# Finding mass per unit length of a string

1. Mar 5, 2009

### whiterobot

i am a non physics or math major taking a 'physics of sound and music' course that deals with different wave forms. i am enjoying the class very much (more than i thought i would!) but am having trouble with the math, as the last math class i took was pre-calculus my junior year of high school. here's the question i am having the problem with:

The 4th string on a guitar is normally tuned to the D below middle C (D3). Suppose the string is 646 mm long. If I want the tension to be 30 N, what mass per unit length do I need?

i think (but could definitely be wrong) that the equation to use is V = sqrt (T/mu)

mu is what i am trying to find, and i am guessing that v would be the frequency of D3, which is 146.83Hz.

so, 146.83 = sqrt (30N/mu)

that's about as far as i have gotten - i don't know if i am on the right track and, if i am, how do i solve for mu? where does the length of the string come into play, if it does at all? i am lost!

Last edited: Mar 5, 2009
2. Mar 5, 2009

### alphysicist

Hi whiterobot,

No, the V in that equation is the velocity of the wave. How is the wave velocity related to the wave fequency?

3. Mar 5, 2009

### whiterobot

well, v = wavelength/period, correct? so, the new equation would be:

wavelength = 344/146.8 = 2.3
period = 2.3/344 = .007

so v = 2.3/.007 = 385.71

385.71 = sqrt (30N/ mu)?

4. Mar 6, 2009

### alphysicist

That's true; and since period = (1/frequency), the more standard way to write this (and more convenient for this problem) is:

$v=f\lambda$

This is the wavelength of the sound wave (in the air), but here you need the wavelength of the string wave. What would that be?