Sound
Pressure Waves You Can Hear
A Push Handed On
Clap your hands and you shove the air between them aside. That air was never still. Its molecules fly about at some 500 meters a second, and each one strikes another about seven billion times a second. A sound is a small shared push riding on all that motion: a layer where the molecules are a little more crowded, then one where they are a little thinner, handed on from layer to layer by the collisions.
That is why sound in air runs at 343 meters a second at room temperature, somewhat slower than the molecules themselves. In a gas, the news is carried by the molecules, and it cannot outrun its messengers. So in a given gas what sets its speed is how fast they move, which is to say the temperature. Warm air carries sound faster, by about 0.6 meters a second for every degree Celsius. The pressure does not matter: thin air on a mountain carries sound as fast as thick air at sea level, if it is as warm. Squeezed harder, air springs back harder, but it is denser by just as much, and the two cancel. In helium, whose atoms are seven times lighter than air’s molecules and fly faster, sound runs at about 1,000 meters a second. In water and in steel the news is not carried by flying molecules. It is handed from neighbor to neighbor through the forces between them, packed close and springing back hard, so it runs far faster than any molecule moves: about 1,480 and 5,960 meters a second.
Work the speed out from how hard air springs back when squeezed slowly, at a steady temperature, and it comes out about a sixth too little. In a sound, a squeezed layer of air warms up, and a thinned one cools. The two lie half a wavelength apart, too far for heat to cross before the wave swings back. So the squeezed air pushes back harder than that reckoning allows.
Sound itself cannot be seen, but the air it squeezes bends light a little, as hot air over a road does, and that can make it visible. Send a beam through a patch of air and cut off part of it with a knife edge where it comes to a focus, and the slightest bending shows as light and dark. Color filters there show the way the light was bent as a color. A spark gives a sound short and loud enough to catch: a thin shell of squeezed air racing away from it.
The shell leaves and the air stays: the air the spark heated is still there after the sound has gone. Fire spark after spark at a steady rate, and the shells follow one another, evenly spaced. That is a steady note, and its pitch is the rate of the sparks. With no matter there is no sound, so space is silent to any ear. The thin gas between galaxies can still carry pressure waves, though: around the black hole at the heart of the Perseus galaxy cluster, astronomers have found ripples in X-ray images that make a note about 57 octaves below middle C: one swing every ten million years.
That is the sharpest difference between sound and light. Light is a ripple in a field that is already everywhere, empty space included. Sound is not a ripple in anything that exists on its own. It is a pattern in the arrangement of matter, something a material does rather than something that passes through it.
Faint and Loud
The ear is astonishingly sensitive. At the faintest sound it can hear, the air’s pressure rises and falls by two ten-billionths of an atmosphere, and the air at the eardrum moves back and forth by less than a tenth of the width of an atom. A sound loud enough to hurt carries a trillion times as much power. Decibels count those powers of ten: every 10 decibels is ten times the power, so the faintest sound is at 0 and a painful one at about 120.
There is a loudest smooth sound, too. The quiet half of every sound wave is air a little thinner than usual, and air cannot be thinner than empty. At about 191 decibels the thin half of such a wave in ordinary air would reach a vacuum. Long before that, a loud wave stops being a gentle swing. In its crowded parts the air itself is rushing forward and is warmed by the squeeze, so they run faster than its thin parts and catch up with them. The wave steepens into a shock, a front of crowded air that runs ahead of sound itself, as the first front of a big blast does. A blast can crowd the air far beyond 191 decibels, with no limit; only its thin half is capped, at empty.
How the Ear Takes a Sound Apart
Pitch is the rate at which a sound repeats. People hear from about 20 to 20,000 swings a second, or hertz, and middle C on a piano is 262. Few sounds are a single pure rate. A plucked string or a voice sounds a lowest rate and many whole-number multiples of it at once, and the mix of those harmonics, with how it starts and changes, is the sound’s color, its timbre: why a violin and a flute differ on the same note. Any repeating shape with a finite number of bumps and jumps can be built from pure swings in this way. A sound that does not repeat, a clap or a hiss, can be built from pure swings too, but from a smooth spread of rates rather than a ladder of them.
The ear takes a sound apart into those pure swings, largely by place. Inside the snail-shaped cochlea runs a coiled membrane about 3.5 centimeters long, narrow and stiff at the end where sound comes in, wide and slack at the far end. Each part of it answers its own pitch. In ears from the dead it can be watched: every sound starts a wave along the membrane that swells as it goes and dies just past the place tuned to its pitch. High notes peak near the start, low ones far along.
Rows of hair cells sit along the membrane, and the nerve fibers from each place tell the brain which pitches are there. For low pitches, the fibers also fire in step with the swings, and that timing tells the brain too. A living ear does more than a dead one can show. Its outer hair cells push back on each swing in time with it, and for a faint sound they make the membrane’s swing a hundred to a thousand times larger at its peak. They push hard enough to be heard: sound comes out of ears, faint tones that a sensitive microphone in the ear canal picks up, made by the ear itself.
A Source on the Move
A source moving toward you sends each crest from a little closer than the last, so the crests reach you crowded together, at a higher pitch. Moving away, it spreads them out, and the pitch drops. That is why a siren falls in pitch as it passes. This is called the Doppler effect.
Light does the same. The light of a galaxy moving away from us reaches us stretched to longer, redder waves. For distant galaxies the stretch is usually described another way: while the light travels, the distances between galaxies grow, and the light’s waves grow with them. The farther away a galaxy is, the larger its stretch, and that pattern was the first evidence that universe is expanding.
The faster a source goes, the more its crests crowd ahead of it. At the speed of sound they pile up at its nose, and faster than that the air ahead gets no warning at all. Every push the source gives the air still spreads at the speed of sound, but now the pushes trail behind it, and where they crowd together they make a cone, a shock wave. A rifle bullet shows both: fired at twice the speed of sound, it drags a cone behind it; slowed by the air to below the speed of sound, it is outrun by its own pushes again.
The Boom That Follows
The cone round a bullet in flight can be photographed, with a spark for a flash and a knife edge to show the squeezed air. The faster the bullet, the narrower the cone: at twice the speed of sound its sides open at 30 degrees to the line of flight, at three times at under 20. A speed counted in speeds of sound is called a Mach number.
A sonic boom is that cone sweeping over the ground. It is not a bang made once, at the moment an aircraft passes the speed of sound. The cone travels with the aircraft for as long as it flies faster than sound, and everyone it sweeps over hears its passing, a little after the aircraft has gone overhead. Usually that is a double crack: one from the cone at the nose and another from the one at the tail, a fraction of a second apart. Just above the speed of sound, the warmer air near the ground can bend the cone upward so that it never reaches the ground at all. The crack of a whip is a small sonic boom, made near the whip’s end, where the loop running along it outruns sound.
Light has a version too. In water, light slows to three quarters of its speed in empty space, and a charged particle can outrun it there. It leaves a cone of light behind, the blue glow seen in the water round a reactor’s core: the same geometry, in a different wave.
Sound in a Crystal
In a solid the atoms do not fly about. Each jiggles about its own place in a crystal, tied to its neighbors, and sound runs through them as through a mattress of springs. A solid can also be sheared, so it carries a second kind of sound as well, in which the atoms move across the way the wave runs. And like light, each of these waves takes and gives energy only in whole steps, whose size is set by its pitch. One step is called a phonon. In crystals that do not conduct electricity phonons carry the heat, and in ordinary superconductors the vibrations bind electrons into the pairs that flow without resistance.
