The mass per unit length of a uniform wire is $0.135 \mathrm{~g} / \mathrm{cm}$. A transverse wave of the form $y=-0.21 \sin (x+30 t)$ is produced in it, where $x$ is in meter and $\mathrm{t}$ is in second. Then, the expected value of tension in the wire is______ $x \times 10^{-2} \mathrm{~N}$. Value of $x$ is (Round-off to the nearest integer)
(1215)
$y=-0.21 \sin (x+30 t)$
$v=\frac{\omega}{K}=\frac{30}{1}=30 \mathrm{~m} / \mathrm{s}$
$v=\sqrt{\frac{T}{\mu}}$
$\mathrm{T}=\mathrm{v}^{2} \times \mu$
$\mathrm{T}=(30)^{2} \times 0.135 \times 10^{-1} \quad \mu=0.135 \mathrm{gm} / \mathrm{cm}$
$\mathrm{T}=900 \times 0.135 \times 10^{-1} \quad \mu=0.135 \times \frac{10^{-3} \mathrm{~kg}}{10^{-2}} \frac{\mathrm{kg}}{\mathrm{m}}$
$\mathrm{T}=12.15 \mathrm{~N}$
$\mathrm{~T}=1215 \times 10^{-2} \mathrm{~N}$
$\mathrm{X}=1215$
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