How tightening a string affects frequency?

[N53nick]

Homework Statement

How does tightening or loosening a string affect the frequency of the note? make specific references to the relationship between fundamental frequency and the standing wave in the string.

Use mathematical arguments from physics to demonstrate the relationships between the variables that you include in your answer.

Homework Equations

None as far as I know

The Attempt at a Solution

I figure that tightening the string increases wavelength, but decreases frequency. I don't know how to incorporate fundamental frequency and standing waves.

 

[CompuChip]

Have you ever played the guitar, by any chance? If so, think about how you tune it!

As for the mathematical / physical argument: do you happen to know of any formulas that relate length to frequency? (Or something else to frequency, with a standing wave)?