# Fundamental frequency of a guitar string?

1. Nov 3, 2005

### erik-the-red

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?

Last edited: Nov 3, 2005
2. Nov 3, 2005

### Chi Meson

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