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Fundamental frequency of a guitar string? 
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#1
Nov305, 07:09 PM

P: 89

Question:
One of the 63.5cmlong 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? 


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