Thanks to Einstein's theory of special relativity, we know the speed of light in a vacuum is the ultimate speed limit in the universe but other waves are expected to also have limitations. Of particular interest are sound waves. Now, the maximum speed limit of sound moving through dense materials like solids and liquids has been calculated for the first time.

Reporting in the journal Science Advances, the team estimates that sound waves can propagate with a maximum speed of 36 kilometers (22 miles) per second. That’s twice as much as the speed of sound in diamonds and over 100 times the speed of sound through air. It's also about 8,000 times lower than the speed of light in a vacuum.

Sound waves are a type of vibration that propagates through a medium, whether solid, liquid, or gas. In solid and liquids, the speed of sound is much faster because of their higher density. Their constituent particles are much closer together allowing for the vibration to spread faster. 

The researchers' calculations started from a simple consideration about how the speed of sound is calculated using the physical characteristics of a material. The standard formula shows that the speed is dependent on how much you can deform your material and how dense it is. The team realized that they could expand this calculation to create a more idealized case, arriving at a formula that depends on three physical constants: the speed of light in a vacuum, the ratio between the mass of electrons and the mass of protons, and the fine-structure constant, which characterizes the strength of electromagnetic interactions between particles. 

They believe that this idealized formula can predict the upper limit of the speed of sound since you no longer need the properties of the material as a whole (with its imperfections) but you are only taking into account its constituent particles and how these interact with one another.  

“Soundwaves in solids are already hugely important across many scientific fields. For example, seismologists use sound waves initiated by earthquakes deep in the Earth interior to understand the nature of seismic events and the properties of Earth composition,” co-author Professor Chris Pickard, Professor of Materials Science at the University of Cambridge, said in a statement. “They’re also of interest to materials scientists because sound waves are related to important elastic properties including the ability to resist stress.”

The team performed several tests on a wide range of materials to confirm that their assumptions – that the maximum speed of sound in a solid would decrease with increasing mass of the atoms in the material – was indeed correct.

The limiting case is hydrogen, the lightest atom, in its solid form. Unfortunately, hydrogen is not an easy element to turn solid. The team suspects that this upper limit could be achieved in an actual substance when hydrogen is in its rare metallic phase, as expected to exist under incredible pressures at the center of planets such as Jupiter.

“We believe the findings of this study could have further scientific applications by helping us to find and understand limits of different properties such as viscosity and thermal conductivity relevant for high-temperature superconductivity, quark-gluon plasma, and even black hole physics,” lead author Professor Kostya Trachenko, professor of physics at Queen Mary University of London, concluded.