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.

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Chapter1: Units, Trigonometry. And Vectors
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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-source
interference equations and to be able to use them in a standard
problem.
For solving two-source interference problems, there exists a
standard set of equations that give the conditions for constructive
and destructive interference. These equations are usually derived in
the context of Young's double slit experiment, though they may
actually be applied to a large number of other situations. The
underlying assumptions upon which these equations are based are
that two sources of coherent, nearly monochromatic light are
available, and that their interference pattern is observed at a
distance very large in comparison to the separation of the sources.
Monochromatic means that the wavelengths of the waves, which
determine color for visible light, are nearly identical. Coherent
means that the waves are in phase when they leave the two
sources.
In Young's experiment, these two sources corresponded to the two
slits (hence such phenomena are often called two-slit interference).
Under these assumptions, the conditions for constructive and
destructive interference are as follows:
for constructive interference
d sin 0 = m) (m = 0, +1, +2,...).
and for destructive interference
d sin 0 = (m + )A (m = 0, ±1, ±2, ...).
where d is the separation between the two sources, A is the
wavelength of the light, m is an arbitrary integer, and 0 is the angle
Figure
< 1 of 1 >
S2
d sin 0
r2
To screen
Transcribed Image Text:Learning Goal: To understand the assumptions made by the standard two-source interference equations and to be able to use them in a standard problem. For solving two-source interference problems, there exists a standard set of equations that give the conditions for constructive and destructive interference. These equations are usually derived in the context of Young's double slit experiment, though they may actually be applied to a large number of other situations. The underlying assumptions upon which these equations are based are that two sources of coherent, nearly monochromatic light are available, and that their interference pattern is observed at a distance very large in comparison to the separation of the sources. Monochromatic means that the wavelengths of the waves, which determine color for visible light, are nearly identical. Coherent means that the waves are in phase when they leave the two sources. In Young's experiment, these two sources corresponded to the two slits (hence such phenomena are often called two-slit interference). Under these assumptions, the conditions for constructive and destructive interference are as follows: for constructive interference d sin 0 = m) (m = 0, +1, +2,...). and for destructive interference d sin 0 = (m + )A (m = 0, ±1, ±2, ...). where d is the separation between the two sources, A is the wavelength of the light, m is an arbitrary integer, and 0 is the angle Figure < 1 of 1 > S2 d sin 0 r2 To screen
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