The transverse standing wave on a string fixed at both ends is vibrating at its fundamental frequency of 250 Hz. What would be the fundamental frequency on a piece of the same string that is twice as long and has four times the tension?

Question

I know the equation f=v/2L. and that v=(F/(m/L))^(1/2). But i don't know where to go from there.

Answer 1

tension 4x, so v must be 2x. Now, string twice as long halves freq, right. So the freq is 2x/2x=same freq.

check my reasoning.