Traveling waves are generated at each end of a tightly stretched rope 24 ft long, with equations y =0.2 sin(1.047x -0.524t) and y=0.2 sin(1.047x+ 0.524t) (a) Find the equation of the combined wave, and find the nodes. (b) Sketch the graph for t = 0, 1, 2, 3, 4, 5, and 6. Is this a standing wave?

Traveling waves are generated at each end of a tightly stretched rope 24 ft long, with equations y =0.2 sin(1.047x -0.524t) and y=0.2 sin(1.047x+ 0.524t) (a) Find the equation of the combined wave, and find the nodes. (b) Sketch the graph for t = 0, 1, 2, 3, 4, 5, and 6. Is this a standing wave?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter18: Superposition And Standing Waves

Section: Chapter Questions

Problem 22PQ

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Concept explainers

Stretched string

A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.

Question

Traveling waves are generated at each end of a tightly stretched rope
24 ft long, with equations y =0.2 sin(1.047x -0.524t) and y=0.2 sin(1.047x+ 0.524t)
(a) Find the equation of the combined wave, and find the nodes.
(b) Sketch the graph for t = 0, 1, 2, 3, 4, 5, and 6. Is this a standing wave?

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