The equation of a wave travelling on a string isY = (0.10 mm) sin[(31.4 m-1)x + (314 s-1)t].(a) In which direction does the wave travel? (b) Find the wave speed, the wavelength and the frequency of the wave. (c) What is the maximum displacement and the maximum speed of a portion of the string?

Sol. The equation of the wave is given by y = (0.1 mm) sin [(31.4 m–1)x +(314 s–1)t] y = r sin {(2πx / λ)} + ωt) a) Negative x-direction b) k = 31.4 m–1 ⇒ 2 λ / λ = 31.4 ⇒ λ = 2π/31.4 = 0.2 mt = 20 cm Again, ω = 314 s–1 ⇒ 2πf = 314 ⇒ f = 314 / 2π = 314 / (2 * (3/14)} = 50 sec–1 ∴ wave speed, v = λf = 20 * 50 = 1000 cm/s c) Max. displacement = 0.10 mm Max. velocity = aω = 0.1 * 10–1 * 314 = 3.14 cm/sec.