Consider a road that runs parallel to the line connecting a pair of radio towers that transmit the same station (assume that their transmissions are synchronized), which has an AM frequency of 1000 kilohertz. If the road is 5 kilometers from the towers and the towers are separated by 400 meters, find the angle θ to the first point of minimum signal (m=0). Hint: A frequency of 1000 kilohertz corresponds to a wavelength of 300 meters for radio waves. Learning Goal:To understand the assumptions made by the standard two-sourceinterference equations and to be able to use them in a standardproblem.For solving two-source interference problems, there exists astandard set of equations that give the conditions for constructiveand destructive interference. These equations are usually derived inthe context of Young's double slit experiment, though they mayactually be applied to a large number of other situations. Theunderlying assumptions upon which these equations are based arethat two sources of coherent, nearly monochromatic light areavailable, and that their interference pattern is observed at adistance very large in comparison to the separation of the sources.Monochromatic means that the wavelengths of the waves, whichdetermine color for visible light, are nearly identical. Coherentmeans that the waves are in phase when they leave the twosources.In Young's experiment, these two sources corresponded to the twoslits (hence such phenomena are often called two-slit interference).Under these assumptions, the conditions for constructive anddestructive interference are as follows:for constructive interferenced sin 0 = m) (m = 0, +1, +2,...).and for destructive interferenced sin 0 = (m + )A (m = 0, ±1, ±2, ...).where d is the separation between the two sources, A is thewavelength of the light, m is an arbitrary integer, and 0 is the angleFigure< 1 of 1 >S2d sin 0r2To screen

AM frequency= 1000 kHz Distance between towers= 400 m angle=?

Consider a road that runs parallel to the line connecting a pair of radio towers that transmit the same station (assume that their transmissions are synchronized), which has an AM frequency of 1000 kilohertz. If the road is 5 kilometers from the towers and the towers are separated by 400 meters, find the angle θ to the first point of minimum signal (m=0). Hint: A frequency of 1000 kilohertz corresponds to a wavelength of 300 meters for radio waves.

Consider a road that runs parallel to the line connecting a pair of radio towers that transmit the same station (assume that their transmissions are synchronized), which has an AM frequency of 1000 kilohertz. If the road is 5 kilometers from the towers and the towers are separated by 400 meters, find the angle θ to the first point of minimum signal (m=0). Hint: A frequency of 1000 kilohertz corresponds to a wavelength of 300 meters for radio waves.

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 34P: Two slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of...

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