Wave Speed on a String

This formula gives the speed of a transverse pulse or wave traveling along an ideal stretched string. It comes from balancing the string’s sideways inertia, set by its mass per unit length μ, against the restoring pull from the tension T: a tighter string pulls disturbances back more strongly, while a heavier string is harder to accelerate, so waves move faster on the former and slower on the latter. The square-root form shows that wave speed grows more slowly than tension itself and falls as the string becomes heavier.

Use this for waves on strings or wires when you know the tension and the linear density, such as guitar strings, laboratory string waves, or textbook wave-speed calculations. It is most appropriate for an ideal string under uniform tension, where the wave amplitude is small compared with the string length.

• Using the total mass of the string instead of the mass per unit length μ
• Forgetting that tension T must be in newtons and μ in kg/m to get speed in m/s
• Reversing the ratio and calculating √(μ/T) instead of √(T/μ)