Explanation The obstacle is moved towards right direction which increases its distance from the source and detector. This increase in distance between the waves from the source results in change in path difference. Consider the above figure for better explanation. Write the expression for initial path through obstacle. p i = 2 A B − A D (I) Here, p i is equal to initial path, A B is the distance between the source and obstacle and A D is the distance between source and detector. Write the expression for distance between A and B . A B = ( l 2 ) 2 + d 2 Here, l is the distance between the source and detector and d is the distance of obstacle from midpoint of distance between source and detector. Substitute ( l 2 ) 2 + d 2 for A B and l for A D in equation (I). p i = 2 ( l 2 ) 2 + d 2 − l Write the expression for final path difference. p f = 2 A C − A D (II) Here, p f is the final path difference, A C is the new distance between source and obstacle. Write the expression for the distance between source and new position of obstacle. A C = ( l 2 ) 2 + ( d + x ) 2 Here, x is the distance obstacle is moved rightwards. Substitute ( l 2 ) 2 + ( d + x ) 2 for A C and l for A D in equation (III). p f = 2 ( l 2 ) 2 + ( d + x ) 2 − l (III) Write the expression for net path difference. Δ p = p f − p i (IV) Here, Δ p is the new path difference. Substitute 2 ( l 2 ) 2 + ( d + x ) 2 − l for p f , 2 ( l 2 ) 2 + d 2 − l for p i and λ 2 for Δ p in equation (IV)

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

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Chapter 16, Problem 106GP

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How far the obstacle should be moved to obtain the phase difference of λ2.

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Chapter 16, Problem 105GP

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Chapter 16 Solutions

Physics for Scientists and Engineers with Modern Physics

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How far the obstacle should be moved to obtain the phase difference of λ 2 .

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