Suppose a long train with a caboose travels down a level section of track at a constant velocity, v. There is an observer in the caboose and an engineer in the engine car. It is a windless day. This observer may ask: What is the speed of the train relative to the air, or a nearby platform (both at rest relative to train)?
She has a light source (lantern, maybe) to send a signal to the engine car and engineer. The light signal is effectively instantaneous. He blows the whistle when he receives the signal (disregard reaction time). If she starts the clock when she sends the light signal, then she can measure the time, t, for her to hear the returning sound (speed of sound, c) signal.
During the same time that the train is in forward motion, the whistle sound is in rearward motion. She speculates that she will meet the sound wave somewhere within the distance, D, from the engine to the caboose. By algebra:
♦ ct = D - vt (t = t)
Is she correct that she can find the velocity, v, of the train?
She has a light source (lantern, maybe) to send a signal to the engine car and engineer. The light signal is effectively instantaneous. He blows the whistle when he receives the signal (disregard reaction time). If she starts the clock when she sends the light signal, then she can measure the time, t, for her to hear the returning sound (speed of sound, c) signal.
During the same time that the train is in forward motion, the whistle sound is in rearward motion. She speculates that she will meet the sound wave somewhere within the distance, D, from the engine to the caboose. By algebra:
♦ ct = D - vt (t = t)
Is she correct that she can find the velocity, v, of the train?
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