Question

A string vibrates in its first normal mode with a frequency of 220 vibrations/s. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. Find the tension in the string.

Answer 1

Frequency of first normal mode or fundamental frequency is given by $f_1=\frac{1}{2l}\sqrt{\frac{T}{\mu }}=220Hz$

$⟹\frac{1}{2\times 0.7}\sqrt{\frac{T}{1.2\times {10}^{-3}/0.7}}=220$

$⟹T=163N$