INTRODUCTION
This is a proposal for an experiment which could be conducted within a university research wind tunnel. Its objective would be to measure the time intervals between two sound events which occur with respect to two inertial reference frames which may be at rest or in motion relative to each other. The results would contradict the definition of time from the Special Theory of Relativity.
METHODOLOGY
An experimental apparatus consisting of two heavy stanchions could be placed within the wind tunnel a distance L apart on a straight line which is parallel to the direction of the wind flow. A sound pulse would be emitted from the emitter/sensor atop one stanchion and received at the clock/receiver/sensor atop the other stanchion.
The clock and the emitter would be activated simultaneously by an electrical signal so that the clock would start simultaneously with the pulse emission event. Then, the clock would stop simultaneously with the pulse reception event. Therefore, the clock would measure the time interval, ∆t, between the events.
In inertial reference frame S′ the air would be at rest (Tipler & Mosca 2008, 522). In inertial reference frame S an observer and the experimental apparatus would be at rest. The x′-axis of S′ and the x-axis of S would be parallel to each other and parallel to the direction of wind flow.
The pulse would propagate from the emitter to the receiver along the length L at the constant velocity c relative to the air. The letter c is used for both the speed of light and the speed of sound because of some of their shared wave characteristics (Born 1965, 227). One such characteristic is that both of their wave velocities are independent of the source velocity (Tipler & Llewellyn 2012, 12).
This experiment could be conducted in two stages. In the first stage, S′ could be at rest relative to S. The pulse would propagate from the emitter to the receiver in the time: ∆t = L / c. This is just a rearrangement of the classical velocity formula: time = distance / velocity.
In the second stage, S′ could be in motion at the constant velocity v (v < c) relative to S in a direction which is parallel to the x′-axis of S′, the x-axis of S, and the wind flow. The pulse would propagate from the emitter to the receiver in the time: ∆t = L / (c ± v). In this formula, the wind velocity would be added to or subtracted from the emitted pulse velocity depending upon whether the wind flow passes the emitter or the receiver first (Morin 2008, 505).
CONCLUSION
In this experiment, sound propagating relative to some medium would produce measurable time differences according as to whether the medium is at rest or in motion relative to the clock. The Special Theory of Relativity does not adequately address sound propagating relative to a medium.
References
Born, Max. 1965. Einstein's Theory of Relativity. New York: Dover Publications.
Morin, David. 2008. Introduction to Classical Mechanics. Cambridge: Cambridge University Press.
Tipler, Paul & Ralph Llewellyn. 2012. Modern Physics. New York: W. H. Freeman & Company.
Tipler, Paul & Gene Mosca. 2008. Physics for Scientists and Engineers. New York: W. H. Freeman & Company.
