Illustrated Physics
physics, drawn
Concept

Elastic waves — where it appears

Disturbances that travel through a solid by stretching and restoring it, as compressions, shears or bending. Their speeds are set by the solid's stiffness and density, and they carry energy away from an impact faster than the impact can reclaim it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

How far into the ground a surface wave goes. The horizontal and vertical displacements of a Rayleigh wave against depth, in wavelengths, at Poisson's ratio 0.25, each divided by the largest displacement anywhere. Both fall off exponentially, and at one wavelength down the vertical component is 19.3 per cent of its surface value — so the wave is confined to a skin about a wavelength thick, and the thickness is set by the wavelength rather than by anything about the material. The horizontal component changes sign at 0.193 wavelengths, which is not a node of a standing wave but a reversal: above that depth the ground moves one way round its elliptical orbit and below it the other. A long-period wave therefore samples deep rock and a short-period one samples only the surface, which is what makes a seismogram's dispersion a measurement of the structure underneath.

The wave a surface is enough to hold

A pipe guides with walls and a fibre guides with a slower core. A solid needs neither: one free surface binds a wave that is not a bulk wave bouncing but a separate solution, travelling slower than any wave in the material, dying away exponentially into it, and carrying its energy round a circle instead of over a sphere — which is why it is the part of an earthquake that knocks buildings down.

waves · Guided waves Restitution with nothing lossy in it. The coefficient of restitution of a perfectly elastic ball striking a large, perfectly elastic plate, against Zener's parameter λ, which grows as the square of the ball's radius over the plate's thickness and weakly with speed. At λ = 0 the ball comes back at its arrival speed. The rebound falls below half at λ ≈ 0.65, with no friction, plasticity or damping anywhere — the missing energy is travelling outward through the plate as bending waves. Marked: a steel ball 20 mm across at 1 m/s on steel plates 5 mm thick (λ = 0.94), 10 mm thick (λ = 0.23), 20 mm thick (λ = 0.06).

The bounce an elastic plate cannot give back

Drop a steel ball on a thick steel block and it bounces almost to where it started. Drop it on a steel plate five millimetres thick and it comes back at barely half its speed, although steel on steel is about as elastic as materials get and nothing in the impact is plastic, sticky or damped. The energy has not been turned into heat. It has been turned into waves, running out through the plate faster than the ball can take them back — and a ball striking a longer rod loses energy the same way, by leaving it ringing.

mechanics · Momentum

Named alongside it

The objects these essays reach for when they reach for this one.

Bending stiffnessBoundary conditionCoefficient of restitutionCollisionDispersionEnergyEvanescent waveFree surfaceGeometric spreadingGuided wavesHertz contactImpedance

All concepts