Question

Two radio antennas A and B radiate in phase at a frequency of 15 MHz. Antenna B is 115 m to the right of antenna A. Consider point Q along the line connecting the antennas, a horizontal distance x to the right of antenna A.
A.)What is the smallest nonzero value of
x for which there will be constructive interference at point Q?
Express your answer in meters to two significant figures.
B.) What is the smallest nonzero value of
x for which there will be destructive interference at point Q?
Express your answer in meters to two significant figures.

Answer 1

distance travelled by wave from A r1 = x

distance travelled by wave from B , r2 = d - x

path difference = r2 - r1 = d - 2x

for constructive interference path difference = m*lambda

lambda = wavelength = c/f = 3*10^8/(15*10^6) = 20 m

115 - 2x = m*20

for m = 1

115 - 2x = 1*20

x = 47.5 m

for m = 2

115 - 2x = 2*20

x = 37.5 m

for m = 3

115 - 2x = 3*20

x = 27.5 m

for m = 4

115 - 2x = 4*20

x = 17.5 m

for m = 5

115 - 2x = 5*20

x = 7.5 m

for m = 6

115 - 2x = 6*20

x = -2.5 m

x is small for m = 5

A)

smallest non zero value of x = 7.5 m

(B)

for constructive interference path difference = (m + 1/2)*lambda

115 - 2x = m*20

for m = 0

115 - 2x = 1/2*20

x = 452.5 m

for m = 1

115 - 2x = (1+ 1/2)*20

x = 42.5 m

for m = 2

115 - 2x = (2+ 1/2)*20

x = 32.5 m

for m = 3

115 - 2x = (3 + 1/2)*20

x = 22.5 m

for m = 4

115 - 2x = (4 + 1/2)*20

x = 12.5 m

for m = 5

115 - 2x = (5 + 1/2)*20

x = 2.5 m

for m = 6

115 - 2x = (6 + 1/2)*20

x = -7.5 m

smallet value of x = 2.5 m <<<<==========ANSWER