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July 23, 2025, 02:37:57 am
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Author Topic: interesting question :)  (Read 10599 times)  Share 

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kamil9876

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interesting question :)
« on: June 07, 2009, 01:02:58 am »
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Two radio antennas are seperated by 2.0m. Both broadcast identical 750MHz waves. If you walk around the antennas in a circle of radius 10m(im assuming about the midpoint of the line segment connecting the two antennas) , how many maxima will you detect? 8-)
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

evaporade

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Re: interesting question :)
« Reply #1 on: June 14, 2009, 04:27:18 pm »
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20 in/out of phase
« Last Edit: June 14, 2009, 04:30:32 pm by evaporade »
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methodsboy

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Re: interesting question :)
« Reply #2 on: June 14, 2009, 04:30:57 pm »
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OMG have u already started unit 4 work?
im assuming this is relevant to unit 4?
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kamil9876

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Re: interesting question :)
« Reply #3 on: June 14, 2009, 08:23:13 pm »
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Quote from: evaporade on June 14, 2009, 04:27:18 pm
20 in/out of phase

yes. can you prove it?
Quote from: evaporade on June 14, 2009, 04:27:18 pm
20 in/out of phase

Correct, but can you prove it? My friend was also able to get the answer but his proof had a gap. I actually spent more time on this step than the other parts.
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

evaporade

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Re: interesting question :)
« Reply #4 on: June 14, 2009, 08:36:43 pm »
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Consider in phase. Look between the two antennas (2.0 m), max are separated by 0.2 m because wavelength is 0.4 m. So there are 9 antinodal plane between antennas. Also 2 along the line joining them. Total 2x9+2=20 maxima around.

Out of phase by 180 deg (for simplicity): 10 antinodal plane between antennas. Total 2x10=20 maxima around.

This is an explanation, not a proof.
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kamil9876

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Re: interesting question :)
« Reply #5 on: June 14, 2009, 09:29:33 pm »
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Yes. The way i did it was that I realised that If I find how many there are in one quadrant, I can just multiply by 4 due to symmetry (and subtract any that lie in both quadrants to avoid double counting). And that the biggest path difference is 2m, while the smallest is 0. So I *assumed* that in that one quadrant u get 2/0.4 +1 different maximums since there are that many multiples of 0.4 in the range [0,2]. However how do you know that say, 0.4 does not appear twice? This way you show that the answer is at least 20, but doesn't show that there may be more due to repeats.
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."
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