A vibrating string (clamped at both ends) that has a fundamental frequency 400 Hz is 50 cm long and its mass is 1.25 gram. What is its tension?

I'm just checking if what I did below is correct since I don't have an answer key:

Given:

f = 400 Hz

L = 50 cm--> 0.50 m

m = 1.25 g --> 0.00125 kg

I know that speed of transverse wave equation is v = sqrt(F_T/) and when you isolate F_T on one side you get: F_T = v² and that = m/L. To get the v value, I used the fundamental frequency equation f = v/ = v/2L and isolated v on one side:

So to plug in, v = f x 2L --> (400 Hz)(2)(0.50m) = 400 (would the units be m/s?)

Then I used that value to F_T = (0.00125 kg/0.50 m)(400 m/s)² = 400 kg*m/s² or 400 N

Is that correct?