The mass per unit length of a uniform wire is $0.135\, g / cm$. A transverse wave of the form $y =-0.21 \sin ( x +30 t )$ 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)
JEE MAIN 2021, Diffcult
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$\mu=0.135 gm / cm =0.0135 kg / m$
$y =-0.21 \sin ( x +30 t )$
$(x$ in meter $\&$ $t$ in sec)
$v =\frac{\omega}{ k }=\frac{30}{1}=30 m / s$
$v =\sqrt{\frac{ T }{\mu}} \Rightarrow T = v ^{2} \mu=(30)^{2}(0.0135)$
$=12.15$
$= x \times 10^{-2} N$
$\Rightarrow x =1215$
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