Tension and fundamental frequency

[raindrops]

Homework Statement

A particular violin string plays at a fundamental frequency of 294Hz. If the tension is increased 15%, what will be the new fundamental frequency?

Homework Equations

f=v/2L
v=sqrt(T/(m/L))

The Attempt at a Solution

294 = sqrt(T/(m/L))/2L so T=(294*2L)^2/(m/L)

T2 = T1*1.15

T2 = 1.15 * (((588L)^2)/(m/L))

I could go on and plug this into f2 = sqrt(T2/(m/L)) but it's a lot of typing and it didn't get me anywhere.

I'm not sure if I'm maybe making this problem more difficult than it has to be but I'm at a loss as to what to do. Any help would be greatly appreciated.



***second attempt at this problem

u=m/L

v = sqrt(1.15T/u)

sqrt(T/u)=v/sqrt(1.15)

f= v/(sqrt(1.15)*2L)

294*sqrt(1.15) = 315.28Hz

No idea if this is right, but it's all I could come up with.

 

[rl.bhat]

Hi raindrops, welcome to PF.
Your second attempt is correct.

 

[kerimek]

Your second attempt at solving the problem is correct. The fundamental frequency of the violin string will indeed increase to 315.28Hz when the tension is increased by 15%. Your approach of using the equation f = v/(2L) and substituting in the new value for velocity (calculated using the equation v = sqrt(T/u)) is a valid way to solve this problem. Good job!