Answer
$0.19$ seconds
Work Step by Step
To find the speed of the wave on a string, use the formula $$v=\sqrt{\frac{F_T}{\mu}}$$ Find the mass-length density $\mu$. $$\mu=\frac{M}{L}=\frac{32g}{9.5m}=3.4g/m=0.0034kg/m$$ Substituting known values of $\mu=0.0034kg/m$ and $F_T=8.6N$ yields a speed of $$v=\sqrt{\frac{8.6N}{0.0034kg/m}}=50.m/s$$ Use the kinematics formula $$v=\frac{\Delta x}{\Delta t}$$ to solve for $\Delta t$. $$\Delta t=\frac{\Delta x}{v}$$ Substitute known values of $\Delta x=9.5m$ and $v=50.m/s$ to get a time of $$\Delta t=\frac{9.5m}{50.m/s}=0.19s$$
