Question:
The mass per unit length of a uniform wire is $0.135 \mathrm{~g} / \mathrm{cm}$. A transverse wave of the form $\mathrm{y}=-0.21 \sin (\mathrm{x}+30 \mathrm{t})$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x \times 10^{-2} \mathrm{~N}$. Value of $x$ is. (Round-off to the nearest integer)
Solution:
$\mu=0.135 \mathrm{gm} / \mathrm{cm}=0.0135 \mathrm{~kg} / \mathrm{m}$
$y=-0.21 \sin (x+30 t)$
$(x$ in meter \& $t$ in $s e c)$
$\mathrm{v}=\frac{\omega}{\mathrm{k}}=\frac{30}{1}=30 \mathrm{~m} / \mathrm{s}$
$\mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}} \Rightarrow \mathrm{T}=\mathrm{v}^{2} \mu=(30)^{2}(0.0135)$
$=12.15$
$=\mathrm{x} \times 10^{-2} \mathrm{~N}$
$\Rightarrow x=1215$