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I work in a 4 story building that is approx. 150 feet away from a set of train tracks. When a large (40+ car) freight train goes by, the shaking in the building is perceptible. As I've watched the train go by, there does not appear to be any side to side movement and the speed is constant. What exactly is causing the vibrations in the ground? Is it simply the train's traversal over each segment of track? Surely the train itself is not "bouncing" along the track with enough energy transfer to shake the ground, right?

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The track probably uses sleepers (timber or concrete) instead of having continuous support? – MSalters Jun 11 '14 at 10:34
@MSalters you are correct, Sir. – Nick DeVore Jun 19 '14 at 20:26
up vote 25 down vote accepted

There's a nice article on exactly this subject in this PDF file.

Summarising from the article: the vibration arises because the track is not completely smooth and the train wheels are not perfectly circular. As the train moves along thetrack, the result is an oscillating force at each wheel/track contact, and this is transmitted to the ground at each sleeper/ground contact. It's this force that shakes the ground.

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I'm missing the explicitly crossing between two segments, which seems (to me) the key thing that you feel when you are on a train yourself. Also, if the segments would be different-prime-number-lengthed, would the 'problem' be less? :) Or should you just make sure that segment lengths and car lengths don't match (up to some factor)? Like cars should be length 7 and track segments should be length 17. – Keep these mind Jun 10 '14 at 18:10
I thought most rail tracks were continuous these days? Obviously if you live near a set of points there will junctions and associated vibration, but not once out on any high or even medium speed area. – John Rennie Jun 10 '14 at 18:16
Oh, I don't know. I guessed there was a cm or two between each segment to allow for expansion due to hot weather. And also because of the clear rhythm of the noise, which seems slower than the frequency of rotating wheels. – Keep these mind Jun 10 '14 at 18:21
I've seen the rails near the junctions recede by more than 5cm here. This is enough to account for the rhythmic sound and vibration as the train passes by, because the frequencies match. – auxsvr Jun 11 '14 at 0:26
If you're near a TGV, it's remarkable how LITTLE vibration there is, if the set is going "slowly" 100mph or so. – Joe Blow Jun 11 '14 at 13:38

With the sleeper question confirmed, I'm pretty sure I know what happens. friend of mine wrote his thesis on rail vibrations.

Basically, the rail sags between sleepers. Not a lot, normally, but the sagging is quite periodic. John Rennie got the basic assumption right about rails not being straight, but the wheel issue probably doesn't cause earth vibrations - the wheels are out of phase with respect to each other. (They're noisy, though. Modern trains have ABS for this reason). But that periodic sagging of the rails over the sleeper, excited by the train passing over will add up. Those vibrations will cause that earth shaking.

Modern high-speed tracks are moving to ballastless track beds, without those sleepers. Trains bounce a lot more at 250 km/h than at 25 km/h. Even so, the Dutch can't run their high speed train at 300 km/h; the vibrations would cause the track bed to sink in the muddy soil.

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Interesting. An obvious exaggeration would be the way a sway bridge sinks and rises when a person walks across, but I'm assuming it is a similar concept, yes? – Nick DeVore Jun 20 '14 at 5:12
A person only has two legs. But an army marching is instructed to walk normally over bridges for the same reason, yes: the rhythm of marching can cause the same vibrations. – MSalters Jun 20 '14 at 7:25
Ah, but what if a person had THREE legs? Oh wait, this is not the philosphy site! Sorry ;) – Nick DeVore Jun 20 '14 at 14:46

Since "enough" information is not available, one can only guess. My guess is that "most likely" resonance is what's causing the perception. The length, height, width, and composition of the building and its distance from the tracks, determines its "natural" oscillating frequency and the train's length and speed must create an oscillation that closely matches the building's frequency (or its harmonics), so that the small train vibrations get amplified to the point of being felt in the building. In order to find out if this is the case, there should be a train length that causes the "most noticeable" shaking. Longer or shorter than this, should produce less noticeable shaking.

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