Physics - Wave on String Question with Solution | TestHub

Mass per unit length of the string is $m=10^{-6}\text{ kg/cm}=\frac{10^{-6}}{10^{-2}}\text{ kg/m}=10^{-4}\text{ kg/m}$.

The given equation of the wave is $Y=0.2\sin (2x+80t)$.

Comparing this with the standard wave equation $Y=A\sin (kx+\omega t)$, we get:
$k=2\text{ rad/m}$
$\omega =80\text{ rad/s}$

The wave speed $v$ is given by:
$v=\frac{\omega }{k}=\frac{80}{2}=40\text{ m/s}$

The speed of a transverse wave on a string is also given by $v=\sqrt{\frac{T}{m}}$, where $T$ is the tension.

Squaring both sides and rearranging for $T$:
$T=m{v}^2$

Substituting the values:
$T=10^{-4}\times (40{)}^2$
$T=10^{-4}\times 1600=0.16\text{ N}$

Answer: 0.16 N