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CALC A thin, taut string tied at both ends and oscillating

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

Solution for problem 43E 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 43E

CALC A thin, taut string tied at both ends and oscillating in its third harmonic has its shape described by the equation y(x, t) = (5.60 cm) sin [(0.0340 rad/cm)x] sin[(50.0 rad/s)t], where the origin is at the left end of the string, the x -axis is along the string, and the y -axis is perpendicular to the string. (a) Draw a sketch that shows the standing-wave pattern. (b) Find the amplitude of the two traveling waves that make up this standing wave. (c) What is the length of the string? (d) Find the wavelength, frequency, period, and speed of the traveling waves. (e) Find the maximum transverse speed of a point on the string. (f) What would be the equation y(x, t) for this string if it were vibrating in its eighth harmonic?

Step-by-Step Solution:

Solution 43E Step 1of 8: Introduction: Since the string is tied at both the ends, the wave is a non traveling one i.e. it is a standing wave. The third harmonic equation is given by, y(x, t) = (5.60 cm) sin [(0.0340 rad/cm)x] sin[(50.0 rad/s)t]

Step 2 of 8

Chapter 15, Problem 43E is Solved
Step 3 of 8

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

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CALC A thin, taut string tied at both ends and oscillating