Question

A wire of density $9\times 10^{3}kgc{m}^{-3}$ is stretched between two clamps $1m$ 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 $Y=9\times 10^{10}N{m}^{-2}$ ), (to the nearest integer), _____

Answer 1

Answer: 35

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