What is the fundamental frequency of a guitar string that is 1 m long, the mass per unit length is 50 g/m and the Tension in the string is 50 N.

We have to find the fundamental frequency of a string. The
formula for the fundamental frequency of a stretched string is given
by

sqrt [ T/ (m/L)]/ 2*L , where T is the tension in the
string, m is the mass per length and L is the length of the
string.

Using the values given to
us:

L = 1m

m= 50g /m = .05
Kg/m

T = 50 N

Therefore sqrt [
T/ (m/L)]/ 2*L

=> sqrt [ 50/ (.05/1)]/
2*1

=> sqrt [ 50 / .05] /
2

=> sqrt 1000
/2

=> 31.62 /
2

=> 15.81
Hz

Therefore the fundamental frequency is
15.81 Hz