2X? What do they say it is?
 
  • #5
okay.. my last comment.. ignore it, i wrote too soon! it was my fault i kept entering the wrong numbers in my calculator. thanks so much!
 
  • #6
:biggrin:

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1. What is the purpose of having two radio antennae radiating in phase?

Having two radio antennae radiating in phase allows for constructive interference, which can significantly increase the strength and range of the radio signal. This can be especially useful for long-distance communication.

2. How does having two radio antennae radiating in phase affect the radio signal?

Having two radio antennae radiating in phase results in a stronger and more focused radio signal. This is because the waves from each antenna are aligned and reinforce each other, rather than canceling each other out.

3. Is it necessary for the two radio antennae to be in the exact same location?

No, the two radio antennae do not have to be in the exact same location, but they should be relatively close to each other in order to maintain the phase alignment and achieve constructive interference.

4. Can two different types of radio antennae be used for this setup?

Yes, two different types of radio antennae can be used as long as they both have the ability to radiate in phase. However, it is typically more effective to use two identical antennae for better synchronization.

5. Are there any drawbacks to using two radio antennae radiating in phase?

One potential drawback is the increased complexity and cost of setting up and maintaining two antennae. Additionally, if the antennae are not properly aligned, it can result in destructive interference and a weaker signal.

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