A young woman stands before a high flat concrete wall on a blustery day. She directly faces it, at a distance of L meters away. The wind sweeps down past the wall at the constant velocity v and blows directly perpendicular from the wall to her face. She feels compelled to shout at the wall in some way, but she takes the stopwatch from her pocket and decides upon the experiment that she shall perform (akin to the Michelson-Morley aether wind experiment).

The formula for a sound wave to echo back from a hard reflective surface fixed to the earth, when the air is still (medium at rest) is:

♦ 2L = cT

However, I speculate that this is not the formula when there is a wind blowing at the constant velocity v in the direction directly opposite to the sound wave emission source. The velocity of the air molecules (medium) will have a measurable impact on the velocity of the sound wave as it travels from the source to the wall, and then back.

Our home planet hurtles through interstellar space at a tremendous speed, 30 km/second, but the atmosphere does not get swept away, off into the cosmos. Fortunately for us, the molecular bonds of attraction and repulsion, and the force of gravity, hold a thin layer of atmosphere snugly against the earth’s surface. Though terrestrial winds may surpass 120 km/hour, most of the air molecules we depend upon to fill our lungs cannot attain enough velocity to escape the earth’s embrace. This balancing of hydrostatic pressure and gravity thus bestows upon us, the breath of life. So the earth makes its yearly orbital journey with a thin layer of atmosphere grasping tenuously to it; tornadoes and hurricanes may blow, but we shall breathe.

So, when the air appears still, it is actually moving at the velocity of the earth. It is supposed that we cannot detect this motion by any mechanical experiment in the reference frame of the earth; however, it is worth exploring the scenario when the air molecules are disengaged, such as by a wind, from the rapidly moving surface of the land and sea. She stands, with her mouth and ears at the ready, opposite the high and hard reflective surface, forming a moving tandem with it; that any shout she might make would come back to her some moments later. If she is standing at a reasonable distance from this reflective surface on a windless day, then the first formula applies; but if a wind is blowing as I have described before, then the maths are different.

The hydrostatic pressure casts a cloak of invisibility over the motion of the stationary earthbound tandem, and the stationary air molecules trapped near the surface of the earth. The earth, the tandem, the earthbound air molecules, are all traveling through the galaxy at the same velocity v locked together in their motion. That is, when the air is still, but a wind will cleave this triumvirate.

Despite the tandem being fixed to the earth’s surface during its daily gyre, there is no Doppler effect upon the sound wave traveling from the girl to the wall because the wave crests are squeezed together near the source (girl), but pulled apart near the receiver (wall) by an equal amount; and vice versa on the reflection’s trip, so she would observe no change in the wavelength or frequency of the wave. In the presence of a wind, the Doppler change in frequency vanishes, but the Doppler wind formula remains present and measurable:

♦ c` = c ± w, where c` is the Dopplerian speed of the sound wave in the presence of the wind.

Because of the wind’s speed and direction, the new wave speed is c` = c – w as the sound wave travels away from the emitter (her mouth); but it is c`= c + w when the wave is reflected back towards its original source (her ear). That is, when compared to speed of sound in still air, the wind slows down (subtract from) the sound wave speed as it travels in one direction; but speeds up (adds to) the sound wave speed when it travels in the opposite direction. Thusly, the total trip time interval for the sound wave is:

♦not, T = [2L/c]

♦but, T` = [L / (c + w)] + [L / (c – w)] = [2Lc] / (c² – w²) = [2L / c] [1 / (1 – [w²/c²])

♦time = distance / speed.

With the pen and pad from her other pocket, she begins to make her calculations. The given variable values for her experiment are: c = speed of sound in still air, 340 meters/second; w = speed of wind, 50 m/s; L = 100 meters.

So, in the first echo scenario (no wind):

♦T = [2L] / c; T = [2 × 100m] / [340m/s] = 0.588s

And, in the second echo scenario (wind):

♦T ` = [2Lc] / (c<sup>2</sup> – w<sup>2</sup>); T ` = [2 × 100m × 340m/s] / [(340m/s)²] – [(50m/s)²] = 0.601s

She makes note of these differing measured time values. This leads her to ponder her two scenarios of air motion: molecules at rest in a stationary reference frame, and molecules passing unencumbered through the porous walls of an apparently stationary reference frame. There is a measureable difference between an enclosed compartment and a reference frame. The “conceptual walls” of the reference frame do not compel the air molecules within it to go at the velocity of the reference frame. These free-spirit airy particles are not possessed by the earthbound reference frame. But it is difficult to say to which reference frame they belong; they belong to no reference frame, and are in all earthly reference frames. This alternative echo formula is only a close approximation.

The moving air/medium has been disengaged from the stationary earthbound girl-wall tandem in a mathematically revelatory way. This has profound implications for the motion of any material object, when that motion is investigated by sound waves. At the slow speeds of the wind, the measured time interval does not suffer the Special Relativistic effects of time dilation and length contraction; the gamma factor value is negligible at this speed. Thus, the passage of time is nearly absolute, on the scale of her everyday life behind the wall.