INTRODUCTION
This is a proposal for an experiment which could be conducted within the University of Toledo 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 central hypothesis of this experiment would mainly come from a definition from the Special Theory of Relativity (SR) which states that the proper time would be a time interval measured by a clock which is at rest relative to the inertial reference frame where two events occur at the same location (Tipler & Mosca 2008, 1324).
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 activation event would occur at the same location as the pulse reception event. At the same time as the clock activation event a nearly instantaneous electrical signal would be sent to the emitter so that the clock would measure the time interval, ∆t, between the sound emission and sound reception events.
In inertial reference frame S′ the air would be at rest (Morin 2008, 505). 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 have propagated 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 have propagated 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, the clock activation event and sound reception event would occur at the same location in both inertial reference frames for both stages. In the first stage, the time interval measurements would follow the classical velocity formula and fit the definition of proper time from SR.
However, in the second stage the time interval measurements would use the formula containing v which would not be available under SR for an observer at rest in a moving inertial reference frame. As a consequence, any clock could measure any time intervals between two sound events in any inertial reference frame no matter whether the clock is at rest or in motion. Sound propagating relative to a medium would not comfortably fit into the Special Theory of Relativity.
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.
