A simple harmonic wave of amplitude 8 unit travels along the positive x-axis. At given instant of time, for a particle at a distance of 10 cm from the origin, the displacement is + 6 unit and for a particle at a distance of 25 cm from the origin, the displacement is + 4 unit. Calculate the wavelength.

Step-by-step solution

Y = A sin ⁡ 2 π λ v t - x Y A = sin ⁡ 2 π t T - x λ In first case, Y 1 A = sin ⁡ 2 π t T - x 1 λ Here, Y 1 = +   6 , A = 8 , x 1 = 10   cm 6 8 = sin ⁡ 2 π t T - 10 λ .... (i) Similarly in the second case, 4 8 = sin ⁡ 2 π t T - 25 λ ... (ii) From equation (i), 2π​  t T - 10 λ = sin - 1 ⁡ 6 8 = 0.85   rad ⇒     t T - 10 λ = 0.14 .... (iii) Similarly from equation (ii), 2 &#960