  In this paper, we study the blow-up of solutions for semilinear wave
equations with scale-invariant dissipation and mass in the case in which the
model is somehow 'wave-like'. A Strauss type critical exponent is determined as
the upper bound for the exponent in the nonlinearity in the main theorems. Two
blow-up results are obtained for the sub-critical case and for the critical
case, respectively. In both cases, an upper bound lifespan estimate is given.
