  We prove that mean multiplicities in the length spectrum of a non-compact
arithmetic hyperbolic orbifold of dimension $n \geqslant 4$ have exponential
growth rate $$ \langle g(L) \rangle \geqslant c \frac{e^{([n/2] - 1)L}}{L^{1 +
\delta_{5, 7}(n) }}, $$ extending the analogous result for even dimensions of
Belolipetsky, Lal\'in, Murillo and Thompson. Our proof is based on the study of
(square-rootable) Salem numbers.
  As a counterpart, we also prove an asymptotic formula for the distribution of
square-rootable Salem numbers by adapting the argument of G\"otze and Gusakova.
It shows that one can not obtain a better estimate on mean multiplicities using
our approach.
