Thank you. The diagram at right shows an arbitrary point, point A, that lies nea

Question

Thank you.

The diagram at right shows an arbitrary point, point A, that lies near two point sources of waves. In this problem, we consider how the path length difference to point A changes as point A is moved along the dark line shown, away from the sources. Point Z on the diagram below was chosen so that point Z and source S_2 are equidistant from point A. How do the angles alpha and beta compare? Explain. Suppose that point A is moved away from the sources along the dark line. In the limit that point A is very far from the sources, what values do the angles alpha, beta, and y approach? On the diagram above, indicate the line segment that represents how much farther point A is from 5, than it is from S2. Label this distance A D. The enlarged diagram at right illustrates the limit in which point A is moved very far from the sources. In this limit, find an expression for delta D in terms of the angle theta and the source separation d. For what values of AD (in terms of lambda) will there be: maximum constructive interference? complete destructive interference (i.e., a node)? Use your answers from parts d and e to write equations that can be used to determine the angle(s) for which there will be: lines of maximum constructive interference nodal lines Determine the angles for which there will be nodal lines and lines of maximum constructive interference for the case of two sources in phase, a distance 1.5 lambda apart. Use your results to draw accurate nodal lines and lines of maximum constructive interference on the diagram at right. Label each line from part i with the corresponding value of delta D and theta. If the distance between the sources were increased, would the angle 0to the first nodal line increase, decrease, or stay the same? Explain your reasoning. Consider the following incorrect statement referring to problem 3: "As point A moves farther and farther away from the sources, the distances to the sources become more nearly equal, so the difference in distances is negligible. Thus the waves are more nearly in phase as point A moves farther and farther away from the sources." What is the flaw in this argument? Explain your reasoning.

Explanation / Answer

a. alpha = beta ( as its an isosceles triangle)
b. At infinity, alpha = beta = 90 deg, gamma = 0
c. line segment Z-S1 is the additional path
d. dD = sin(delta)*d
   here theta = delta
   so dD = d*sin(theta)
  

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