Two radio antennas radiating in phase are located at points A and B, d = 195 m a

Question

Two radio antennas radiating in phase are located at points A and B, d = 195 m apart (see figure below). The radio waves have a frequency of 5.62 MHz. A radio receiver is moved out from point B along a line perpendicular to the line connecting A and B (line BC shown in the figure below). At what distances from B will there be destructive interference? (Note: The distance of the receiver from the sources is not large in comparison to the separation of the sources, so the equation dsin = ( m + a (m-0, ±1, ±2, ) does not apply. Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) blank. Eter None tns sinuti rthatn in the oure below) o

Explanation / Answer

distance travelled by waves from B to receiver = rB

distance travelled by waves from A to receiver = rA = sqrt(rB^2 + d^2)

pathe difference = dr = rA - rB

dr = sqrt(rB^2 + d^2) - rB

for destructive interference

dr = (m + 1/2 )*lambda

lambda = wavelength = c/f = 3*10^8/(5.62*10^6) = 53.4 m

for first constructive interference

m = 0

sqrt(rB^2 + 195^2) - rB = (0 + 1/2)*53.4

rB = 698.7 m

m = 1

rB = 197.3 m

m = 2

rB = 75.7 m

m = 3

rB = 8.28 m

8.28 m

75.7 m

197.3 m

698.7 m

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