We show that the quasinormal modes, in the eikonal limit, for accelerating (non-rotating) black holes, are related to the angular velocity of the circular null geodesics and to the corresponding Lyapunov exponent, in a similar, but generalized way as the ones for spherically symmetric black holes are. We compute those quasinormal modes and greybody factors for neutral and charged accelerating black holes by considering massless test scalar fields. Later we show that the obtained results are universal for perturbations of any spin. We also determine the radius of the shadow cast by these black holes. Our results for charged accelerating black holes simplify to the ones of the Reissner-Nordstrom black hole simply by setting acceleration to zero.