Two linear antennas, located at a distance of 1 m

Two linear emitters installed parallel to the Z axis at a distance of 1 m from each other generate coherent electromagnetic waves at a frequency of 150 MHz. If the maximum intensity is observed in a direction forming an angle of 30° with the beam, what is the phase difference between the radiation of the antennas?

To determine the phase difference between antenna emissions, you can use the formula:

φ = 2π(d/λ)sinth

where φ is the phase difference, d is the distance between the emitters, λ is the wavelength, θ is the angle between the direction of radiation and the line perpendicular to the plane of radiation.

For this problem, wavelength λ = c/f, where c is the speed of light (310^8 m/s), f - radiation frequency (150 MHz = 15010^6 Hz). We get:

λ = c/f = 2 m

Thus, the distance between the emitters is d = 1 m, and the wavelength λ = 2 m.

Angle θ is 30°. We substitute all the values ​​into the formula and get:

φ = 2π(1/2)sin30° = π

Thus, the phase difference between the radiation of the antennas is π radians or 180 degrees.

Product Description: Two linear antennas Digital product Distance between antennas: 1 m These antennas are designed to generate coherent electromagnetic waves at a frequency of 150 MHz. The waves emitted by antennas can be used in various applications such as radio broadcasting, wireless communications and others. Due to their compact size and high performance, these antennas are an excellent choice for any project involving the generation of electromagnetic waves at a frequency of 150 MHz.

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two linear antennas located 1 m apart parallel to the Z axis. The antennas emit coherent electromagnetic waves at a frequency of 150 MHz.

To solve problem 40443, it is necessary to find the phase difference between the radiation of the antennas when observing the maximum intensity in a direction that makes an angle of 30° with the beam.

To begin with, you can use the interference condition: when two waves are superimposed, they interfere, which can be constructive (if the phases coincide) or destructive (if the phases are opposite).

For linear antennas located parallel to each other and emitting electromagnetic waves at the same frequency, the phase difference between them depends on the geometric difference in the wave path from each antenna to the observation point. This phase difference can be expressed by the following formula:

Δφ = 2pΔL/λ,

where ΔL is the geometric difference in the wave path from each antenna to the observation point, λ is the wavelength.

To find the geometric path difference, you can use the geometry of the problem and the law of cosines:

ΔL = d*cosθ,

where d is the distance between the antennas, θ is the angle between the beam and the Z axis.

Thus, the formula for finding the phase difference will look like:

Δφ = 2pdcost/min.

Substituting the data from the problem, we get:

Δφ = 2π1cos30°/(150*10^6) ≈ 0.000209 rad.

Answer: the phase difference between the radiation of the antennas, if a maximum intensity is observed in the direction making an angle of 30° with the beam, is about 0.000209 rad.

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