Fundamental frequency of a guitar string?

[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?

 

[Chi Meson]

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