Fundamental frequency of a guitar string?

  1. Question:

    One of the 63.5-cm-long strings of an ordinary guitar is tuned to produce the note [tex]{\rm B_3}[/tex] (frequency 245 Hz) when vibrating in its fundamental mode.

    1.

    If the tension in this string is increased by 1.0%, what will be the new fundamental frequency of the string?

    The first part of the question asked for the speed of transverse waves on the string.

    I used the equation [tex]f_n = n\frac{v}{2L}[/tex]. The fundamental frequency is given, so [tex]f_1 = 245 = \frac{v}{2*.635}[/tex], so [tex]v = 311[/tex] m/s.

    This is correct.

    In approaching the second part, I'm thinking [tex]T_2 = 1.01T_1[/tex]. Since [tex]v = \sqrt{\frac{T}{\mu}}[/tex], should I assume that the new speed will be [tex]311 * \sqrt{1.01}[/tex]?

    Thus giving a new fundamental frequency of 246 Hz?
     
    Last edited: Nov 3, 2005
  2. jcsd
  3. Chi Meson

    Chi Meson 1,772
    Science Advisor
    Homework Helper

    Not only is this correct, it shows good insight into proportionalities. Keep it up!
     
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