> For example, [sound waves] move through solids much faster than they would through liquids or gases, which is why you're able to hear an approaching train much faster if you listen to the sound propagating in the rail track rather than through the air.
I am sceptical, I don't think this makes a big difference until the train approaches the speed of sound. What makes a difference, however, is that the energy is constrained into moving one-dimensionally, along the rail, so that it travels much further.
Sound travels through steel ~17 times faster than through air at 1 atmosphere.
At 500 meters, the "kachunck" of a train wheel going over a bump will take ~1.4 seconds to reach you by air, but only ~0.08 seconds to reach you through the rail.
The assumption behind my comment is: Most of the time, you only care about whether the train is coming. A 1-second advantage isn't really interesting. Of course, maybe that's the interesting part in that kind of situation? I doubt it, though.
At 5km, sound will take 15 seconds to cover the distance. That's negligible compared to the time the train will take, assuming a good old train going at ~40 km/h (7'30"). Using the quoted 6 km/s, that gives ~ 0.8 s inside the rail.
I admit I was initially expecting a smaller difference. But I still think that the 14 seconds advantage is negligible over just knowing that the train is arriving from a far away distance: to hear the train at all, wind needs to blow in the right direction, and the train needs not be too far away (~d^2 energy propagation, so ~log(d) in dB vs virtually no attenuation in a simplified model). I wish I had time to look up and compute the attenuation in both cases....
The fact that the sound will arrive much faster through the rail was not presented as having practical value in this scenario. The delay is merely an interesting fact of physics to observe, just like observing the delay from lightning to thunder can be interesting.
As for energies, I used a short example of 500 meters to make it more probable, but near ~150 meters you still have around half a second of difference, which is more than enough to notice.
Next time you are in a swimming pool, listen with one ear in the water and one out. You’ll hear sounds that have come through the water before they come through the air. It works best with a big pool and something noisey at the other end.
I am sceptical, I don't think this makes a big difference until the train approaches the speed of sound. What makes a difference, however, is that the energy is constrained into moving one-dimensionally, along the rail, so that it travels much further.