Question

A wire of density $9 \times 10^{3}\, kg \,cm ^{-3}$ is stretched between two clamps $1 \,m$ apart. The resulting strain in the wire is $4.9 \times 10^{-4}$ . The lowest frequency (in $Hz$ ) of the transverse vibrations in the wire is (Young's modulus of wire $Y=9 \times 10^{10}\,Nm ^{-2}$ ), (to the nearest integer), _____

Answer 1

$f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}=\frac{1}{2 l} \sqrt{\frac{T}{\rho A}}=\frac{1}{2 l} \sqrt{\frac{Y \Delta l}{\rho l}}$
$f=\frac{1}{2 \times 1} \sqrt{\frac{9 \times 10^{10} \times 4.9 \times 10^{-4}}{9 \times 10^{3} \times 1}}$
$=\frac{1}{2} \sqrt{49 \times 100}=35 \,Hz$