This paper shows that one cannot "hear" the rational cohomology ring of a hyperbolic 3manifold. More precisely, while it is well-known that strongly isospectral manifolds have the same cohomology as vector spaces, we give an example of compact hyperbolic 3-manifolds that are strongly isospectral but have nonisomorphic rational cohomology rings. Along the way we implement a computer program which finds the nullity of the cup product map H 1 (M ; Q) ∧ H 1 (M ; Q) → H 2 (M ; Q) for any aspherical space in terms of the presentation of the fundamental group.

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