1. The problem statement, all variables and given/known data In order to decrease the fundamental frequency of a guitar string by 4%, by what percentage should you reduce the tension? 2. Relevant equations f = sqrt [T/(m/L)] / 2L I believe that is the equation that relates frequency to tension... 3. The attempt at a solution I plugged in some theoretical values and got 76.96% which seemed wrong, and it is :) How can I go about solving this problem?
[tex] f_1 = (1/(2L)) * \sqrt(F/\mu)[/tex] Your formula is correct. First, do f and F vary directly or inversely with each other?
Whoops, I misread what you typed. We don't care whether the tension and length vary directly or inversely. We want how frequency and tension are related. The rest of the equation isn't important, since this is just asking for a relative number. [tex]f \alpha \sqrt(F)[/tex]
No problem. As [tex]f \alpha \sqrt(F)[/tex], it makes sense that [tex]0.96 \alpha \sqrt(x)[/tex], right? Use [tex] 0.96 = \sqrt(x)[/tex] to solve for x. This will give you a decimal value, which you multiply by 100 to turn into a percent. This is the percent of the original length needed to change the frequency by 4%, so to get the answer, you subtract it from 100%. % to decrease = 100% - (100x)
okay, that's what i was thinking, but i didn't know if i could use an equals sign since we were working with a proportion :) thank you!