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?

 

[kyle8921]

I would like to clarify a few things before providing a response to the content. Firstly, electromagnetic waves are a form of energy that do not require a medium to travel through. They can travel through vacuum and are characterized by their frequency, wavelength, and amplitude. Therefore, the statement "Suppose the station has two antennas separated by 80m" may be misleading as the distance between the antennas does not affect the frequency or wavelength of the electromagnetic waves being emitted.

Moving on to the questions, for part a) the phase difference between the signals at a point north of the two antennas would depend on the distance of the point from each antenna and the wavelength of the electromagnetic waves. In this case, if the point is 20m from antenna s1 and 100m from antenna s2, the phase difference would be 12.56 degrees or 0.213 radians, as you have calculated.

For part b), 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 would depend on the distance of the points from each antenna. However, since both points are at the same distance from the center of the antennas, the ratio would be 1. This is because the intensity of an electromagnetic wave decreases with distance from the source, and since both points are equidistant from the antennas, the intensity would be the same.

For part c), the phase difference required for the maximum intensity in the antenna radiation pattern to lie on the line running from North-East to South-West would depend on the distance of the point from each antenna, the wavelength of the electromagnetic waves, and the angle of the line from North-East to South-West. Without knowing these values, it is not possible to calculate the exact phase difference. However, in general, to achieve maximum intensity in a specific direction, the phase difference between the signals from the two antennas needs to be adjusted in such a way that the waves combine constructively in that direction. This can be achieved by changing the distance between the antennas, the wavelength of the waves, or by using a phase shifter.