What is sound?

Before any definition, try this experiment. Pluck the open 5th string firmly and look at it from the side, around the 12th fret. You'll see a blurry "spindle": the string moves so fast your eyes can't follow it. Now touch the string with your fingertip: the sound stops instantly.

Play: The open 5th string

That experiment already holds the central idea of this whole lesson: no movement, no sound. The string makes a vibration, a very fast back-and-forth around its resting position, and while it vibrates, it sounds. When you stop it, silence is immediate.

A steel string is so thin that on its own it barely moves any air: an unplugged electric guitar is very quiet. That's why an acoustic guitar has a body. The string passes its vibration to the bridge, the bridge to the top, and the top, being large, pushes a lot of air at once.

Every time the top moves forward, it squeezes the air molecules in front of it (a compression); every time it moves back, it leaves them more spread out (a rarefaction). Those squeezed and loose zones spread out like ripples on a pond, although the molecules don't travel to you: they just push their neighbours and return to where they were.

The wave moves at about 343 metres per second (in air at 20 °C). The distance between two consecutive compressions is the wavelength. A low note has long waves and a high note, short ones: the open 6th string makes waves more than 4 metres long; the open 1st string, just over a metre.

Listen to these two notes. The first is the open 6th string; the second, the open 1st string:

Play: Open 6th string and open 1st string

The difference you hear, low against high, is pitch. And it depends on one measurable thing: how many complete vibrations the string makes every second. That's frequency, measured in hertz (Hz): 1 Hz is one vibration per second.

These are the frequencies of your open strings at the reference tuning, which you'll explore in the next stop:

The higher the string, the faster it vibrates. Young human ears hear roughly from 20 Hz to 20,000 Hz; the guitar's fundamental notes run from 82 Hz up to just over 1,000 Hz at the highest frets.

Doubling the frequency

Look at the top pair in the illustration: 110 Hz and 220 Hz. When a frequency doubles exactly, something special happens: the two notes sound "the same, but higher". That relationship has a name, the octave, and the next stop is all about it. Hear how A repeats, octave after octave:

A1	55.00 Hz	Play: ▶
A2	110.00 Hz	Play: ▶
A3	220.00 Hz	Play: ▶
A4	440.00 Hz	Play: ▶
A5	880.00 Hz	Play: ▶
A6	1760.00 Hz	Play: ▶

What decides how fast a string vibrates? Three things, and you can check all three right now on your guitar:

1. The vibrating length. Fretting a note shortens the part that vibrates (from your finger to the bridge) and the note goes up. Shorten it to half and the frequency doubles. Where is the exact middle of the string? At the 12th fret.
2. The tension. Turning the tuning peg tightens the string and the note goes up; loosening it brings it down. That's exactly what you do when you tune.
3. The thickness (mass). A thicker, heavier string vibrates more slowly. That's why the 6th string is the thickest: to give a low note without being floppy.

Check it: pluck the open 5th string, then at the 12th fret. The second note vibrates twice as fast, at 220 Hz:

String 5, Open: A2 · 1 · Scale tone

Play: String 5: open (110 Hz) and 12th fret (220 Hz)

Theory deep diveThe string formula (Mersenne's law)

For an ideal string, the fundamental frequency is

$$f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$

where $L$ is the vibrating length, $T$ the tension and $\mu$ the mass per unit length (how "thick and heavy" it is). Read the formula as a summary of the three checks: half the length → double the frequency; four times the tension → double the frequency; four times the mass per metre → half the frequency.

Frets aren't evenly spaced because each one shortens the string by the same ratio, not by the same amount: each fret multiplies the frequency by $\sqrt[12]{2} \approx 1.0595$ (the twelfth root of 2). Twelve frets in a row give $\left(\sqrt[12]{2}\right)^{12} = 2$, the octave. That's why the frets get closer together towards the body.

Now play the open 5th string four times: very soft, soft, loud and very loud. The note doesn't change, but the volume does. When you pick harder, the string swings further from its resting position: it has more amplitude. More amplitude moves more air, the wave carries more energy and you hear it louder.

The decibel scale is logarithmic: a conversation is around 60 dB and a rock concert can go above 100 dB. A rule of thumb: about 10 dB more is heard as roughly twice as loud.

If a piano and your guitar play the same A at the same volume, you can tell them apart instantly. Same frequency, same amplitude, but different timbre. Where does that difference come from?

Go back to the first illustration in this stop: the string doesn't only vibrate as a whole. At the same time it vibrates in two halves, three thirds, four quarters… Each of those shapes produces a harmonic at a multiple of the main frequency, the fundamental frequency. For the open 5th string:

Play: The first six harmonics of string 5, one by one

You don't hear those notes separately: your ear blends them into one sound and perceives them as "colour". Timbre depends on how much of each harmonic sounds and on how the sound starts and dies away (the pick attack, the string's decay). A flute has few harmonics and sounds sweet; a distorted guitar has a huge number and sounds gritty.

Change the timbre, keep the note

Pluck the open 5th string very close to the bridge: the sound is bright and metallic. Now pluck it over the 12th fret: it sounds round and soft. Same note, but you've changed the mix of harmonics. If you pluck exactly in the middle of the string, the harmonics with a node (a still point) in the middle, the 2nd, 4th, 6th…, are barely excited. Close to the bridge, on the other hand, lots of high harmonics are excited.

Your first natural harmonics

You can isolate a harmonic: rest a finger very lightly on the string, directly over the 12th fret (not behind it, over the metal), without pressing it down, and pluck. Touching the middle stops the string from vibrating as a whole, leaving only the harmonics that have a node there: you hear the 2nd harmonic, like a little bell, an octave above the open string. Over the 7th fret (a third of the string) you get the 3rd harmonic, and over the 5th fret (a quarter), the 4th.

String 5, Fret 12: A3 · 1 · Scale tone

Play: String 5 harmonics: frets 12, 7 and 5

Practice

The string 5 lab

5 min

1. Play the open 5th string and let it ring. Think: 110 vibrations per second.
2. Fret the 12th fret and play: half the string, double the frequency.
3. Now touch the string over the 12th fret and play the harmonic. Lift your finger right after picking so it rings longer.
4. Alternate the three versions and listen: all three are "the same note", two of them an octave higher.
5. If it works, try the harmonics at frets 7 and 5.

Goal: Get a clean 12th-fret harmonic three times in a row and recognise by ear that it is the octave of the open string.

Practice

Volume ladder

60 BPM4 min

With the metronome at 60, play the open 5th string in quarter notes: 4 beats very soft, 4 soft, 4 loud and 4 very loud. Then walk back down. Keep your hand relaxed even on "very loud": volume comes from the pick's travel, not from squeezing.

Metronome

−60 BPM+

Goal: Four clearly different volumes without the note or the rhythm changing.

Practice

Timbre walk

3 min

Strum an Em chord three times in each zone: near the bridge, over the soundhole (or between the pickups) and over the 12th fret. Then do it with your eyes closed and guess where your hand is from the sound alone.

Goal: Three clearly different timbres on the same note, recognisable with your eyes closed.

Self-assessment

What mainly changes when you pick a string harder?

AThe frequency: the note goes upBThe timbre disappearsCThe amplitude: it sounds louderDThe length of the string

Listen. How does the second note compare with the first?

Listen

AA lower noteBThe same note, an octave higherCA different, unrelated note

If you halve the vibrating part of the string, what happens to the frequency?

AIt doublesBIt halvesCIt doesn't changeDIt rises slightly

Listen. Which note has the higher frequency?

Listen

AThe firstBThe secondCBoth the same

What does timbre depend on?

AOnly on the volumeBOnly on the fundamental frequencyCOn the size of the roomDOn the mix of harmonics and how the sound starts and dies away

A string has a fundamental of 220 Hz. At what frequency does its 2nd harmonic sound?

A330 HzB440 HzC220 HzD110 Hz

Optional reinforcement in the portalExperiment with waves, frequencies and harmonics in the sound lab(opens in a new tab)