A string with a linear density of 0.035 kg/m and a mass of 0.014 kg is clamped at both ends. Under what tension in the string will it have a fundamental frequency of 100 Hz?

Question

The correct answer is 270N but I don't know how to get there.

Here are some of the equations we can use but if you know of others feel free to mention them.
T=1/f
f=1/T
v=(square root)F/(m/L)
Fn=nv/2L

Thanks for the help and please indicate which equation you chose if you end up picking one of the ones I have above.

Answer 1

freq*lambda= v=sqrt(F/linearmassdensity)

lambda= 2*length= 2* mass/(massdenstiy)
= .028/(.035) meters=.8m

solve for tension F.

100*.8=sqrt(F/.035)

6400*.035=F=224N

recheck my work to see if there is an error, I don't see it.

Answer 2

The final answer is 270 N not 224N,how come?