Using the binomial theorem, with D2large and a2+ x2small, we approximate this expression: ()22/2 .LDaxD≈++The distance traveled by the direct wave is LDax122=+−bg. Using the binomial theorem, we approximate this expression: 21xD≈+−Thus, LLDaaxxDDxxDaxD212222222−≈+++−−−+=. Setting this equal to m+12bgλ, where mis zero or a positive integer, we find xmDa122bgbgλ. 87. The wave that goes directly to the receiver travels a distance L1and the reflected wave travels a distance L2. Since the index of refraction of water is greater than that of air this last wave suffers a phase change on reflection of half a wavelength. To obtain constructive interference at the receiver, the difference L2– L1must be an odd multiple of a half wavelength. Consider the diagram below. The right triangle on the left, formed by
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