Physics - Wave on String Question with Solution | TestHub

Comparing the given wave equation $Y=0.05\sin (x+15t)$ with the standard wave equation $Y=A\sin (kx+\omega t)$, we get:

$k=1\text{rad/m}$

$\omega =15\text{rad/s}$

The wave speed $v$ is given by:

$v=\frac{\omega }{k}=\frac{15}{1}=15\text{m/s}$

The speed of a transverse wave on a string is related to the tension $T$ and linear mass density $\mu$ by the formula:

$v=\sqrt{\frac{T}{\mu }}$

Squaring both sides and rearranging for $T$:

$T=\mu v^2$

Substituting the given values $\mu =10^{-3}\text{kg/m}$ and $v=15\text{m/s}$:

$T=10^{-3}\times (15{)}^2$

$T=10^{-3}\times 225=0.225\text{N}$

Answer: $0.225\text{N}$