The Off-Key Bard
Technology

How Do Speakers Turn Digital Music Back Into Sound?

Or: how a stream of numbers becomes a guitar, a human voice, or an explosion you can feel. The speaker doesn't know what it's playing. It just moves.

Or: How a Stream of Numbers Becomes a Guitar, a Human Voice, or an Explosion You Can Feel

Press play and the room fills with music. A guitar, a drummer's cymbal, a singer's breath before the chorus. Yet none of that arrived at your speaker as sound. If you're streaming or playing a file, it arrived as information: numbers describing audio samples, captured, compressed, stored, and transmitted. Somewhere between your phone and your ears, those numbers have to become physical movement of air.

Yesterday's post followed the trip in one direction, from vibrating air to a microphone to numbers. This is the return leg, and it runs the chain in reverse: numbers to voltage, voltage to power, power to force, force to motion, motion to pressure waves. Every link does a different job, and the surprise is where the work actually happens.

Step One: Numbers Become a Voltage

Your device first decodes the compressed file back into a stream of samples, commonly 48,000 per second at 16 or 24 bits each. That stream is still just numbers. A digital-to-analog converter, the DAC, turns each sample into a voltage and strings the voltages into a continuous electrical waveform.

A raw DAC doesn't produce a smooth curve. It produces a staircase of held values, and the staircase leaves two problems. Analog Devices' tutorial on interpolating DACs explains them: the stepped output rolls off at higher frequencies, and copies of the signal, called images, appear around multiples of the sampling rate. Those images are junk that was never in the music, and they have to be filtered away without touching what you can hear.

The elegant fix is oversampling. A digital filter inserts extra calculated points between the real samples, effectively running the converter at a multiple of the original rate. As the tutorial puts it, "the high oversampling rate moves the image frequencies higher." With the unwanted images pushed far from the audio band, the analog filter that removes them can be gentle and cheap instead of a steep, finicky cliff. Sigma-delta designs take the idea further with very high oversampling and noise shaping, which is why the analog filtering afterward gets simpler still.

This is also why the DAC rarely decides how your music sounds. The technique is mature, the parts are cheap, and the chip in your phone does it competently. The parts of the chain that most shape the sound come later, and they're made of magnets, paper, and air.

Step Two: A Small Signal Gets Muscle

The DAC's output is a faithful but feeble electrical copy of the music. It can't move a speaker cone. That's the job of the power amplifier.

The common misconception is that the amplifier makes the signal "bigger," like a magnifying glass. A better picture is a faucet. The incoming waveform is the hand turning the handle; the energy comes from the water main, which in the amplifier is its own power supply. The weak signal only tells the amplifier how much of that stored energy to release, moment by moment, with the shape of the original waveform. The result is the same pattern at much higher voltage and current.

Amplifiers have limits. Ask for more than the power supply can deliver and the peaks flatten, a distortion called clipping. And they have to cope with a load that isn't simple. Wikipedia's loudspeaker article notes that a speaker's impedance, nominally 4 or 8 ohms, is not constant across its frequency range; it changes with pitch, so the amplifier faces a different load for a kick drum than for a cymbal. Headroom, meaning spare capacity for the loudest passages, is what keeps a dramatic crescendo from turning harsh.

Step Three: Current Becomes Force

Now the part that is finally mechanical. Most speakers use a moving-coil driver. A permanent magnet creates a strong magnetic field in a narrow gap. Sitting in that gap is the voice coil, a coil of wire attached to a diaphragm, the cone. Run current through the coil and it becomes an electromagnet that pushes against the permanent one. Reverse the current and the force reverses.

That's the whole trick. If the amplifier delivers a 1,000 hertz waveform, the coil and cone move forward and back a thousand times each second, accelerating, stopping, and reversing over and over. Forward motion squeezes the air slightly; backward motion thins it. Those alternating compressions and rarefactions travel outward as sound, the same kind of pressure wave that pushed the diaphragm in your microphone. The loudness of what you hear doesn't come from the amplifier or the cone's material. It comes from how much air the cone moves, and how forcefully.

Notice the symmetry with the microphone. A dynamic microphone is a voice coil in a magnetic field moved by sound, generating a signal. A moving-coil speaker is the same assembly driven by a signal, generating sound. Same physics, opposite direction.

Why Bass Needs Big Things and Treble Needs Small Ones

If one cone could do everything, speakers would be simple. It can't, because different frequencies make opposite demands.

Bass is about volume. Low notes are slow, long waves, and creating a strong one means shoving a large amount of air back and forth. A big cone moving a long distance does it; a small one has to work absurdly hard and still falls short. This is why the tiny speaker in a phone can suggest a bass line but can't make your chest rattle, and why subwoofers exist. Wikipedia's article defines them as covering below roughly 200 hertz in consumer systems, and lower in professional and THX-style setups.

Treble is about speed. A tweeter has to wiggle many thousands of times per second, so its diaphragm is small and light, a thin dome, ribbon, or similar membrane, easy to accelerate and stop. Make it heavy and it can't keep up. Try to run a large woofer cone at high frequencies and it stops moving as a single piston, flexing and breaking up into messy vibration patterns.

So a typical speaker has several drivers, and a crossover splits the music between them. It's a set of filters that sends low frequencies to the woofer, high frequencies to the tweeter, and the middle to a midrange driver if there is one. Where the ranges meet, both drivers play at once, so the filters' slopes and phase have to combine smoothly or you get a gap or bump at the handoff. Passive crossovers do this after the amplifier using coils and capacitors; active ones split the signal earlier and give each driver its own amplifier. Each approach trades simplicity against control.

The Box Matters As Much As the Cone

A cone moving forward also moves backward, and the rear wave is opposite in phase to the front one. Left uncontrolled, the two cancel at low frequencies, which is why a bare driver sounds thin. The enclosure's job is to deal with that rear wave, and it comes in two main flavors.

In a sealed box, the trapped air behaves like a spring. Eminence's explanation says pressure drops inside as the cone moves out and rises as it moves in, so the air pushes back and helps control the cone. Sealed designs tend to be punchy, with tight transients, and forgiving to build, but they give up some efficiency and deep extension.

A ported box adds a tuned opening. The port is sized so that the air inside resonates at a chosen frequency, and the port reinforces the front output near it, boosting bass and reducing how far the cone moves there. The cost, per the same source, is weaker control below the tuning frequency and a design that is less forgiving overall, plus the occasional "chuffing" if the port is too small and the air rushes through it noisily. Neither type is better. Bass depth, punch, power handling, and size trade against each other, and the engineering is choosing which to give up.

Loudness Is Expensive

Speakers are surprisingly inefficient at converting electrical energy into sound. Only a small fraction of the power delivered to a conventional loudspeaker becomes acoustic energy, with much of the remainder dissipated as heat in the voice coil. As that coil heats up, its electrical resistance increases, reducing the current flowing through it and causing the speaker to produce less sound at high power levels. Engineers call this effect power compression. Extreme heat can damage the coil's insulation or adhesives, potentially destroying the driver. Heat isn't the only danger, either. At low frequencies, a speaker cone can be driven beyond its mechanical travel limits, damaging the suspension or voice coil even when the amplifier is delivering less than the speaker's rated power.

Sensitivity, the sound level a speaker produces for a standard input, tells you how well it turns watts into volume. The usual yardstick is the level at one meter for one watt, often measured with 2.83 volts into 8 ohms. Because decibels are logarithmic, small numbers hide big differences: a speaker with 3 decibels more sensitivity needs about half the amplifier power for the same loudness. A speaker rated 92 decibels with 100 watts matches the level of an 89-decibel speaker with 200. Quality speakers and phones add protection to match, limiters that cap output and high-pass filters that stop a small driver attempting bass it can't survive.

Then the Room Gets a Vote

You've now followed the signal from numbers to moving air, and the story still isn't over, because sound has to cross a room. Low frequencies have long wavelengths, and wavelength is just speed divided by frequency. Sound travels about 343 meters per second, so a 40 hertz note is about 8.6 meters long, and 20 hertz is about 17. Those are comparable to or larger than the room itself.

When that happens the room becomes part of the instrument. Vicoustic's explanation of room modes describes them as natural resonances that depend mostly on the room's dimensions rather than the speakers, linked to standing waves formed when a wave and its reflection interfere. At some positions the pressure peaks and the bass sounds boomy; at others it nearly vanishes and the bass seems thin. Move a seat or a subwoofer and the bass can change dramatically, and the page notes that bass can vary significantly between seats. Modes can't be eliminated, only managed, with placement, bass traps, or several subwoofers that smooth things out. Room-correction microphones measure the result and adjust the signal, but they can only help so much.

Off-axis behavior matters too. Treble spreads in narrower beams than bass, so how a speaker sounds depends on where you sit, and reflections from walls add their own coloration. Stereo makes use of this: with two speakers, sounds mixed equally to both seem to float in a phantom center between them. Surround systems add more speakers, or height channels and object-based mixing, to place sounds around you instead of just in front.

What the Speaker Doesn't Know

Headphones play the same game at a smaller scale: tiny drivers a few centimeters from your ear, where the seal against your head or the fit of the ear tips has a huge effect on bass. Planar magnetic, electrostatic, and ribbon designs replace the cone-and-coil arrangement with a thin membrane driven across its whole surface. The goal is unchanged: move air in the pattern the signal describes.

And the ceiling is set long before any of this. A speaker can only reproduce what is on the recording. A better speaker reveals a better recording and a worse one more cruelly. And loudness isn't quality: turning it up makes more of everything, including distortion.

The Bard's Take

A digital song is not sound. It's information describing sound. When that information reaches your speaker, it goes through conversion, amplification, and electromechanical transformation until a copper coil and a paper or polymer cone are physically vibrating the room.

A microphone begins with vibrating air and turns it into electrical information. A speaker does the reverse. And the speaker doesn't need to understand music. It doesn't recognize a guitar, hear the words, or know that a deep rumble is an explosion. It receives an electrical waveform and moves, turning a stream of digital numbers back into the vibrating air of the physical world.

A coil moves. A cone follows. The air vibrates. And suddenly, a room full of silent electronics becomes music.

Sources

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