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. Determine the frequency of vibration when the string vibrates in three segments.

Answer 1

Frequency of $n^{th}$ normal mode is given by $f_n=\frac{n}{2l}\sqrt{\frac{T}{\mu }}$

When the string vibrates in three segments, it is basically vibrating in third normal mode.

Thus $f_3=3f_1=660Hz$