Question

Tension is maintained in a string by attaching one end to a wall and by hanging a 2.34 kg object from the other end of the string after it passes over a pulley that is 2.00 m from the wall. The string has a mass per unit length of 3.45 mg/m. What is the fundamental frequency of this string?

Please help. do I use f=1/2L sqrt(tension/wavelenght)? Thank you.

Answer 1

The tension T = mg = 2.34•9.81 = 23 N.

m(o) = 3.45•10^-6 kg/m
v = sqrt(T/m(o)) =
=sqrt(23/(3.45•10^-6)) = 2582 m/s.
The fundamental frequency occurs when there is only one standing wave, or half a wavelength.
So, λ is equal by twice the 2 m length.
Thus, f = v/λ = v/2L = 2582/(2•2) = 645,5 Hz

Answer 2

I think,
Fundamental frequency,
f = v/lamda = v/(4L)
Because one end is node(fixed) and other is antinode (free to vibrat)