Question

A transverse wave described by

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

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

$=1.2\times {10}^{-4}kg/m$

Y = (0.02 m) sin

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

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

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

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

$v=\lambda f=\frac{\omega }{k}=\frac{30}{I}$

$=30m/s$

$\Rightarrow v=\left(\frac{T}{m}\right)$

$\Rightarrow 30=\sqrt{(\frac{T}{1.2}\times {10}^{-4}N)}$

$\Rightarrow t=10.8\times {10}^{-2}N$

$\Rightarrow T=0.08$ Newton