Sound has a speed limit. Under normal circumstances, its waves can travel no faster than about 36 kilometers per second, physicists propose October 9 in Science Advances.
Sound zips along at different rates in different materials — moving faster in water than in air for example. But under conditions found naturally on Earth, no material can host sound waves that outpace this ultimate limit, which is about 100 times the typical seed of sound traveling in air.
The team’s reasoning rests on well-known equations of physics and mathematical relationships. “Given the simplicity of the argument, it suggests that [the researchers] are putting their finger on something very deep,” says condensed matter physicist Kamran Behnia of École Supérieure de Physique et de Chimie Industrielles in Paris.
The equation for the speed limit rests on fundamental constants, special numbers that rule the cosmos. One such number, the speed of light, sets the universe’s ultimate speed limit — nothing can go faster. Another, known as the fine-structure constant, determines the strength with which electrically charged particles push and pull one another. When combined in the right arrangement with another constant — the ratio of the masses of the proton and electron — these numbers yield sound’s speed limit.
Sound waves, which consist of the vibrations of atoms or molecules, travel through a material as one particle jostles another. The wave’s speed depends on various factors, including the types of chemical bonds holding the material together and how massive its atoms are.
None of the sound speeds previously measured in a variety of liquids and solids surpass the proposed limit, condensed matter physicist Kostya Trachenko and colleagues found. The fastest speed measured, in diamond, was only about half the theoretical maximum.
The limit applies only to solids and liquids at pressures typically found on Earth. At pressures millions of times that of Earth’s atmosphere, sound waves move faster and could surpass the limit.
One material expected to boast a high sound speed exists only at such high pressures: hydrogen squeezed hard enough to turn into a solid metal (SN: 6/28/19). That metal has never been convincingly created, so the researchers calculated the expected speed instead of using a measurement. Above about 6 million times Earth’s atmospheric pressure, the sound speed limit would be broken, the calculations suggest.
The role of the fundamental constants in sound’s maximum speed results from how the waves move through materials. Sound travels thanks to the electromagnetic interactions of neighboring atoms’ electrons, which is where the fine-structure constant comes into play. And the proton-electron mass ratio is important because, although the electrons are interacting, the nuclei of the atoms move as a result.
The fine-structure constant and the proton-electron mass ratio are dimensionless constants, meaning there are no units attached to them (so their value does not depend on any particular system of units). Such dimensionless