Velocity of a Pulse on a String

The Velocity of a Pulse calculator computes the velocity of a pulse on a string based on the string tension and mass per unit length.

INSTRUCTIONS: Choose units and enter the following:

• (T) Tension
• (μ) Mass per centimeter

Velocity of Pulse (V): The calculator returns the velocity in centimeters per second.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

For mechanical waves in general: 

1. The speed at which a wave moves does not depend on the size or shape of the wave.
2. The speed of a mechanical wave depends on a combination of two properties of the medium: some measure of its inertia and some measure of its tightness, i.e., the strength of the force trying to bring the medium back toward equilibrium.

The formula for the velocity of a pulse is:

        `v=sqrt(T/μ)`,

where:

• T = tension
• μ = mass per unit length (grams per centimeter in this calculator)
• v = velocity of pulses 

References

19.2 Waves on a string  by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.