so and so (b) is unchanged. so so (c) so so so 12.23. Set Up: An open end is a displacement antinode. A closed end is a displacement node. Adjacent nodes are a distance apart. Adjacent antinodes are also a distance apart, and the node to antinode distance is Let x be the distance from the left-hand end of the pipe. Solve: (a) There is an antinode at The first node is at and each successive node is farther to the right. Each successive overtone adds one node. fundamental: There is a node at 1 st overtone: There are a nodes at 0.90 m. 2 nd overtone: There are a nodes at 0.60 m, and 1.00 m. (b) There now is a node at Successive nodes are farther to the right. fundamental: There only a node is at 1 st overtone: There are a nodes at and 2 nd overtone: There are a nodes at 0.48 m, and 0.96 m. Reflect: In each case the fundamental has one node, the 1 st overtone has two nodes, and the 2 nd overtone has three nodes. 12.24. Set Up:
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Standing wave, Hz, Musical tuning, tuning fork, M.