1. Two radio antennas A and B radiate 2.0-m waves in phase with each other. Ante

Question

1. Two radio antennas A and B radiate 2.0-m waves in phase with each other. Antenna B is 6.0 in to the right of antenna A. Observer 1 is 8.0 m away from antenna B and observer 2 is 21.0 m away from antenna B. What is the phase difference between the signals from both antennas at each observer's position if (a) both observers lie along the line connecting the antennas to the right of antenna B? (b) both observers lie directly in front of antenna B along the line perpendicular to the line connecting the antennas?

Explanation / Answer

Wavelength, w = 2m

(a) For Observer 1:

Path difference, L = 6m

Phase difference = 2*pi*L/w = 6*pi

Effectively this is zero phase difference as it is an even multiple of 2*pi

For Observer 2:

Path difference, L = 6m

Phase difference = 2*pi*L/w = 6*pi

Effectively this is zero phase difference as it is an even multiple of 2*pi

(b)

For Observer 1:

Path difference, L = (62 + 82 )0.5 - 8 = 2m

Phase difference = 2*pi*L/w = 2*pi

Effectively this is zero phase difference as it is an even multiple of 2*pi

For Observer 2:

Path difference, L = (62 + 212 )0.5 - 21 = 0.84 m

Phase difference = 2*pi*L/w = 0.84*pi

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