Two radio antennas radiating in phase are located at points A and B, middot. a r

Question

Two radio antennas radiating in phase are located at points A and B, middot. a radio receiver antennas are emitting radio waves with a frequency of 5.80 MHz. Consider a radio receiver being moved from point B along a line perpendicular to the line connecting A and B(line BC shown in the figure). Question: At what locations along line BC will constructive a destructive interference occur? In terms of the distance d from point B, how far does & the radio signal from A have to travel? In terms of the distance d from point B, what is the path difference delta r between the signals from A and B. Write down an equation for delta r that will result in constructive interference. Then solve this equation to find all locations along line BC at which constructive interference occurs (and how many such locations). Go back to part b and write down an equation for delta r that will result in destructive interference. Then solve this equation to find all locations along line BC at which destructive interference occurs (and how many such locations).

Explanation / Answer

wave length = c/f = (3*10^8)/(5.8*10^6) = 51.72 m

(a)

rA = sqrt(d^2+200^2)

(b)

rB = d

c)

path difference dr = rA - rB

path difference = m*lambda

for m = 1

sqrt(d^2+200^2) - d = 51.72

d = 361 m

for m = 2

sqrt(d^2+200^2) - d = 2*51.72

d = 142 m

for m = 3

sqrt(d^2+200^2) - d = 3*51.72

d = 51.3 m

(d)

path difference dr = rA - rB

path difference = m*lambda/2

for m = 1

sqrt(d^2+200^2) - d = 51.72/2

d = 760.5 m

for m = 3

sqrt(d^2+200^2) - d = 3*51.72/2

d = 219 m

for m = 5

sqrt(d^2+200^2) - d = 5*51.72/2

d = 90.03 m

for m = 7

sqrt(d^2+200^2) - d = 7*51.72/2

d = 20 m

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