Question

how the frequency of transverse vibration of string depends of the length of the loop

Answer 1

Dear Student,

Speed of waves in a stretched string: A string means a wire or a fiber which has a uniform diameter and is perfectly flexible. The speed of a wave in a flexible stretched string depends upon the tension in the string and mass per unit length of the string.
$f=\sqrt{\frac{T}{\mu }}$
Where the tension T in the string equal to Mg.
M - Mass suspended and g is acceleration due to gravity.

μ - linear density or mass per unit length of the string.
(2)
Where m is the mass of the string and L is the total length of the string.

Regards