Question

The mass per unit length of a uniform wire is $0.135g/cm.$ 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

Answer: 1215

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