Illustrated Physics
physics, drawn
Concept

Sound — where it appears

A wave of compression and rarefaction passed through a medium by its particles pushing on their neighbours. In a gas it travels at a fixed fraction of the molecules' mean speed and needs many molecular collisions in each period to exist.

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

A bottle as a mass on a spring. A 750 ml bottle with a neck 8 cm long and 19 mm across, and its equivalent: the plug of air in the neck, 32 milligrams, moving in and out as a piston on the air in the body, which acts as a spring of stiffness 15 N/m because squeezing it raises its pressure. The plug's mass and the spring's stiffness give a frequency of 109 Hz, the note heard when air is blown across the mouth. The effective neck length includes about one and a half radii of air beyond its two ends that moves with the plug. Nothing in the body's air moves much — it is compressed and released almost uniformly, because the wavelength, three metres, is far larger than the bottle. That is what makes the resonator lumped: one mass, one spring, one note.

The note a bottle sings whatever its shape

Blow across the mouth of an empty wine bottle and it sounds a low note, about 109 hertz for a 750-millilitre bottle. Its wavelength is three metres, ten times the bottle's height, so it is not a standing wave in the bottle the way a flute's note is a standing wave in the flute. It is a mass bouncing on a spring: the plug of air in the neck, thirty milligrams of it, riding on the springiness of the air in the body. The note depends on the body's volume and the neck's size and on nothing about the body's shape, which is why a sphere, a cube and a tall cylinder of the same volume all sing the same note — and why a car driven with one window open throbs at eighteen hertz.

waves · Resonance The highest note the air can carry, with height. The frequency at which a sound wave in the air loses its amplitude by a factor e in a single wavelength, in hertz on a logarithmic scale, against height, with the band of human hearing shaded. Because viscosity does not depend on pressure, the collision time grows as the pressure falls, and the ceiling falls with it. It is about 212 MHz at sea level, 0.17 MHz at 50 km and 3 kHz at 80 km. It passes the top of human hearing, 20 kHz, at about 68 km, and the bottom, 20 Hz, at about 110 km; at 100 km it is 92 Hz. Above about a hundred kilometres the air cannot carry anything a person could hear, at any loudness: the molecules are too far apart to pass a compression on before it has dispersed.

The note too high for thin air

Sound in a gas is a compression handed from molecule to molecule by collisions, and it can only be handed on if the molecules collide many times in each period of the wave. At sea level they collide seven thousand million times a second, and the limit is far above anything audible. But a gas's viscosity does not depend on its pressure, so as the air thins with height the time between collisions grows in proportion, and the highest note the air can carry falls with it: two hundred megahertz at the ground, three kilohertz at eighty kilometres, below twenty hertz above a hundred and ten. The upper atmosphere is not silent for want of loudness. It is silent because its molecules are too far apart to pass a sound along.

thermodynamics · Kinetic theory

Named alongside it

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

Acoustic absorptionAcoustic impedanceAdiabatic compressionCollision timeContinuum limitHelmholtz resonatorKnudsen numberLumped elementMean free pathQuality factorResonanceStanding wave

All concepts