When a players finger presses a guitar string down ontoa

Chapter 16, Problem 16.45

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When a players finger presses a guitar string down ontoa fret, the length of the vibrating portion of the string isshortened, thereby increasing the strings fundamentalfrequency (see Fig. 16-35). The strings tension and mass perunit length remain unchanged. If the unfingered length of thestring is = 65.0 cm, determine the positions x of the first sixfrets, if each fret raises the pitch of the fundamental by onemusical note in comparison to the neighboring fret. Onthe equally tempered chromatic scale, the ratio of frequenciesof neighboringnotes is 21/12.

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