(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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ISBN: 9780321902788

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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Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if (a) the pipe is open at both ends and (b) the pipe is closed at the left end and open at the right end.

Standing sound waves are produced in a pipe that is 1.80 m long. a)If the pipe is open at both ends, determine the locations along the pipe (measured from the left end) of the displacement nodes for the first and second overtone? b)If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the fundamental frequency, first and the second overtone?

A pipe that is open at both ends has a fundamental frequency of 311 Hz when the speed of sound in air is 346 m/s. (a) What is the length of the pipe? m(b) What are the next two harmonics? 1st Harmonic = Hz 2nd Harmonic = Hz

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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 both ends.

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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