quantity

speed of sound

The speed at which sound waves propagate through a medium.
25 related articles · 4 formulas

Description

The speed of sound is the rate at which a mechanical pressure disturbance travels through a given medium. It is not a universal constant but a material property, determined by how quickly neighboring particles can respond to a perturbation. In air at room temperature, sound travels at about 343 meters per second; in water, roughly 1,480 m/s; in steel, about 5,960 m/s. The speed varies with temperature, pressure, and composition, and it sets the fundamental timescale for many physical processes — from the propagation of seismic waves through Earth's interior to the behavior of shock waves in solar wind.

History

The first quantitative measurement of the speed of sound in air was performed by Marin Mersenne in 1636, who obtained a value close to the modern one. Newton later derived a theoretical formula, though it underestimated the measured speed until Laplace corrected it by accounting for adiabatic heating in 1816.

How it works

The speed of sound emerges from the balance between the medium's stiffness (how strongly it resists compression) and its inertia (how much mass must be accelerated). In a gas, the speed depends on temperature and molecular mass: hotter molecules move faster and transmit disturbances quicker. In solids, the speed is governed by elastic moduli and density, with stiffer materials like diamond transmitting sound at over 12,000 m/s. The concept also applies to exotic media: in the dense interior of a neutron star, the speed of sound can approach a significant fraction of the speed of light.

In practice

The speed of sound is critical in designing ultrasonic imaging systems, calibrating acoustic sensors, modeling earthquake wave propagation, and understanding the behavior of supersonic flows in aerospace engineering.

Fun fact

In the ultra-dense matter of a neutron star, the speed of sound can reach about half the speed of light, making these dead stars the fastest acoustic conductors in the universe.

Concept graph →

Formulas

$$c_s^2 = \frac{dP}{d\varepsilon}$$
Speed of sound squared is the derivative of pressure with respect to energy density.
What is in the formula
c_svariablespeed of sound — speed of sound metre per second
Pvariablepressure — pressure pascal
εvariableenergy density — energy density joule per cubic metre
d/dεoperatorderivative with respect to energy density — derivative
$$k_J = \sqrt{\frac{4\pi G \rho}{c_s^2}}$$
Scale where thermal pressure supports against collapse.
What is in the formula
k_JvariableJeans wavenumber — wavenumber reciprocal metre
\rhovariableMass density — mass density kilogram per cubic metre
c_svariableSound speed — speed of sound metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$c_s = \sqrt{\frac{K}{\rho}}$$
Sound speed depends on stiffness and density.
What is in the formula
c_svariableSpeed of sound in the medium — speed of sound metre per second
KvariableBulk modulus (stiffness) of the medium — bulk modulus pascal
ρvariableMass density of the medium — mass density kilogram per cubic metre
√operatorTakes the square root of the argument — square root
$$\mathcal{M} = \frac{v}{c_s}$$
Ratio of flow velocity to local speed of sound.
What is in the formula
\mathcal{M}variableMach number — mach number
vvariableflow velocity — velocity metre per second
c_svariablelocal speed of sound — speed of sound metre per second

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