How tightening a string affects frequency?

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Tightening a string increases tension, which raises the frequency of the note produced. The fundamental frequency is inversely related to the string length and directly related to the square root of the tension. As the string is tightened, the wavelength decreases, leading to a higher frequency. The relationship can be expressed mathematically using the formula f = (1/2L)√(T/μ), where f is frequency, L is length, T is tension, and μ is linear density. Understanding these principles is essential for applications like tuning musical instruments.
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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.
 
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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)?
 

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