A standing wave on a string is y = 0.04 sin(5π x) cos(200π t), with x and y in metres and t in…

(a) $k = 5\pi\ \text{rad/m}$, so $\lambda = \dfrac{2\pi}{5\pi\ \text{rad/m}} = 0.4\ \text{m}$. $\omega = 200\pi\ \text{rad/s}$, so $f = \dfrac{200\pi\ \text{rad/s}}{2\pi} = 100\ \text{Hz}$.

(b) $v = f\lambda = 100\ \text{Hz} \times 0.4\ \text{m} = 40\ \text{m/s}$.

(c) $\lambda/2 = 0.2\ \text{m}$.

(d) $2a = 0.04\ \text{m}$, so $a = 0.02\ \text{m}$.

(e) $0.04\ \text{m} \times \sin(5\pi \times 0.05) = 0.04\ \text{m} \times \sin(\pi/4) = 0.0283\ \text{m}$.