Question

A transverse wave described by $y=\left(0.02m\right)\sin \left({1.0m}^{-1}\right)(x+{30s}^{-1}t)$ propagates on a stretched string having a linear mass density of $1.2\times {10}^{-4}$ kg $m^{-1}$. find the tension in the string.

Answer 1

m = mass per unit length $=1.2\times {10}^{-4}kg/mt$

$Y=\left(0.02m\right)\sin \left[\right(1.0m^{-1})x+(30s^{-1}\left)t\right]$

Here, $k=1m^{-1}=2\pi /\lambda$

$\omega =30s^{-1}=2\pi f$

$\therefore$ velocity of the wave in the stretched string

$v=\lambda f=\omega /k=30/I=30m/s$

$\Rightarrow v=\sqrt{T/m}\Rightarrow 30\sqrt{\left(T/1.2\right)\times {10}^{-4}N)}$

$\Rightarrow T=10.8\times {10}^{-2}N\Rightarrow T=1.08\times {10}^{-2}$ Newton.