# Supersonic train?

In which the author writes not about Hyperloop, as some readers might think, but about trains running at the speed of sound on very conventional railway track, hoping to repay in this way the readers for his so very long blogging absence. The author also hopes the last comma was sufficient for the readers to understand the repayment hope is his and not of the supersonic train – he (the author, not the train) still struggles with the subtleties of English syntax and grammar (Should he have used here ‘the’ or not?!).

Oh, yes! Supersonic trains!
Note: This is an over-simplified perspective on the subject.

Sound?
The dictionary says the sound is “vibrations that travel through the air or another medium and can be heard when they reach a person’s or animal’s ear”. As the evil Greek smith Procustres used his iron bed, we – the humans – measure so many things relative to our subjective perception … that’s why we call ‘sound’ those vibrations we can hear and ‘ultrasound’ or ‘infrasound’ the vibrations which are outside of our perception range.
So, the sound is a vibration and it requires a medium to propagate.
In gases and liquids, sound, vibrations in general, propagates by compression waves. In solids, beside compression waves, the vibration propagates by shear waves and surface waves. These last type of waves are fancily called Rayleigh waves.

#### Speed of sound?

Generally speaking, denser the medium, higher the speed of sound. The sound travels slow in gases, faster in liquids and even faster in solids.
In air, the speed of sound is around 340 m/s (1230 km/h, 750 mph). In salt water, sound travel at the speed of 1500 m/s (5400km/h, 3350 mph) and in iron at 5100 m/s (18400 km/h, 11450 mph) …
But is not everything about density. Compressibility, molecular composition, temperature, porosity and probably so many other properties come into place to influence the speed of sound and the figures quoted here are just indicative, for a well-defined set of properties of the propagation medium.
Quite often, complex materials show a wide range of variation of the speed of sound.
In soils, for example, the speed of sound and other vibration waves varies between 45 m/s (160 km/h, 100 mph) and 260 m/s (940 km/h, 580 mph).

#### Objects moving at the speed of sound?

When an object moves below the speed of sound, the sound pressure waves are moving in front of the object, faster than the object itself and don’t overlap with each other.

When the object reaches the sound speed or goes above it, the pressure waves are forced together, merging into a single shock wave which travels at the speed of sound, generating, for large enough objects, a very loud thunder-like sound – way above the sound the movement of the object makes at low speed. This shock wave is called sonic boom.

We know this concept of sonic boom from supersonic planes but there are other occurrences of this phenomenon. The crack-like sound some whips make is a mini-sonic boom. There is a theory saying that the diplodocus was whipping his tail at supersonic speed, using it as a terrible defence weapon.
The thunder, even though it has a different cause, is similar to a sonic boom.
The amount of energy generated by this phenomenon is quite significant. The sonic waves generated by air planes travelling at trans- and supersonic speed, if flying low enough, can be quite a nuisance and even cause damage to structures (i.e. breaking windows, shaking walls).

#### Trains running at the speed of sound?

There are no trains travelling at the speed of sound in air (at normal pressure and temperature), at least not yet. Hyperloop might get close, but Hyperloop is still a fantasy.
However, there are trains travelling close to the speed of sound/vibration in some types of soil, as there are soils for which the ‘speed of sound’ is as low as 160 km/h – 100 mph. For most soils that is in a higher range, significantly above the speed of modern high-speed trains. But, in particular locations, there are cases where the train speed might be close enough to this critical speed, when the vibrations caused by the train passage merge into a ground vibration boom, the soil equivalent of the sonic boom. The surface (Rayleigh) waves generated in this case are significantly greater than the ones generated by the train at lower speeds and we have practically an earthquake travelling with the train.

Theoretically predicted by Professor Victor Krylov in 1994, the ground vibration boom was first observed in 1997-1998 on a high-speed railway line in Sweden, where a speed increase from 140 km/h to 180 km/h increased by ten times the intensity of the ground borne vibration.
Ground-borne noise and vibration is a general issue of the railway transportation system. But when the train speed is getting close to or even goes beyond the ‘speed of sound’ of the soil on which the railway track is laid, this becomes an even more important railway engineering challenge, especially when the structures and buildings located close enough to the track resonate with the frequency of the vibrations caused by the fast moving train.

That might not be an issue for countries like Japan, where earthquakes are common occurrences – they started building their high speed network in 1964 and nobody cared too much about a tiny earthquake produced by moving trains. True, they have quite a robust slab track system. But other countries with high speed networks, either existing or under development, are not that lucky to have natural earthquakes testing their buildings to see if they will withstand the passage of a ground booming train … especially for such locations this is a challenge!