Two radio antennas are 130 m apart on a north-south line. The two antennas radia

Question

Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a frequency of 5.5 MHz. All radio measurements are made far from the antennas. The smallest angle, reckoned north of east from the antennas, at which destructive interference of the two radio waves occurs, is closest to: Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a frequency of 5.5 MHz. All radio measurements are made far from the antennas. The smallest angle, reckoned north of east from the antennas, at which destructive interference of the two radio waves occurs, is closest to: 6.1° 12° 9.1° 15° 18°

Explanation / Answer

use the condition

   a sin =( m+0.5)

   where

   a = 130 m

   m = 1

   if v is the velocity of light and n isfrequency then we know that

   v = n

   v = 3 x 108 m / s

   = v / n

=( 3 x 108 m / s)/(5.5x106 Hz)

= 54.5o

Now calculate the angle,

a sin =( m +0.5)

  = sin-1 ((m+0.5) /a)

= sin-1 (0.5*54.5/130 )

=12o

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