Question

a long string is moved up and down with simple harmon motion with a frequency of 42 Hz. The string is 543 m long and has a total mass of 47.2 kg. The string is fixed at both ends. What is the tension in the string?

Answer 1

T = 6051.70 N

Step-by-step explanation:

Given;

Frequency, f = 42 Hz

Length of the string, L = 543 m

Mass of the string, m = 47.2 kg

Now,

the frequency is given as:

`f = (1)/(2\pi)\sqrt(T)/(M)`

where, T is the tension in the string

M is the mass per unit length = m/L = 47.2/543 = 0.0869

on substituting the values in the above equation, we get

`42 = (1)/(2\pi)\sqrt(T)/(0.086)`

or

`({42}*{2\pi})^2 = (T)/(0.0869)`

or

T = 6051.70 N