Question

The mass per unit length of a uniform wire is $0.135\,g/cm.$ A transverse wave of the form $y=-0.21\sin\left(x+30t\right)$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x\times 10^{- 2}N$ Value of $x$ is (Round-off to the nearest integer)

Answer 1

$y=-0.21 \sin (x+30 t )$
$v=\frac{\omega}{K}=\frac{30}{1}=30 \,m / s$
$V=\sqrt{\frac{T}{\mu}}$
$T=(30)^{2} \times 0.135 \times 10^{-1} \mu=0.135\, gm / cm$
$T=900 \times 0.135 \times 10^{-1} \mu=0.135 \times \frac{10^{-3}}{10^{-2}} \frac{ kg }{ m }$
$T=12.15 \,N$
$T=1215 \times 10^{-2} N$
$x=1215$