Two radio antennas A and B radiate in phase. Antenna B is a distance of 100 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. Required:
a. What is the longest wavelength for which there will be destructive interference at point Q?
b. What is the longest wavelength for which there will be constructive interference at point Q?

a. 200 m

b. 100 m

Explanation:

Solution:-

- We will first draw three points marked A,B and Q from left most to right most.

- We are told that the antennas at A and B radiate in phase. This means the radio-waves emitted by each antenna are synchronous in terms of ( frequency and wavelength ).

- We will denote the common wavelength of coherent sources of radio-waves ( A and B ) with λ.

- The relation between the wavelength ( λ ) and the path difference between the source and observation point ( Q ) for the case of destructive interference is:

                             AQ - BQ = n*λ/2

Where,

             n: The order of wavelength

             AQ: The distance between antenna A and point Q

             BQ: The distance between antenna B and point Q

- The point Q is positioned ( 100 + 50 ) m away from antenna A and 50 m from antenna B. Hence,

                            150 - 50 = n*λ/2

- To determine the longest wavelength ( λ ) to meet destructively at point Q with the given path difference. The order of wavelength ( n ) must be minimum ( 1 ). Therefore,

                           100 = λ/2

                           λ = 200 m   Answer

- The relation between the wavelength ( λ ) and the path difference between the source and observation point ( Q ) for the case of constructive interference is:

                             AQ - BQ = n*λ

Where,

             n: The order of wavelength

             AQ: The distance between antenna A and point Q

             BQ: The distance between antenna B and point Q

- The point Q is positioned ( 100 + 50 ) m away from antenna A and 50 m from antenna B. Hence,

                            150 - 50 = n*λ

- To determine the longest wavelength ( λ ) to meet constructively at point Q with the given path difference. The order of wavelength ( n ) must be minimum ( 1 ). Therefore,

                           100 = λ

                           λ = 100 m   Answer

answer would be letter choice (a),   a ball resting on a shelf. would be another example of potential energy   >   stored energy > not moving.

a ball spinning on a finger   >   kinetic energy > moving energy

a ball rolling on the ground   >   kinetic energy   > moving energy

a   ball flying through the air   > kinetic energy   >   moving energy

hope that                                         : )