Speed of sound from fundamental physical constants

Two dimensionless fundamental physical constants, the fine structure constant alpha and the proton-to-electron mass ratio mp/me', are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant that provides the upper bound for the speed of sound in condensed phases, v(u). We find that vu/c = alpha (me/2m(p))(1/2), where c is the speed of light in vacuum. We support this result by a large set of experimental data and first-principles computations for atomic hydrogen. Our result expands the current understanding of how fundamental constants can impose new bounds on important physical properties.