Two radio antennas are separated by 1.20 m . Both broadcast identical 750 MHz waves.
If you walk around the antennas in a circle of radius 10.0 m , how many maxima will you detect?
I already asked this but the explanation was vague and did not get me any closer to the answer. I don’t know how the hell to set this up and I’ve drawn it every which way, even using a compass to try and figure it out. At this point I just need to get the answer before midnight. Bonus if you can explain it in terms an imbecile like me can understand.
Thank you.
1 Answer

I know you saw this question, since you left a comment:
https://answers.yahoo.com/question/index?qid=20120…
“a” is what you need to calculate — it is the distance from the center of the speakers to an amplitidemaximum hyperbola. So the distance between the two hyperbolas is 2a, and you need this to be an integer number of wavelengths:
2a = nλ
λ = v / f = 3e8m/s / 750e6/s = 0.4 m
so
a = nλ/2 = n * 0.4m / 2 = n * 0.2m
The distance from the center of the speakers either speaker is d = 0.6 m, and we need to find out if there exists a hyperbola such that
b² = d² – a²
n = 1 → a = 0.2 m → b = √(0.6² – 0.2²) m = 0.57 m
n = 2 → a = 0.4 m → b = √(0.6² – 0.4²) m = 0.45 m
n = 3 → a = 0.6 m → b = √(0.6² – 0.6²) m = 0 m ← I don’t think this one counts
So that tells me there are two amplitudemaxima hyperbolas (on each side of the speaker arrangement) and two points on each hyperbola that lie on the circle, for a total of 8 maxima. ◄
I borrowed heavily from @OssiG’s work — let me know if it’s right. I’ve tried to solve these problems using trig with limited success.
Hope this helps!