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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?

Respuesta :

Answer:

T = 6051.70 N

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:

[tex]f = \frac{1}{2\pi}\sqrt\frac{T}{M}[/tex]

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

[tex]42 = \frac{1}{2\pi}\sqrt\frac{T}{0.086}[/tex]

or

[tex]({42}\times{2\pi})^2 = \frac{T}{0.0869}[/tex]

or

T = 6051.70 N

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