Two radio antennas A and B radiate in phase. Antenna B is a distance of 130 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 50.0 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.(a) What is the longest wavelength for which there will be destructive interference at point ?(b) What is the longest wavelength for which there will be constructive interference at point ?

constructive  λ = 130 m

destructive  λ = 260 m

Explanation:

a) the expression for constructive interference is that the difference in amino is equal to a multiple of the average wavelength

                   AQ - BQ = 2m λ/ 2       m = 0, 1, 2, ...

Where

     AQ = 130 +50 = 180 m

     BQ = 50 m

To find the smallest wavelength let's use m = 1

                       180 - 50 = 2 1 λ/ 2

                        λ = 130 m

b) for destructive interference

                 AQ –BQ = (2m + 1) λ/2

The smallest value is for m = 0

                  130 = λ / 2

                  λ = 260 m

they should be similar or the same