Please Show your work Thank you PO Twosource interference HW

Please Show your work. Thank you.

PO Two-source interference HW-162 3. 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 S2 are equidistant from point A. S, How do the angles and 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 , , and approach? b. On the diagram above, indicate the line segment that represents how much farther point A is from S, than it is from S2-Label this distance D c. To point A (far away) The enlarged diagram at right illustrates the limit in which point A is moved very far from the sources. d. In this limit, find an expression for D in terms of the angle and the source separation d. (Hint: How do the angles and compare?) e. For what values of D (in terms of ) will there be: maximum constructive interference? complete destructive interference (i.e., a node)?

Solution

c)

On the diagram above, source S2 is further from point A than source S1 is. The extra distance traveled by waves from S2 can be determined if a line is drawn from S1 perpendicular to the line segment S2A.