Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs?

the smallest angle from the antennas is 47.3°

Explanation:

We first need to write the expression for the relation between the wavelength (λ) and the frequency (f) of the wave, and then solve for the wavelength.

Therefore, the relation is:

λ = c / f

where

c is the speed of light constant λ is the wavelength f is the frequency

Thus,

λ = (3 * 10⁸ m/s) / (3.4 MHz)

= (3 * 10⁸ m/s) / (3.4 MHz) (10⁶ Hz/1 MHz)

= 88.235 m

Therefore, the smallest angle measured (from the north of east) from the antennas for the constructive interference of the two-radio wave can be calculated as

θ = sin⁻¹ (λ / d)

where

d is the distance between the two radio antennas

Thus,

θ = sin⁻¹ (88.235 / 120)

θ = 47.3 °

Therefore, the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs is 47.3 °.