rlc: Physikalische Zugfahrt - Level 1 (PhysiCache)

Nice calulation puzzle for all train travellers and non train travellers

Everybody, who already travelled in a fast moving train that is going through a tunnel, might have noticed pressure changes, occurring at a certain time pattern (however, it doesn't work in an ICE, because those are built pressure proof).

Only few people know about the background of this effect, and the fact that it can be used for calculating useful things:

When entering the tunnel, the front of the train creates a pressure pulse. This pressure pulse is moving towards the distant tympanum at the speed of sound. Since the tympanum is effectively an open end, the pressure pulse is reflected and moves backwards towards the entrance tympanum, where it is reflected once again and so forth (of course, in reality reflections on the train's surfaces are occurring as well). If one looks on a watch when entering the tunnel, and each time the pressure pulses can be felt, it is possible to calculate the speed of the train as well as the length of the tunnel (assuming a constant speed of the train).

Exceptionally, Hartmut is travelling in an IC today, instead of using an ICE as usual. The very moment the train enters the tunnel, he is starting his stopwatch. At t₁=25,33920338 s and t₂=35,03423789 s, he notices the above described pressure pulse.

The location, where the final can be found can be derived from the length of the tunnel and the speed of the train (skip the first digit). Use the usually used metric units.

To make things easier for him, Hartmut is sitting at the very front of the train (therefore, the distance between the front of the train and his position within the train can be neglected); as the speed of sound, v_s=330 m/s has been used.

If you are interested in doing some more calculations, you can look up GC22M73. Here, Hartmut is sitting at a certain distance from the train front.

Here you can verify your solution.