Illustrated Physics
physics, drawn
Concept

Seismic waves — where it appears

Elastic waves that travel through the Earth from an earthquake: compressional P waves, which cross solids and liquids, and slower shear S waves, which need a solid. Their arrival times at distant stations are the main evidence for the structure of the planet's interior.

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

The speed of sound in dry sand rises with the load on it. The speeds of compressional and shear waves in a dry random packing of quartz grains, porosity 0.36, against the pressure on it, from the Hertz–Mindlin effective-medium theory, for coordination numbers from 6 to 9 (the bands). The pressure axis is logarithmic. Both speeds rise as the sixth root of the pressure. At 1 kPa — the load about six centimetres down in dry sand — compressional waves travel at 316–362 m/s; at 100 kPa, about six metres down, 681–780 m/s; at 10 MPa, 1468–1680. The dashed lines are the speed of sound in air, 343 m/s, and in water, 1,480 m/s. Near the surface dry sand carries sound no faster than air; measured shallow speeds are lower still, by up to a factor of two, because real contacts are fewer and weaker than the theory assumes.

The sound sand carries faster the deeper it goes

A solid carries sound at a speed set by what it is made of. A heap of quartz grains is made of quartz, and near its surface it carries sound more slowly than the air above it. The grains are not the solid; their contacts are, and a contact between two spheres grows stiffer the harder it is pressed. So the speed of sound in dry sand rises as the sixth root of the load on it — from about air's speed a few centimetres down to twice that at six metres — the paths of sound in a beach curve back up to the surface, and a water table is a mirror to one kind of wave and almost invisible to the other.

fluids · Granular matter Earthquake waves through the Earth, and the ring they do not reach. Paths of compressional (P) waves from an earthquake at the top of the Earth, traced through the mantle, the liquid outer core (orange) and the solid inner core (darker), drawn in one half of a cross-section: rays that stay in the mantle (blue) and rays that pass through the core (red), with Snell's law applied shell by shell to a reference model of the Earth's speeds. The mantle rays curve back up because the speed rises with depth, and reach the surface no further than 97° from the source. Rays that strike the core are bent sharply inward, because the speed drops from 13.7 to 8.1 km/s at its surface, and those that turn in the liquid outer core come out no closer than 144°. Between the two, marked on both sides, is a ring of the surface that these direct P waves do not reach: the P-wave shadow, which is how the core was found. A few rays that just enter the solid inner core (purple, dashed), where the speed jumps up again, are bent back out early and land inside the shadow, as close as 115° — the faint arrivals from which the inner core was found.

The shadow that shows the core is liquid

Nobody has been more than a few kilometres into the Earth, and its interior was mapped from the timing of earthquake waves alone. The decisive observations were of waves that do not arrive. Seismometers between about 100° and 140° from a large earthquake record no direct compressional wave, because something deep inside bends the rays away; and over two-fifths of the planet beyond 100° no direct shear wave arrives at all, because that something cannot be sheared. A slow, liquid core casts both shadows, and a few faint waves inside the first one revealed a solid core within it.

waves · Wave motion

Named alongside it

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

RefractionCausticEarths coreEffective mediumElastic modulusGranular matterHertz contactJammingShadow zoneShear modulusSnell's lawSpeed of sound

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