Result

Speed of sound

v = \frac{B}{ρ}

Statement

The speed of a sound wave, set by the medium's stiffness (bulk modulus B) and inertia (density ρ) — the same restoring-force-over-inertia pattern as a wave on a string.

Symbols and units

$v$	speed of sound	m/s
$B$	bulk modulus of the medium	Pa
$ρ$	density	kg/m³

When it applies

A fluid or solid medium; B is the relevant elastic modulus for that medium.

Don't use when

The elastic modulus B must match the medium — using the wrong modulus (e.g. Young's modulus for a fluid) gives an incorrect speed.

Derivation

As with a string, wave speed is the square root of a restoring property divided by an inertial one — here elasticity divided by density:

v = \frac{B}{ρ}

Watch out for

Sound travels faster in stiffer, less dense media — faster in solids than liquids, and faster in liquids than gases, despite gases often feeling 'thinner'.

Connects to

Wave speed on a string