Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundamental frequency of a guitar string?

  1. Nov 3, 2005 #1

    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.


    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. Nov 3, 2005 #2

    Chi Meson

    User Avatar
    Science Advisor
    Homework Helper

    Not only is this correct, it shows good insight into proportionalities. Keep it up!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook