A progressive wave is described by y = 0.05·sin(4πx − 200πt) metres. Find (a) amplitude, (b) wavelength, (c) frequency, and (d) wave speed and direction. Step 1: Compare with y = A·sin(kx − ωt): A = 0.05 m; k = 4π rad/m; ω = 200π rad/s. Step 2: (b) λ = 2π/k = 2π/4π = 0.5 m. Step 3: (c) f = ω/2π = 200π/2π = 100 Hz. Step 4: (d) v = ω/k = 200π/4π = 50 m/s; the minus sign in (kx − ωt) means travel along +x. Answer: (a) 0.05 m, (b) 0.5 m, (c) 100 Hz, (d) 50 m/s toward +x. Check: v = fλ = 100 × 0.5 = 50 m/s. ✓