# The velocity of guitar strings

1. Dec 3, 2011

### forestmine

Hello again!

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

You are designing a two-string instrument with metal strings 35.0 cm long. Both strings are under the same tension. String S$_{}1$ has a mass of 8.00 g and produces the note middle C (frequency 262 Hz) in its fundamental mode. (a) What should be the tension in the string?

2. Relevant equations
f=nv/2L
v=λf
λ=2L/n
v=$\sqrt{}T/μ$

3. The attempt at a solution

I believe the first thing I need to do is calculate the velocity of the string. Since we are talking about its fundamental frequency, I set n=1. Therefore given that f=nv/2L, I did (262)(2)(.35)=183.4. Now, I had worked this problem earlier on a black board and my velocity I believe came out to be around 366 m/s, which seems to make much more sense to me, considering the speed of sound in the air is 344 m/s. My question is, for a string or an object to create an audible noise, must the velocity of the string be greater than 344 m/s. And if so, I don't understand what I'm doing differently this time around to produce exactly half the velocity I found last time.

Hope this was clear enough.

Thank you!

Last edited: Dec 3, 2011
2. Dec 4, 2011

### forestmine

Just bumping this at this point...