# When tightening a guitar string, what happens to velocity, wavelength, and frequency? [closed]

I'm thinking about the following physics problem. (I'm a freshman in high school.)

A guitarist plucks a string, producing string wave #1 (fundamental vibration) in the string. He then tightens its tension and plucks again, producing string wave #2 (fundamental vibration). Compare the following factors for string wave #1 vs string wave #2:

• velocity
• wavelength
• frequency
• which string wave creates the sound wave that makes your ear drum vibrate the fastest?

I think the velocity should increase after tightening, because the velocity of a wave on a string is $\sqrt{T/\mu}$, and tightening increases $T$.

I think the frequency should increase, too, but that's only based on empirical evidence: I know that when someone tightens a guitar string and then plucks again, the pitch is higher. Is there any way to justify my reasoning besides appealing to this empirical evidence?

I'm not sure what to say about wavelength. I know $v=\lambda f$, but if $v$ and $f$ increase, I can't conclude anything about $\lambda$. If $v$ and $f$ increase by the same factor, then $\lambda$ stays constant; if they increase by different factors, then $\lambda$ could increase or decrease. So I don't know what to think about the wavelength.

I think the last question is asking about which sound wave has a higher frequency. Since the frequency of a string wave is the same as the frequency of the induced sound wave, the second string wave should create the sound wave that makes my ear drum vibrate faster, right?

• You can conclude something about $\lambda$ by looking at the string: has its length changed? – tfb Apr 26 '18 at 12:15
• @tfb: what about justifying my claim about the frequency....... – josh milligan Apr 26 '18 at 17:15
• Well, you know what happens to $v$, and $\lambda$, and you have an equation relating them to $f$... – tfb Apr 26 '18 at 18:04