Question

Two radio antennas are 110 m apart on a north-south line. The two antennas radiate in phase at a frequency of 3.3 MHz. All radio measurements are made far from the antennas. The smallest angle, reckoned east of north from the antennas, at which constructive interference of two radio waves occurs, is closest to:

Answer 1

The difference in path length between the two antennas for an observer in quadrant I would be:

ΔL = d*Cos(θ)

You can check this by letting θ=0 (i.e. the observer is north of the stations), so ΔL should be d, or 110 m.

The wavelength is:

λ = c / f = 2.9989*10^8 / 3.3*10^6 = 90.875m

Constructive interference occurs when the path difference is equal to an integer multiple of a wavelength. At the given spacing, and from an observation point north of the stations, they are more than a wavelength apart,

so they are not in constructive interference. Looking for the first peak:

d*Cos(θ) = λ

Cos(θ) = λ/d

θ = arcCos(λ/d) = arcCos( 90.875 / 110 ) = 34.296°