Illustrated Physics
physics, drawn
Concept

The Mach cone — where it appears

The cone of wavefronts left behind a source moving faster than the waves it makes, with a half-angle whose sine is the wave speed over the source speed. A sonic boom, a Cherenkov flash and a seismic head wave are all such cones.

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

Wavefronts from a moving source. Circles showing where each crest has reached, centred on where the source was when it emitted them. Ahead of the source the crests are closer together and the frequency heard is higher; behind, they are spread out and it is lower.

The note that changes on approach, and the two ways of getting it

A moving source and a moving listener produce different formulas for the same shift, because the medium is watching. The difference is small, real, and the reason light had to be treated differently.

waves · Doppler Three arrivals, and the one that overtakes. Arrival time against distance from the shot for a 35 km crust at 6 km/s over a mantle at 8 km/s: the direct wave, a line through the origin with slope 1/v₁; the reflection from the base of the crust, a hyperbola; and the head wave, a straight line of slope 1/v₂ that begins at the critical distance, 79 km, where it touches the reflection. Close to the shot the direct wave arrives first. The head wave starts later but travels most of its path at the faster speed, and beyond the crossover distance, 185 km, it arrives first and stays first. At 300 km it beats the direct wave by 4.8 s, though it has travelled 26 km further.

The wave that arrives first by going the long way

A shot fired at the ground sends a wave straight along the surface layer to a distant listener, and another down to a faster rock beneath, along the boundary and back up. The second path is longer, and beyond a certain distance it arrives first, because most of it is run at the faster speed. Huygens's construction shows what the second wave is: a front drawn by wavelets that the disturbance racing along the faster floor sends up into the slower layer, the Mach cone of a source moving faster than the layer can carry sound. Reading where it overtakes the direct wave gave Andrija Mohorovičić the thickness of the Earth's crust in 1909, and gives every refraction survey since the depth to whatever lies beneath.

waves · Huygens

Named alongside it

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

Critical angleCrossover distanceDoppler effectFrequencyHead waveHuygens principleMohorovicic discontinuityRedshiftRefraction seismologyRelativistic dopplerTravel timeWave speed

All concepts