Q4. A wave has wavelength 40 cm. What is the phase difference between two points 10 cm apart along the direction of travel?
Δφ = 2π × 10/40 = π/2.
Q5. For y = 2 sin(kx − ωt + π/6) cm, find the displacement at x = 0 and t = 0.
y = 2 sin(π/6) = 2 × 0.5 = 1 cm.
Q6. A wave is y = 0.4 sin(0.5x − 10t), with x and y in cm and t in s. Find its wavelength and period.
k = 0.5 rad cm, so λ = 2π/0.5, about 12.6 cm. ω = 10 rad s, so T = 2π/10, about 0.628 s.