What is the fundamental frequency?

Question

A string is stretched to a length of 147 cm and both ends are fixed. If the density of the string is 0.011 g/cm, and its tension is 1490 N, what is the fundamental frequency? Answer in units of Hz.?

Answer 1

f = √(T/m/L)/2L

where f = frequency, T is tension, m is mass, L is length

It's hard to show on here but the T/m/L is all under the square root.

If the density of the string is 0.011 g/cm, then the weight of a 147 cm piece is 0.011*147 = 1.617 g

f = √1490N/(0.001617 kg)/(.147 m)/2 * (.147 m)

= 2503.68/.294

= 8516 Hz