Physics - Wave on String Question with Solution | TestHub

The given wave equation is $Y=0.01\sin \left[2\pi \left(\frac{t}{0.02}-\frac{x}{0.50}\right)\right]$ m.

Comparing this with the standard wave equation $Y=A\sin (\omega t-kx)$, we get:

$\omega =\frac{2\pi }{0.02}=100\pi {\text{rad s}}^{-1}$

$k=\frac{2\pi }{0.50}=4\pi {\text{m}}^{-1}$

The wave velocity $v$ is given by:

$v=\frac{\omega }{k}=\frac{100\pi }{4\pi }=25{\text{m s}}^{-1}$

The velocity of a transverse wave on a string is also given by $v=\sqrt{\frac{T}{\mu }}$, where $T$ is the tension and $\mu$ is the linear mass density.

Given $\mu =0.02{\text{kg m}}^{-1}$.

$T=\mu v^2=0.02\times (25{)}^2$

$T=0.02\times 625=12.50\text{N}$

Answer: $12.50$ N