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°

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Quizplus · Accepted Answer

The smallest angle at which constructive interference occurs is when the path length difference between the two waves is equal to one wavelength. The path length difference is equal to the distance between the antennas multiplied by the sine of the angle. The wavelength is equal to the speed of light divided by the frequency. So, we have:```path length difference = distance between antennas * sin(angle) = wavelengthdistance between antennas = 130 mspeed of light = 3.00 × 10^8 m/sfrequency = 3.6 MHz = 3.6 × 10^6 Hzwavelength = speed of light / frequency = 3.00 × 10^8 m/s / 3.6 × 10^6 Hz = 83.3 msin(angle) = wavelength / distance between antennas = 83.3 m / 130 m = 0.641angle = sin^-1(0.641) = 40°```Therefore, the smallest angle at which constructive interference occurs is 40°.

Two Radio Antennas Are 130 M Apart on a North-South