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We prove that multiplicities in the length spectrum of a non-compactarithmetic hyperbolic orbifold of dimension $n \geqslant 4$ have exponentialgrowth 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 ofBelolipetsky, Lal\'in, Murillo and Thompson. Our proof is based on the study of(square-rootable) Salem numbers. As a counterpart, we also prove a refinedversion of these asymptotic results, adapting the argument of G\"otze andGusakova for the case of square-rootable Salem numbers, to show that one cannot obtain a better estimate on the multiplicities using our approach.

Multiplicities in the length spectrum and growth rate of Salem numbers