A string with a mass density mu = 6.40e-03 kg/m is under a tension of F = 259 N and is fixed at both ends. One of its resonance frequencies is 622.0 Hz. The next higher resonance frequency is 777.5 Hz. What is the fundamental frequency of this string? Which harmonic does the resonance frequency at 622.0 Hz correspond to? (i.e. what is n at this frequency?) What is the length of the string? Now, suppose the same string is detached at one end and connected by a ring to a frictionless post, so that it can move freely. Find the wavelength of the first (fundamental) harmonic. What is the frequency of the third (n = 3) harmonic in this case?

A string with a mass density mu = 6.40e-03 kg/m is under a tension of F = 259 N and is fixed at both ends. One of its resonance frequencies is 622.0 Hz. The next higher resonance frequency is 777.5 Hz. What is the fundamental frequency of this string? Which harmonic does the resonance frequency at 622.0 Hz correspond to? (i.e. what is n at this frequency?) What is the length of the string? Now, suppose the same string is detached at one end and connected by a ring to a frictionless post, so that it can move freely. Find the wavelength of the first (fundamental) harmonic. What is the frequency of the third (n = 3) harmonic in this case?

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 17PQ: A standing wave on a string is described by the equation y(x, t) = 1.25 sin(0.0350x) cos(1450t),...

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