A radio station operating at 102.2 MHz broadcasts from two identical antennae at

Question

A radio station operating at 102.2 MHz broadcasts from two identical antennae at the same elevation but separated by 7.0-m horizontal distance (d in the diagram below). 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, at what other angle(s) is a maximum signal detected? What about a minimum signal? Assume all measurements are made much farther than 7 meters from the antenna towers.

Explanation / 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, n = c/f = 3*10^8m/s / 102.2*10^6Hz = 2.9354m

Locate other maxima at angular separation using the Double-slit (source) equation ..

theta(rad) n/a .. (a = source separation)

theta(rad) (2.9354m) / 7.0m = 0.4193 rad = 24.0 deg

Maxima occur at angular intervals of 24 deg either side of the central maxima at 0 degree both in-front and behind the antennae.

Minima occur also at an angular separation of 24 deg. having the same separation as maxima but starting at 12 deg either side of 0 deg to place them mid-way between the maxima.(ie. 12 deg, 36 deg, 60 deg ..)

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