A string has mass per unit length of \(10^{-6} \mathrm{~kg} / \mathrm{cm}\) The equation of simple harmonic wave produced in it is \(Y=0.2 \sin (2 x+80 t) \mathrm{m}\). The tension in the string is

Wave velocity, \(v=\sqrt{\frac{T}{\mu}}\)
\(\mathrm{T}=\mathrm{v}^2 \mu=\mathrm{v}^2 \times 10^{-6}\)
Given, \(\mu=10^{-6} \mathrm{~kg} / \mathrm{cm}=10^{-4} \mathrm{~kg} / \mathrm{m}\)
\(\mathrm{T}=\mathrm{v}^2 \times 10^{-4}...(i)\)
Given, \(Y=0.2 \sin (2 x+80 t)\),
Comparing with standard equation,
\(y=A \sin (K x+\omega t) \Rightarrow \omega=80\)
\(\begin{aligned}
\therefore \quad \mathrm{K} & =\frac{\omega}{\mathrm{v}} \\
\mathrm{v} & =\frac{\omega}{\mathrm{K}}
\end{aligned}\)
\(\begin{aligned}
& v=\frac{80}{2} \\
& v=40 \mathrm{~m} / \mathrm{s}
\end{aligned}\)
From equation (i)
\(\begin{aligned}
& \mathrm{T}=(40)^2 \times 10^{-4} \\
& \mathrm{~T}=0.16 \mathrm{~N}
\end{aligned}\)