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129. Problem 19.37 (RHK) A source S and a detector D of high-frequency waves are a
distance d apart on the ground. The direct wave from S is found to be in phase
at D with the wave from S that is reflected from a horizontal layer at an
altitude H. The incident reflected rays make the same angle with
the reflecting layer. When the layer rises a distance h, no signal is detected
at D. We have to find the relation between d, h, H, and the wavelength
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of the
waves. We can neglect absorption in the atmosphere.
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Solution: Click For PDF Version The distance between the source S and detector D of high
frequency waves is d. Let us consider the situation when the direct wave
from S to D is in phase with wave from S that reaches D
on reflection from a horizontal layer at an altitude H. This situation
requires that the path difference between the direct ray and the reflected ray
be an integral multiple of wavelength
where n is some integer. According to the problem, no signal is detected at D when the reflecting
layer rises a distance h. This implies that now the path difference would have
increased by
Using the result that
we get
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. That is
. That is
