Under the Special Theory of Relativity, the units of length are to be measured in terms of a triangle formed by a vertically reflected light bean. This gives rise to the effect of length contraction appearing between an observer in motion and an observer at relative rest. The phenomenon of length contraction is however indiscernible for the observer who shares in motion.

If a sound wave is used to measure the unit of length, the length contraction becomes enshrouded in a mist. The contraction appears only slightly when the sound source is in motion (v << c). So, while measuring a unit of length on a measuring stick across reference frames is impossible for a light beam, it is well within the grasp of a sound wave. An observer in motion will totally agree with an observer at relative rest.

The formula c = L / t or L = ct, is the simplest form of the Newtonian law, or equation of motion in an inertial reference frame by the principle of relativity. A comparison with the result of my thought experiment yields an unmasking of length contraction. The length of the train car, L, can be found from the known speed of sound waves c, and the time measured on the clock. So that the observer on board the train would anticipate the length can be solved for by using algebra.

But if the train is in motion, then the time measured will be different. It will be: t = L - vat / c, or L - vt = ct or L = ct + vt (with t = t) due to the forward motion of the train car at the velocity, v. And thus the length, through the air that, the sound wave has traveled, as interpreted by the train observer, will be shorter than the length of the train car if it were at rest.

The setup of my thought experiment uses a single clock, so that no synchronization is necessary. This has been put forward as a proof for supporting STR. In most examples to illustrate STR it is put forward that the observer at rest has to use two clocks for two events that occur at different locations in space.

However, in my hypothesis there is only one clock and only one observer within the train reference frame. Thus doing an end run around synchronization; it is not a limitation for my hypothesis. I propose that the answer the train car observer measures is identical to that of an observer on the platform, without any sort of communication going on between the two.

This shakes the appearance and reality of Relativity. An axiomatic statement that these two observers, one at rest, one in motion, will measure two different times and velocities for the same event, is at the heart of Relativity. But my setup has done precisely that.

Both the train observer and the platform observer will claim the same, identical formula for the motion of the train car; this is the same formula found by the platform observer by the Galilean transformation. Units of length cannot be measured by light waves, across reference frames, to get a single common value; but it can be measured thusly by sound waves, under easily met conditions.

https://en.wikipedia.org/wiki/Length_contraction