How Do Antenna Phase Differences Affect Radio Wave Intensity and Direction?

[sapiental]

Homework Statement

1. Tune the Antenna Consider an AM radio station broadcasting at the frequency 1500
kHz, and wavelength 200 m.. Suppose the station has two antennas separated by 80m, one north
of the other.
a) (2 pts.) If the two antennas broadcast their signals in phase with each other, what is the phase
difference (in radians) of the radio waves arriving at a point north of the two antennas?
b) (4 pts.) If the two antennas broadcast their signals in phase with each other, what is the ratio
of the intensity of the radio signal at a point north of the antennas to the intensity east of the
midpoint between the antennas? (Both at the same long distance from the center of the antennas.)
c) (4 pts.) Suppose we want the maximum intensity in the antenna radiation pattern to lie on the
line running frm North-East to South-West, 45 degrees from north. What must be the phase difference
between the signals broadcast from the two antennas?



a) phase difference = (2pi/wavelength)(r2-r1)

I picked the point 20m from s1 and 100m from s2 so

phase difference = (2pi/wavelength)(100m-80m) = 12.56deg or .213rad

b) I kept the same point for the one north of the antennas. since they say from the midpoint east; 40m and then I did 40m to the east or -x.

I = I_o cos^2 (phase dif/2)

North point intensity = I = I_o cos^2 (12.56/2)

East from mindpoint = I = I_o cos^2 (0)

so the ratio is 1?

c) Help please :)

 

[OlderDan]

You did not do exactly what you said you did in part a) Try that again. I assume you need to fix a) to do b), so take another look at that. For c) you need to delay the signal from one antenna so that the signals are in phase along a "front" that is perpendicular to the direction of maximum intensity. Find the extra distance one signal has to go and compare that to a wavelength (similar to part a). What time phase shift do you need to compensate for the path difference?