Wave speed on a string
(W2.2.1) W2.2 · Speed on a String →The speed of a transverse wave on a string under tension F_T with mass per unit length μ.
| wave speed | m/s | |
| string tension | N | |
| mass per unit length | kg/m |
A stretched, flexible string or rope; tension approximately uniform along its length.
Assumes tension is approximately uniform along the string's length — a string with significant sag or varying tension needs a more general treatment.
Tension supplies the restoring force on a displaced element; linear mass density μ supplies the inertia resisting that restoring force.
Combining the two in the wave equation for a stretched string gives the propagation speed:
Since v depends on the square root of tension:
Doubling the tension increases speed by a factor of √2, not 2 — a common overestimate.
Speed depends on the square root of tension, not tension directly — doubling the tension increases speed by a factor of √2, not 2.