physics

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When a player's finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string's fundamental frequency. The string's tension and mass per unit length remain unchanged.

If the unfingered length of the string is l= 65 cm, determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note in comparison to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 2^[1/12]

  • physics -

    2^1/12=1.05946

    so each fret increases the frequency by that factor. But wavelength is the reciprocal of this. or w1=w*.94387

    Well, to get this, one has to have adjacent frets .94387 length of the before length.

    original length 65cm
    next length 65*.94387
    next lenght=65*(.94387)^2 and so on.

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