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25 February, 22:05

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?

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  1. 25 February, 22:18
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    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 °.
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