wave equation

A wave packet is like a traveler who either loses steam and spreads out along the way, holds a steady pace, or gathers into a fist. In a 50-meter flume with water 5 meters deep, scientists tracked how a bell-shaped group of waves behaves when its height is changed but not its width.

A spotlight with an adjustable beam width sweeps along the shore. Its light is the long ocean waves that are born in the surf zone and spread in both directions: toward the beach and out to the open sea. Previously, this spotlight was considered a point source, but the actual breaking zone, where short waves break, has a finite width, and it changes as the wave front advances and retreats.

Two massive bodies frozen in a quantum superposition resemble a pair of dancers trying to keep a single rhythm while an orchestra blares around them. Each gravitational wave is a musician throwing them off beat.

In a vast hall, billiard balls are scattered about. At first they lie sparsely, each on its own. Then someone adds more, and suddenly the balls compress into dense clusters. This is a phase transition — the moment when matter abruptly changes its state. Physicists have long described such a picture with the hard-sphere model: particles are identical balls that cannot overlap.

A stone falls into a pond, and ripples spread evenly in all directions. But some media behave as if the wave knows which way to turn, like water that only swirls clockwise. This asymmetry comes from odd viscosity and odd elasticity — properties of media with broken mirror symmetry.

Gravitational waves are not vibrations of matter, but tremors of spacetime itself, predicted by Albert Einstein. They travel at the speed of light and pass through objects, stretching and squeezing them.

When two dead stars collide in a distant galaxy, two messengers bring us the news: a shiver in space, a gravitational wave, and a flash of light. Both messengers race toward us across the entire Universe, but their paths can differ slightly. Light sometimes gets delayed by cosmic dust, while gravitational waves pass through everything almost without noticing obstacles.

In a thin semiconductor channel, electrons behave not like lone runners but like a crowd at rush hour. They constantly bump into each other, and these collisions determine how easily heat and electric current pass through the material.

In winter, a lake freezes over, and this simple process turns out to be a living model of an expanding universe. Ice thickness grows according to the same mathematical law as the distances between distant galaxies. The secret lies in the movement of water beneath the ice crust.

Gravitational waves are ripples in space, born, for example, when pairs of supermassive black holes spiral around each other. To catch them, scientists monitor pulsars — dead stars that emit radio pulses with clockwork precision.

A stone drops into a pond — ripples spread across the water. Do short waves outrun long ones? No, in deep water it's the opposite: long waves overtake short ones. In metal, sound of one pitch travels at one speed, another pitch at another.

The ocean is like a layered cake: warm, light water on top, cold, heavy water below. Between the layers, at the interface, invisible waves roam. They don't lift crests like a storm; instead, they slowly rock the entire water column, as if someone were shaking a giant aquarium from within.