Here’s what you’ll learn when you read this story:

• The way waves propagate through liquids (Kelvin wave patterns) and solids (Rayleigh waves) were thought to be two distinct phenomena.
• A new study analyzing ultra soft solids, such as gels and biological tissue, bridges the gap between these two phenomena by creating a wake-like pattern while also deforming the object.
• Scientists believe they can use this new discovery to create a kind of “soft diagnostic” tool where information can be gleaned about the health of a tissue or organ without needing to cut into it.

If you’ve ever traveled on a boat, then you’ve no doubt seen the tell-tale V-shaped waves that follow in its wake. This behavior in liquids was thoroughly described mathematically by Lord Kelvin in 1887 and fittingly became known as a “Kelvin wake pattern.” However, two years earlier, another British lord—this one by the name of John William Strutt, 3rd Baron Rayleigh—described waves as they pass through solids, such as seismic waves passing through rock. These waves eventually became intrinsically linked with their discoverer and are known today as “Rayleigh waves.”

While both of these theories describe how waves move through a material, they were seen as fundamentally different phenomena—until now. In a new study published in the journal Physical Review Letters, a team of scientists at Harvard University has revealed that ultra-soft solids, such as gels or (more importantly) biological tissue, blur the lines between these two types of waves, and in the process, link their behaviors. And while liquids and solids have been thoroughly studied over the past century, the dynamics of ultra-soft solids, especially their unique mix of inertia, elasticity, and capillarity, have barely been studied at all.

Lakshminarayanan Mahadevan, who led the study, says he was partly inspired by watching boats travel down the Charles River near Harvard University’s campus.

“I suspected that there ought to be a natural way to smoothly interpolate between the behavior of surface waves on solids and fluids,” Mahadevan, a professor of applied mathematics, said in a press statement. “Much of our work reflects a broader scientific instinct: to search for the sublime, and the arcane, hidden within the mundane.”

Kelvin wake patterns radiate out in a V-shape pattern, also known as a “Mach wedge,” and don’t fundamentally deform a material like Rayleigh waves do. But Mahadevan discovered that ultra-soft solids can display a wake-like pattern and be deformed by the wave, meaning that the pattern of the wave carries information about the material itself. Crucially, the team discovered a key relationship between how fast a disturbance moves through material and its softness. For example, a fast-moving disturbance in soft tissue causes the wake to narrow, and this could be vital for creating non-invasive diagnostic tools.

The researchers call this idea “soft diagnostics” and believe that it might be possible to use this strange property of ultra-soft solids to learn about tissues without having to cut into them. Depending on how a waveform behaves when applied to an organ, for example, scientists could understand the stiffness of that material and determine if tumors could be present within the body.

“Our study of surface wakes on ultra-soft elastic surfaces uses experiments and theory to probe a previously unexplored regime where gravity, capillarity, and elastodynamics act together,” the authors write. “Our approach also provides a quantitative foundation for probing the dynamics of ultra-compliant solid surfaces.”