Answer to Question #257827 in Atomic and Nuclear Physics for Milly

Question

A steel wire of length 0.8m and density 8x10³kgm-² is fixed at both ends when vibrating transversely under a tension of 50.0N. the fundamental frequency is 300Hz. Calculate the diameter of the wire in meters. How can the same wire be made produce a note for frequency 600Hz.

Answer 1

We know that

$∆\upsilon=\frac{1}{2lr}\sqrt{\frac{T}{\pi\rho}}$

$D=2r=\frac{1}{l∆\upsilon}\sqrt{\frac{T}{\pi\rho}}$

$D=\frac{1}{0.8\times(600-300)}\sqrt{\frac{50}{\pi\times8\times10^3}}$

$D=\frac{1}{0.8\times300}\sqrt{\frac{50}{\pi\times8\times10^3}}=0.1858\times10^{-3}=0.1858mm$