Two radio antennas A and B radiate in phase at a frequency of 15 MHz. Antenna B

Question

Two radio antennas A and B radiate in phase at a frequency of 15 MHz. Antenna B is 120 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.

Part 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.

Part 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.

Explanation / Answer

given that

f = 15*10^6 Hz

distance b/w A and B= 120m

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

distance b/w A and Q   AQ = x

distance b/w B and Q BQ = 120-x

The path length difference is AQ-BQ = x- 120 +x = 2x-120

part (A)

For constructive interference, the path length difference must be an even number of half wavelengths . the waves meet in phase. so

n*lambda/ 2 = 2x -120

where n = even number

n*20 /2 = 2x-120

x = 120+10 n /2

x = 60 + 5 n

for the smallest nonzero value of x, n should be smallest .

smallest even number n =2

x = 70 m

part(B)

For destructive interference, the path length difference must be an odd number of half wavelengths . the waves meet out of phase.so
n*lambda /2 = 2x-120

5n = x - 60

x = 60 + 5n

for the smallest nonzero value of x, n should be smallest .

smallest even number n =1

x = 65 m

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