Question #42643

Two transverse waves propagate on a taut string of linear mass density $\mu = 0.01 \text{ kg/m}$ under a tension $T = 100 \text{ N}$. The individual wave displacements are given by $y_1(x,t) = A \sin(kx - \omega t)$ and $y_2(x,t) = A \sin(kx + \omega t + \phi)$. The resultant displacement of the string is $y = y_1 + y_2$. At $x = 0$ and $t = 0$, the instantaneous spatial slope of the string is $\frac{\partial y}{\partial x} = 0.03$, and the phase constant is $\phi = \frac{\pi}{3}$. What is the magnitude of the transverse particle velocity of the string at $x = 0$ and $t = 0$?