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 [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?

Chi Meson

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