A wave travelling on a string at a speed of 10 m s-1 causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave? (b) If the displacement of a particle is 1.5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant?

Sol. Wave speed = v = 10 m/sec Time period = T = 20 ms = 20 * 10–3 = 2 * 10–2 sec a) wave length, λ = vT = 10 * 2 * 10–2 = 0.2 m = 20 cm b) wave length, λ = 20 cm ∴ phase diffn = (2π/λ) x = (2π / 20) * 10 = π rad y1 = a sin (ωt – kx) ⇒ 1.5 = a sin (ωt – kx) So, the displacement of the particle at a distance x = 10 cm. [∅ = 2πx/λ = 2π * 10/20 = π] os goven by Y2 = a sin (ωt – kx + π) ⇒ -a sin (ωt – kx) = -1.5 mm ∴ displacement = -1.5 mm