A wave on a rope is y = 0.04 sin(3.0x - 60t), with x and y in metres and t in seconds…

From the formula, $a = 0.04\ \text{m} = 4\ \text{cm}$, $k = 3.0\ \text{rad/m}$ and $\omega = 60\ \text{rad/s}$.

• $\lambda = \dfrac{2\pi}{3.0\ \text{rad/m}} = 2.09\ \text{m}$.
• $f = \dfrac{60\ \text{rad/s}}{2\pi} = 9.55\ \text{Hz}$.
• $v = \dfrac{\omega}{k} = \dfrac{60\ \text{rad/s}}{3.0\ \text{rad/m}} = 20\ \text{m/s}$.

The phase is $kx - \omega t$, so the wave travels towards $+x$. As a check, $f\lambda = 9.55\ \text{Hz} \times 2.09\ \text{m} = 20\ \text{m/s}$.