A radio station operating at 106.9 MHz broadcasts from two identical antennae at
ID: 1498773 • Letter: A
Question
A radio station operating at 106.9 MHz broadcasts from two identical antennae at the same elevation but separated by a 8.75 m horizontal distance d, as seen in the figure beloe. A maximum signal is found along the midline, perpendicular to d at its midpoint and extending horizontally in both directions. If the midline is taken as 0 deg, what is the smallest angles theta where a maximum signal is detected? Assume all measurements are made much farther than 8.75 m from the antenna towers.
What is the second smallest angle theta where a maximum signal is detected?
What is the smallest angle where a minimum signal is detected?
What is the second smallest angle where a minimum signal is detected?
Antenna1 Midline Antenna 2Explanation / Answer
The maxima signals are points where constructive interference occurs between radio waves from the two source antennae (the central maxima being at 0º)
Wavelength = c/f = 3.0*10^8m/s/106.9*10^6Hz = 2.806 m
Locate other maxima at angular separation using the Double-slit (source) equation ..
(rad) /a .. (a = source separation)
(rad) (2.806m) /8.75m = 0.3207 rad = 18.37º
Maxima occur at angular intervals of 18.37º either side of the central maxima at 0º .. both in-front and behind the antennae.
Minima occur also at an angular separation of 18.37º.. having the same separation as maxima but starting at 9.185º either side of 0º to place them mid-way between the maxima.(ie. 9.185º,27.555º, 45.925º ..)