Fundamental frequency of a guitar string?

by erik-the-red
Tags: frequency, fundamental, guitar, string
 P: 89 Question: One of the 63.5-cm-long strings of an ordinary guitar is tuned to produce the note $${\rm B_3}$$ (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 $$f_n = n\frac{v}{2L}$$. The fundamental frequency is given, so $$f_1 = 245 = \frac{v}{2*.635}$$, so $$v = 311$$ m/s. This is correct. In approaching the second part, I'm thinking $$T_2 = 1.01T_1$$. Since $$v = \sqrt{\frac{T}{\mu}}$$, should I assume that the new speed will be $$311 * \sqrt{1.01}$$? Thus giving a new fundamental frequency of 246 Hz?
 Sci Advisor HW Helper P: 1,772 Not only is this correct, it shows good insight into proportionalities. Keep it up!

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