Two antennas located at points A and B are broadcasting radio waves of frequency
ID: 2167506 • Letter: T
Question
Two antennas located at points A and B are broadcasting radio waves of frequency 95.0 MHz, perfectly in phase with each other. The two antennas are separated by a distance d= 12.40 m. An observer, P, is located on the x axis, a distance x= 63.0 m from antenna A, so that APB forms a right triangle with PB as hypotenuse.(a)What is the phase difference between the waves arriving at P from antennas A and B?
(b)Now observer P walks along the x axis toward antenna A. What is P's distance from A when he first observes fully destructive interference between the two waves?
(c)If observer P continues walking until he reaches antenna A, at how many places along the x axis (including the place you found in the previous problem) will he detect minima in the radio signal, due to destructive interference?
Explanation / Answer
?L = (2n + 1)*?/2. ........(1) Find the wavelength of the radio wave. The first destructive interference will occur when ?L = ?/2. Now ?L = sqrt(9.3^2 +x^2) - x...(2) Put ?L = ?/2 and solve for x. Repeat the procedure for ?L = 3?/2, 5 ?/2......until x becomes negative.