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We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities $m₁,...,m_k$ for the Coxeter polynomials of the trees $₁,...{,}_k$ respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least $minm-m₁,...,m-m_k$ where $m=m₁+\cdots +m_k$.