(Solved) Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a ...

Chery

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7 years ago

Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a ...

Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a frequency of 3.6 MHz. All radio measurements are made far from the antennas. What is the smallest angle, reckoned east of north from midway between the antennas, at which constructive interference of two radio waves occurs? (c = 3.00 × 108 m/s)
A) 50°
B) 55°
C) 45°
D) 40°
E) 35°

Textbook

College Physics

Edition: 1^st

Authors: Etkina, Gentile, Van Heuvelen

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Chery Author

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7 years ago

Looked all over the internet for this, thank you for answering correctly

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azmair b.

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2 years ago

thanks my guy

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Enni C.

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2 years ago

I just had a similar question with different numbers:

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°

My answer:

use the condition

   a sinθ =( m+0.5) λ

   where

   a = 130 m

   m = 1

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

   v = n λ

   v = 3 x 108 m / s

   λ = v / n

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

= 54.5o

Now calculate the angle,

a sinθ =( m +0.5)λ

  θ= sin-1 ((m+0.5) λ/a)

= sin-1 (0.5*54.5/130 )

=12o

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