Keith,
Terry nailed that one very nicely.
I'll put my engineering background to good use on the second part.
The speed of the wave is related more to the acceleration than the speed.
The reason you get the effect in the first place is because of the /change/
in speed of one part of the train with respect to another. The locomotive's
acceleration probably varies as the throttle is opened; then there will be
variations based on power fluctuations and all that too.
The jerk on one car depends on the acceleration at that moment. Time passes
as the wave travels down the train. During that time, the accelerations of
the cars ahead of the wavefront can change with respect to the wavefront,
which will change the length of time needed for subsequent jerks. The
bigger the jerk at the front of car A, the faster car A accelerates, and the
faster the slack at the end of car A will be taken up, so the jerk will be
passed on faster.
There's another, possibly illusory effect that makes the wave seem to travel
faster as the wavefront moves down the train. This comes in 2 parts.
1. Humans have a harder time gauging speed if something is coming at or
going away from us compared to something passing "across" our view.
So if you were standing halfway down the train, you wouldn't necessarily
notice the wave travel /'way/ up at the front of the train it's moving
(nearly) at you. But as it got closer to you, you'd notice it zip right by
because by then the wave is travelling orthogonally to your line of sight.
2. The speed of the wave with respect to you must include the train's
speed. So as the train picks up speed as it goes by you, the wave would
seem to travel faster when it's reflected from the end of the train back up
to the front because now it's speed is added to the train's speed.
That's not nearly as tidy as Terry's explanation, but it's late and I'm
tired.
Terry? Did I pass? :)
Cheers.
Fil
2009/11/18 Keith Russell <[log in to unmask]>
> Dear terry
>
> thanks heaps for this excellent account - I've got the first half of my
> answer - now I need to know the forces that determine the speed of the wave
> and whether the speed is related to the overall speed of the train or
> whether it is generated by the wave?
>
>
> keith
>
--
Filippo A. Salustri, Ph.D., P.Eng.
Mechanical and Industrial Engineering
Ryerson University
350 Victoria St, Toronto, ON
M5B 2K3, Canada
Tel: 416/979-5000 ext 7749
Fax: 416/979-5265
Email: [log in to unmask]
http://deseng.ryerson.ca/~fil/
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