(a) Explanation At the open end of a pipe, a displacement antinode is formed. And at the closed end of the pipe, a displacement node is formed. The distance between two antinode is λ / 2 , distance between two successive nodes is λ / 2 , and also the distance between two adjacent node and a antinode is λ / 4 . Let x be the distance from left hand end of the pipe. At the origin or the first point of the pipe, always the displacement is zero. After the antinode there is a node at a distance λ / 4 . Write the equation to find the wavelength of fundamental overtone. λ 1 = 2 L (I) Here, λ 1 is the wavelength of fundamental overtone, L is the length of the pipe. Write the equation to find the distance of the node from the right end. x = λ 1 4 (II) Here, x is the distance of node from the right end. Write the equation to find the wavelength of the first overtone. λ 2 = L (III) Here, λ 2 is the wavelength of the first overtone. Write the equation to find the distance to the first overtone from the right end. x = λ 2 4 (IV) Here, λ 2 is the wavelength of the first overtone, and x is the distance of the first overtone from the right end. Write the equation to find the wavelength of the second overtone. λ 3 = 2 L 3 (V) Here, λ 3 is the wavelength of second overtone, L is the length of the pipe. Write the equation to find the distance of second overtone from the right end. x = λ 3 4 (VI) Here, λ 3 is the wavelength of second overtone, and x is the distance between the right end and the second overtone. Conclusion: Substitute 1.20 m for L in equation (I) to get λ 1 . λ 1 = 2 ( 1 (b) To determine The location of nodes along the pipe if the pipe is open at the right end and closed at left end.

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Author: Hugh D. Young, Philip W. Adams, Raymond Joseph Chastain

Publisher: PEARSON

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Chapter 12, Problem 21P

(a)

To determine

The location of nodes along the pipe if the pipe is open at both ends.

(b)

To determine

The location of nodes along the pipe if the pipe is open at the right end and closed at left end.

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Chapter 12, Problem 20P

Chapter 12, Problem 22P

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The location of nodes along the pipe if the pipe is open at both ends.

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The location of nodes along the pipe if the pipe is open at the right end and closed at left end.

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