Why Big Instruments Play Low Notes

You know that pitch is frequency: how many waves pass in one second. A whistle sends a lot, a tuba sends few, and that is the difference between a high note and a low one.

That leaves the question underneath. When you pluck a guitar string it wobbles a particular number of times each second — not three, not a million. Something decides that number before you hear anything. What?

A wobble is a round trip

Pluck a string and you make a bump in it.

That bump does not sit still. It runs along the string to the fixed end, bounces off, runs all the way back to the other end, and bounces again. Now the string is exactly as it was when you let go, and the next wobble starts.

So one wobble is one lap: down the string and back.

That is the whole answer, and everything else follows from it. Frequency is just how many laps fit into a second. Pitch is a lap time.

A longer string is a slower lap

If the bump has twice as far to travel, the lap takes twice as long, so half as many laps fit into a second. Half the frequency is a lower note.

You can check this on a real guitar in about five seconds. Press a string down exactly halfway along and pluck it. The note jumps up by exactly one octave — the same note, higher. Half the trip, twice the laps, and on a guitar that halfway point is the twelfth fret, put there by the maker for this reason.

Distance is only half of a lap time

A lap time depends on two things: how far, and how fast. So there is a second way to change a note, and instruments use both.

Tighten the string and the bump travels along it faster. Same distance, quicker trip, more laps per second, higher note. That is the entire job of a tuning peg.

Use a heavier string and the bump travels slower, because there is more string to shift out of the way. Slower trip, fewer laps, lower note. Look at a guitar and you can see this being used: the low strings are the fat ones. They are exactly as long as the thin ones and tuned on the same neck, so length is not what makes them low. Their weight is.

Three controls — how long, how tight, how heavy — and all three are doing the same single thing to the lap.

The tuba and the whistle

A wind instrument runs the same lap, but through the air inside the tube rather than along a string.

That is why the shape of a brass instrument is what it is. All that curling is not decoration; it is a way of carrying a very long tube without a very long instrument. Unroll a tuba and its tube runs for several meters. A whistle is a few centimeters of air. Long lap, few laps per second, low note.

Every big instrument in an orchestra is the same argument. A double bass dwarfs a violin because its strings need a far longer trip. A big drum booms and a small drum taps, because the wobble has further to cross the wide skin.

Open a piano lid and the whole idea is laid out for you in one picture: long thick strings at one end, short thin ones at the other, and every length in between, in order.

Next time you hear something low — a tuba, a bass, the deepest key on a piano — you are listening to a long journey. Somewhere in there a wobble is making its way to the far end and back, and the note you hear is simply how long that takes.