# Sound waves from a piano

1. Mar 27, 2008

### gtp405

Ok this problem seems blatantly easy but for some reason I just cannot find the equation.

1. The problem statement, all variables and given/known data

The middle C string of a piano is supposed to vibrate at 261.6 Hz when excited in its fundamental mode. A piano tuner finds that in a piano that has a tension of 900N on this string, the frequency of the vibration is too low (flat) by 15 hz. How much must he increase the tension of the string to achieve the correct frequency?

2. Relevant equations

This is what I can't find.

3. The attempt at a solution

At first glance to me this problem seems extremely easy, just use a certain formula that relates tension to frequency in some way, but I've looked high and low in the book and can't seem to find it. All I really need is an equation to relate the two.

Thanks!

2. Mar 27, 2008

### AstroRoyale

$$f=\frac{n}{2L}{\sqrt{\frac{T}{\mu}}$$

gives the resonant frequencies for a string under tension