Length of a Rod.

Propagating sound could be used to measure the length of a material object with respect to observers at rest in inertial reference frames S′ and S. A straight rigid rod of fixed length D could be oriented parallel to the x′-axis of S′ and the x-axis of S. The rod would have a sound emitter at one end and a sound receiver at its other end. This apparatus could emit a sound pulse which would propagate at the constant velocity c through some medium from the emitter to the receiver. The times between the emission and reception events would be ∆t′ in S′ and ∆t in S as measured by a common clock. If S′ and the rod were at rest relative to S and the medium, then: D = c∆t′ = c∆t. If S′ and the rod were in motion, parallel to the rod's length, at the constant velocity v (v < c) relative to S and the medium, then: D = c∆t′ ± v∆t′ = c∆t ± v∆t.  The formulas containing v could be used by both observers in the same experiment. This would contradict the Special Relativistic effect of length contraction.