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

$f=\sqrt{\frac T{4mL}}=\sqrt{\frac T{4\rho VL}}=\sqrt{\frac T{\pi \rho d^2L^2}},\implies$

$d=\sqrt{\frac T{\pi \rho f^2L^2}}=0.19~mm,$

$f\sim \frac 1d,$

for $f=600~Hz\\$

$\\ d=0.09~mm.$