What Sound Is

Strike a tuning fork and hold it near your ear. Nothing visible travels from the fork to you, yet something does: a ripple of squeezed and stretched air, passed from layer to layer.

How a vibrating body makes sound#

Picture a prong of the fork beside a long column of air, which we imagine as thin layers. When the prong moves right, it pushes the layer next to it, which crowds against the next. That squeezed region, at higher pressure and density than normal, is a compression. The crowded layer pushes on its neighbour, which pushes on the next, so the compression moves away from the fork.

When the prong swings back left, the layers beside it follow and spread out: a region of lower pressure and density, a rarefaction. It too passes down the column. As the fork keeps vibrating, compressions and rarefactions are sent out one after another. Each layer only oscillates about its own position, while the pattern travels. That travelling pattern is a sound wave.

The pressure wave

If the prong moves in simple harmonic motion, the excess pressure (above the normal pressure) at any point varies sinusoidally with time. At the fork itself, say $p = p_0\sin\omega t$. The same disturbance reaches a point a distance x away after a time x/v, so:

The frequency ν = ω/2π is the fork’s frequency. The wavelength is the distance between neighbouring compressions, $\lambda = v/\nu$.

What we can hear#

Sound needs a medium, but it can travel through gases, liquids and solids alike. Human ears respond only to frequencies between roughly 20 Hz and 20,000 Hz (the upper limit falls with age).

A sound with a sinusoidal pressure variation contains one frequency. Most everyday sounds, such as a clap or a slammed door, are not sinusoidal. They are a mixture of many frequencies, which is why they sound like noise rather than a note.

Longitudinal, so no polarization#

In the air column the layers move back and forth along the direction in which the wave travels, so sound in a gas or liquid is a longitudinal wave. Fluids cannot resist a sideways shear, so they cannot carry transverse waves at all. (Solids can carry both kinds.) A longitudinal wave looks the same in every plane containing its direction of travel, so it cannot be polarized. A slit that blocks a transverse wave on a string has no special effect on sound.

Wavefronts#

A small source sends sound out in all directions. All the points at the same distance from it are disturbed in the same way at the same moment: they share the same phase. A surface joining points of equal phase is a wavefront.

• Around a small (point) source the wavefronts are spheres: a spherical wave.
• Far from the source, a small patch of a huge sphere is nearly flat, so the wave behaves as a plane wave. A large vibrating sheet also sends out plane waves.