Percent change in tension to achieve specified change in frequency

[Jennifer_ea]

% change in tension to achieve specified change in frequency

Homework Statement

A particular guitar string is supposed to vibrate at 219 Hz, but it is measured to actually vibrate at 224 Hz. By what percentage should the tension in the string be changed to get the frequency to the correct value?

Homework Equations

v=f(lambda)=sqrt(tension/mu)

Rearranged and combined to give:
(T1/T2) = (F1/F2)^2

The Attempt at a Solution

This seemed like it should be a very simple problem, I must be doing something basic wrong.

Subbing in the values and changing for %:
%change in Tension = 100 * [1 - (219/224)^2]
= 4.41

However this is shown wrong by the system. I also tried putting in 0.0441 just incase, but no dice. I can't think of any other way to approach this.

Thanks for any help you can give!

 

[tiny-tim]

Welcome to PF!

Hi Jennifer_ea! Welcome to PF!

(have a lambda: λ and a mu: µ and a square-root: √ and try using the X² tag just above the Reply box )

v=f(lambda)=sqrt(tension/mu)
…
Subbing in the values and changing for %:
%change in Tension = 100 * [1 - (219/224)^2]
= 4.41

Why the "1 - " ?

 

[Jennifer_ea]

Oops, didn't notice that option!

Yup, I knew this would be a face palmer. When doing the logic out I knew it had to decrease but somehow deemed the negative unwarranted.

Thanks a million!