  Two dimensionless fundamental physical constants, the fine structure constant
$\alpha$ and the proton-to-electron mass ratio $\frac{m_p}{m_e}$ 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
which provides the upper bound for the speed of sound in condensed phases,
$v_u$. We find that
$\frac{v_u}{c}=\alpha\left(\frac{m_e}{2m_p}\right)^{\frac{1}{2}}$, 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 current understanding of how fundamental constants can impose
new bounds on important physical properties.
