I am mainly using two algebra word problem concepts as the mathematical framework for my hypothesis: meeting and overtaking. That is, the aft vertical pole is meeting the sound wave - air at rest, the train is moving forward; or the aft vertical pole is overtaking the sound wave - air at rest, the train is moving in reverse.
In the reference frame of the moving flatbed train car, the aft pole, the observer and her clock are either overtaking or meeting the fore pole of the train car, depending on whether the train is moving towards or away from the sound emitter. But the aft pole and the observer will never reach the fore pole because they are moving in tandem (except in a train wreck!!!).
At the same time, on a windless day, the air molecules (medium) are in another reference frame (along with another observer and the platform), which is at rest relative to the first reference frame. However this other observer, and the station platform, and this other reference frame are not needed for my calculations. The idea that this other observer gets a similar result to the observer within the flatbed reference frame is what leads me to believe that I have found a new state of motion.
The arrangement of the experimental apparatus is that, affixed to the aft pole is a light emitter and a sound sensor. There is also a single clock and a single observer seated at this position. Affixed to the fore pole, is a light sensor and a sound emitter whose purpose is to send a sound wave back towards the original starting position back at the aft pole.
To set up the algebra word problem, I assign letters to the given knowns and unknowns. The speed of sound is to be represented by c; the speed of the train is to be represented by v; the length of the flatbed is to be represented by L; and the time elapsed while the experiment is conducted is to be represented by t. The next step is to find the equation expressing the relationship amongst the constants and variables.
For the equation expressing the meeting aspect of this word problem, I imagine that as the train is moving forward relative to the arrangement of the apparatus, the aft pole will meet the sound wave traveling back toward the pole through the air. This is somewhere within the distance of the starting positions of the aft pole and sound emitter at the instant when the sound is emitted.
♦ ct = L - vt
♦ ct + vt = L
♦ t = L / (c + v)
To continue, for the equation expressing the overtaking aspect of this word problem, I imagine that as the train is going in reverse relative to the arrangement of the apparatus, the sound wave will overtake the aft pole somewhere beyond the distance that they are originally apart. Thusly, at the same time the aft pole is moving away from the sound.
♦ ct = L + vt
♦ ct - vt = L
♦ t = L / (c - v)
Either of these two equations can be solved for v (unknown), the velocity of the train. All the other values (knowns) can be found from the experiment. Taken together, they are identical to the formula from the Michelson-Morley experiment to detect the aether. So, if they are added, the resulting formula can also be solved for v:
♦ T = [L / (c + v)] + [L / (c -v)] = [2Lc] / (c²-v²)
Due to the idea that the poles are at rest relative to each other, but moving in tandem relative to the medium, creates the scenario that I can algebraically exploit to create this alternative form of echo. Since sound waves are different from light waves, both by Einstein and by Galileo, I believe I have found a new interpretation of motion.
In the reference frame of the moving flatbed train car, the aft pole, the observer and her clock are either overtaking or meeting the fore pole of the train car, depending on whether the train is moving towards or away from the sound emitter. But the aft pole and the observer will never reach the fore pole because they are moving in tandem (except in a train wreck!!!).
At the same time, on a windless day, the air molecules (medium) are in another reference frame (along with another observer and the platform), which is at rest relative to the first reference frame. However this other observer, and the station platform, and this other reference frame are not needed for my calculations. The idea that this other observer gets a similar result to the observer within the flatbed reference frame is what leads me to believe that I have found a new state of motion.
The arrangement of the experimental apparatus is that, affixed to the aft pole is a light emitter and a sound sensor. There is also a single clock and a single observer seated at this position. Affixed to the fore pole, is a light sensor and a sound emitter whose purpose is to send a sound wave back towards the original starting position back at the aft pole.
To set up the algebra word problem, I assign letters to the given knowns and unknowns. The speed of sound is to be represented by c; the speed of the train is to be represented by v; the length of the flatbed is to be represented by L; and the time elapsed while the experiment is conducted is to be represented by t. The next step is to find the equation expressing the relationship amongst the constants and variables.
For the equation expressing the meeting aspect of this word problem, I imagine that as the train is moving forward relative to the arrangement of the apparatus, the aft pole will meet the sound wave traveling back toward the pole through the air. This is somewhere within the distance of the starting positions of the aft pole and sound emitter at the instant when the sound is emitted.
♦ ct = L - vt
♦ ct + vt = L
♦ t = L / (c + v)
To continue, for the equation expressing the overtaking aspect of this word problem, I imagine that as the train is going in reverse relative to the arrangement of the apparatus, the sound wave will overtake the aft pole somewhere beyond the distance that they are originally apart. Thusly, at the same time the aft pole is moving away from the sound.
♦ ct = L + vt
♦ ct - vt = L
♦ t = L / (c - v)
Either of these two equations can be solved for v (unknown), the velocity of the train. All the other values (knowns) can be found from the experiment. Taken together, they are identical to the formula from the Michelson-Morley experiment to detect the aether. So, if they are added, the resulting formula can also be solved for v:
♦ T = [L / (c + v)] + [L / (c -v)] = [2Lc] / (c²-v²)
Due to the idea that the poles are at rest relative to each other, but moving in tandem relative to the medium, creates the scenario that I can algebraically exploit to create this alternative form of echo. Since sound waves are different from light waves, both by Einstein and by Galileo, I believe I have found a new interpretation of motion.
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