Question

Two radio antennas are 140 m apart on a north-south line. The two antennas radiate in phase at a frequency of 5.2 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:

28

Answer 1

the setup is similar to the yoing double slit experiment

we have to find minimum alpha, meaning maximum

here sin() = m/d

wavelength () = 3*10⁸/5.2*10⁶ m

=57.7m

for m =1
sin() = 1*57.7/140

= 24.3

for m = 2
= 55.5

for m = 3
it not possible as m*/d becomes more then 1

so, maximum angle it can go upto 55.5 degrees (this is from horizontal line)

so from north in east direction the corresponding angle is = 34.5 degrees

so answer is 34