Two radio antennas A and B radiate in phase. Antenna B is a distance of 120m to

Question

Two radio antennas A and B radiate in phase. Antenna B is a distance of 120m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40.0m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.

Part A

What is the longest wavelength for which there will be destructive interference at point Q?

Express your answer using two significant figures.

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Part B

What is the longest wavelength for which there will be constructive interference at point Q?

Express your answer using two significant figures.

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Two radio antennas A and B radiate in phase. Antenna B is a distance of 120m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40.0m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.

Part A

What is the longest wavelength for which there will be destructive interference at point Q?

Express your answer using two significant figures.

SubmitMy AnswersGive Up

Part B

What is the longest wavelength for which there will be constructive interference at point Q?

Express your answer using two significant figures.

SubmitMy AnswersGive Up

Explanation / Answer

AQ = 110+50=160m
BQ = 50m
The path length difference is AQ-BQ = 110m.

For destructive interference, the path length difference must be an odd number of half wavelengths so the waves meet out of phase:
? /2 =110 or
3? /2 =110 or
5? /2 =110
etc.
The biggest value of ? satisfying this is when ?/2 =110, so ? =220m (agreed).

For constructive interference, the path length difference must be an even number of half wavelengths (i.e. a whole number of wavelengths) so the waves meet in phase:
? =110 or
2? =110 or
3? =110
etc.
The biggest value of ? satisfying this is when ? =110m

(In fact the 50m distance is not used. The whole of the extended line AB till be a nodal line or an antinodal line.)

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