Sound Waves Carry Mass

Physics 12, 23
Even if you ignore general relativity, sound waves transport a small amount of mass, according to theory.
Massive sound. A small amount of mass is transported along with all sound waves, according to a new theory.

Ordinary sound waves carry a small amount of mass with them as they travel, according to a new theoretical study. The theory assumes Newtonian conditions, so the effect is unrelated to either quantum theory or the equivalence of energy and mass known from relativity. The researchers do not yet have a clear physical explanation of their mathematical results, but they say that the idea should be testable in experiments with ultracold atoms, or possibly in observations of earthquakes.

Last year, high-energy physicists Alberto Nicolis of Columbia University in New York and Riccardo Penco, now at Carnegie Mellon University (CMU) in Pittsburgh, used quantum field theory to analyze the behavior of sound waves moving through superfluid helium [1]. To their surprise, they found that the waves carry a small amount of mass, not only by virtue of Einstein’s famous formula equating energy with mass. The duo found that phonons, the quantum units of sound waves, interact with a gravitational field in a way that requires them to transport mass as they move.

Now Nicolis and two other theorists have extended the analysis to sound waves moving in more familiar materials, such as liquids or solids, finding much the same result. For a 1-second-long, 1-watt sound wave in water, the amount of mass would be about 0.1 milligrams. “It’s honest-to-God gravitational mass, the one we experience every day,” says team member Angelo Esposito of the Swiss Federal Institute of Technology in Lausanne (EPFL). “It is simply a fraction of the total mass of the system that travels with the wave, being displaced from one place to another.”

Most physicists had assumed that sound waves carry energy but not mass, meaning that they would not generate any gravitational field (as long as one ignores general relativity). The team says that their analysis revealed the effect because it goes beyond the simplified linear models typically used in studying sound waves, where, for example, the displacement of a material is always exactly proportional to the force applied. Although this approximation is very good for most purposes, Nicolis says, it misses the mass effect entirely.

Esposito suggests that other researchers studying sound waves may have overlooked the effect because they rarely think about interactions with gravity. But he and his colleagues are high-energy physicists. “I think it helped us to have a different mindset,” he says.

The new calculation indicates that for ordinary sound waves in most materials, the mass carried is equal to the sound wave energy multiplied by a factor that depends on the speed of sound and the medium’s mass density. And the mass carried by sound waves turns out to be negative. It is a depletion of mass, rather an addition of mass. So sound waves in a gravitational field should float upward somewhat, like any buoyant object in water.

But the authors admit that they have more work to do in finding the right physical interpretation of the mass flow. For liquids, the authors note, the effect seems to imply that some small fraction of particles must travel against the motion of the sound wave. But this idea seems less plausible for solids.

“We trust the results,” says Nicolis, “because the mathematics describing solids and fluids is very similar. But trying to interpret these results at the microscopic level for solids is currently confusing.”

“This is certainly surprising,” says high-energy physicist Ira Rothstein of CMU. “You would have thought that results like this in classical physics were completely understood. Hopefully the effect will be measured soon.”

He also suggests a possible physical interpretation for the effect in solids. A wave of elastic compression could progressively shift a small bit of mass in one direction, at least until reaching the far surface. Understanding what happens at a solid’s surfaces will be essential for correctly interpreting the flow of mass, Rothstein says.

The researchers hope the effect might be detectable soon. For example, they estimate that the mass carried by a sound wave in a Bose-Einstein condensate of extremely cold atoms could carry as much as 1 part in 1000 of the total mass of the system, near the limits of current detection techniques. More ambitiously, earthquakes generate strong sound waves traveling through Earth’s crust, and the mass associated with them could be as large as 100 billion kilograms, which could register in sensitive gravitational monitoring devices.

This research is published in Physical Review Letters.

–Mark Buchanan

Mark Buchanan is a freelance science writer who splits his time between Abergavenny, UK, and Notre Dame de Courson, France.


  1. A. Nicolis and R. Penco, “Mutual interactions of phonons, rotons, and gravity,” Phys. Rev. B 97, 134516 (2018).

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