Speed of a Wave on a String

This simulation walks students through the classic derivation of the transverse wave speed on a stretched string, v = √(T/μ). Starting from a moving pulse, it shows how tension T and linear mass density μ determine the propagation speed, using geometric arguments about a small arc of the string near the crest.

In the interactive scene, a row of numbered step buttons lets users advance through six symbolic steps. A switch toggles the view between the laboratory frame and the frame moving with the pulse, letting students see how the string material flows past a stationary pulse. Arrow keys provide quick navigation. The visualisation displays the string, tension forces, and the curvature that produces the centripetal force.

By comparing the two frames, learners discover why the same tension produces the same force balance, reinforcing concepts of inertial frames, vector components of tension, and the origin of the √(T/μ) relationship. The activity deepens understanding of wave mechanics and the role of tension and mass density in oscillatory systems.