Question

A piano wire weighing 6.00 g and having a length of 900 cm emits a fundamental frequency corresponding to the "Middle C" (v = 261.63 Hz). Find the tension in the wire.

Answer 1

$l=90cm=0.9m$

$m=\left(\frac{6}{90}\right)gm/cm$

$=\left\{\frac{(6\times {10}^{-3})}{90\times {10}^{-2}}\right\}kg/m$

$=\left(\frac{6}{900}\right)kg/m$

$f=261.63Hz$

$f=\frac{1}{2L}\sqrt{\left(\frac{T}{m}\right)}$

$\Rightarrow 261.63=$

$\frac{1}{(2\times 0.09)}\sqrt{\left\{\frac{(T\times 900)}{6}\right\}}$

$\Rightarrow 0.18\times 261.63=\sqrt{150T}$

$\Rightarrow 150T=(261.63\times 0.18{)}^2$

$\Rightarrow T=\frac{(261.63\times 0.18{)}^2}{150}$

$=1478.52N=1480N$