Snelheid van een transversale golf

Consider a flexible taut rope in an equilibrium position with a linear mass density μ and a tension force T.

When a constant upward force is applied at the right end, a transverse wave travels through the rope with constant speed.

The small element of length Δx oscillates perpendicular to the wave motion because of the rope's restoring force.

The force at each end is tangent to the rope.

The tension forces in the x-directions have equal magnitude and opposite directions, so they cancel.

The slope of the rope at points x and x plus Δx determines the expressions for the y-components of the force.

Combining these expressions gives the net y-component of the force, which according to Newton's second law, equals the elements' mass times the y-component of acceleration.

Dividing by T-Δx and taking the limit Δx to be zero gives the expression, in the same form as the linear wave equation.

This provides the expression for the speed of the wave, which depends on the tension and the linear density.