A string of total length 30 cm and linear mass density 0.5 g cm ⁻¹ is secured to a fixed wall at one end and to a frictionless ring on a vertical rod at the other end. A symmetric wave pulse, initially peaking at a distance of 20 cm from the ring, travels towards the ring at 20 cm s ⁻¹ . The reflections at both ends are assumed to be energy lossless. The shape of the string changes periodically with time. Determine t

Step-by-step solution

For a string of length L secured to a fixed wall at one end and a frictionless ring (free end) at the other, the boundary conditions dictate how a wave pulse reflects: 1. At the free end (ring), the pulse reflects without any phase change (an upright pulse remains upright). 2. At the fixed end (wall), the pulse reflects with a phase change of (an upright pulse becomes inverted). Let us trace the journey of the initial upright pulse to determine when it returns to its exact initial state (same position, same shape,