Question

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

Answer 1

$v =\sqrt{\frac{ T }{\mu}} \Rightarrow v ^{2}=\frac{ T }{\mu}$
$T = v ^{2} \mu$
(given $\mu=1.2 \times 10^{-4} kg / m$ )
compare given equation with standard wave equation
$\omega=\frac{2 \pi}{ T }=30 \,s ^{-1} $
$ k =\frac{2 \pi}{\lambda}=1.0\, m ^{-1} $
$ v =\frac{\omega}{ k }=\frac{30}{1}=30 \,ms ^{-1} $
$ T =\left(30^{2}\right)\left(1.2 \times 10^{-4} Kg / m \right) $
$900 \times 1.2 \times 10^{-4}=10.8 \times 10^{-2}$
$=0.108\, N$