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.
I know you saw this question, since you left a comment:
“a” is what you need to calculate — it is the distance from the center of the speakers to an amplitide-maximum 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
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 amplitude-maxima 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!