---
title: "Wave Speed on a String from Tension and Linear Density"
description: "The speed of a wave on a stretched string comes from the restoring tension and the inertia per unit length, with no reference to how the wave was made. Tuning an instrument is a change to one of those"
canonical: https://lightmysky.com/learn/science/wave-speed-on-a-string-from-tension-and-linear-density-mt_83x7vwb7UU
source: https://lightmysky.com/learn/science/wave-speed-on-a-string-from-tension-and-linear-density-mt_83x7vwb7UU.md
retrieved: 2026-09-12
---

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# Wave Speed on a String from Tension and Linear Density

The speed of a wave on a stretched string comes from the restoring tension and the inertia per unit length, with no reference to how the wave was made. Tuning an instrument is a change to one of those two quantities.

Subject: Science · Area: Waves, Light & Sound · Ages 18 to 19
Page: https://lightmysky.com/learn/science/wave-speed-on-a-string-from-tension-and-linear-density-mt_83x7vwb7UU

## Ready when they can

- Calculates wave speed from tension and mass per unit length
- Predicts how the note of a string changes when it is tightened or thickened
- Explains why speed is set by the medium and frequency by the source

## Lesson: What sets the speed on a string

A stretched string carries waves at v equals the square root of T over mu, where T is tension and mu is mass per length. Tension restores, inertia resists, and amplitude and frequency never enter. Four times the tension gives twice the speed.

Tighten a string and v rises, so at fixed length the pitch climbs since f equals v over 2L. Swap in a thicker string at the same tension and mu grows, v falls, and the pitch drops.

**Example.** Tune a guitar by turning the peg: more tension means a higher note on the same string. Fit a heavier gauge string instead and the same peg position sounds lower, because the thicker string carries waves more slowly.

**Tip.** Always split the roles: the medium sets v while the source sets f, and lambda follows as v over f. Warmer air changes the speed of sound the same way, by shifting the medium.

**Recap.** Tension up or mass down means faster waves and higher notes, and the medium always owns the speed.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [The Wave Equation and Its Travelling-Wave Solutions](https://lightmysky.com/learn/science/the-wave-equation-and-its-travelling-wave-solutions-mt_Ue-v1cSxNx)

## Opens up

- [Intensity: the Energy and Power Carried by a Wave](https://lightmysky.com/learn/science/intensity-the-energy-and-power-carried-by-a-wave-mt_Hj-yG6g3CD)