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A guitar string of length L is plucked in such a way that

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 79P Chapter 15

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 79P

A guitar string of length L is plucked in such a way that the total wave produced is the sum of the fundamental and the second harmonic. That is, the standing wave is given by y?? ,? ?t?) = ?y?1 (?x,? ?t?)? ?)y?2(?x,? t where y?1(? ?? ?) ? ? sin ???1?t? sin ?k? 1 ?x y?2(? ?? ?) ? ? sin? ? t sin ?? ?x with ???1 = ??k?1 and ???2 = ??k?2 (a) At what values of ?x are the nodes of ?y?1? (b) At what values of ?x are the nodes of y ?? ? (c) Graph the total wave at ?t = 0, (d) Does the sum of the two standing waves ?y1 ? and ?y2? produce a standing wave? Explain.

Step-by-Step Solution:

Solution 79P Introduction In this question we have to first find the nodes for the standing waves. Then we have to draw the graph of the wave for the given times and then we have to discuss if two standing wave makes a standing wave or not. Step 1 The notes are the point for which y(x,t) is zero for all t. Hence for the fundamental mode we can write that y(x) = C sin(k1x) = 0 Now for fundamental mode, we know that = 2L, hence the wavenumber is given by 1 k = 2= 2 1 1 2L Using this values in the above equation we have y(x) = C sin(2L) = 0 x L n x = nL = 0,L Hence the position of the nodes for y1are 0 and L.

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Chapter 15, Problem 79P is Solved
Step 3 of 4

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

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A guitar string of length L is plucked in such a way that