A guitar makes music when a stretched string vibrates back and forth. Those vibrations push on the air and create sound waves that travel to your ear. The note you hear depends mostly on the string's vibrating length, tension, and mass per length.
Understanding these factors helps explain why pressing a string on different frets makes different pitches.
When a finger presses a string against a fret, the fret becomes a new endpoint for the vibrating part of the string. This shortens the string section that can vibrate, which raises the frequency and makes a higher note. Tightening the string also raises the pitch, while using a thicker or heavier string lowers the pitch.
The guitar is a useful example of standing waves, because the string vibrates in patterns with nodes at the ends.
Understanding How a Guitar String Makes Different Notes
A string does not move as one simple arc. After it is plucked, several vibration patterns exist at the same time. The largest, slowest pattern gives the fundamental note.
Smaller patterns divide the string into halves, thirds, quarters, and other sections. These are called harmonics or overtones. They have higher frequencies than the fundamental.
Their mixture gives a guitar its tone colour. A nylon classical string, a steel acoustic string, and an electric guitar string can play the same named note but sound noticeably different because their harmonic mixtures differ.
The fret positions are carefully chosen. They are not spaced at equal physical distances. Each step of one fret raises the pitch by one semitone, which is the smallest usual step in Western music.
Twelve semitone steps make an octave. At the octave, the frequency is twice the starting frequency. To create these equal pitch steps, each new vibrating length must be a fixed fraction of the one before it.
This makes the frets get closer together near the guitar body. Students can see this directly by comparing the large gaps near the nut with the narrow gaps at high frets.
A real guitar is not perfectly ideal. Pressing a string down bends it slightly and can increase its tension. If a player presses very hard, the note may become a little sharp.
High action, meaning a large gap between string and fret, makes this effect stronger. The bridge saddle is placed with a small adjustment called compensation. It helps notes played high on the neck stay close to the intended pitch.
Players check intonation by comparing an open string with the note at the twelfth fret. If they do not match closely, the saddle position may need adjustment.
Plucking position changes the sound even when the pitch stays the same. A pluck near the middle allows a strong fundamental pattern. A pluck close to the bridge encourages more high harmonics, creating a brighter and thinner sound.
Lightly touching a string at certain points can prevent some vibration patterns while allowing others. This produces clear bell-like harmonics. The pickup on an electric guitar matters too.
A pickup near the bridge senses more of the fast, detailed motion than one near the neck. When learning this topic, separate pitch from tone colour. Pitch depends on the vibration rate, while tone colour depends on which vibration patterns are strongest.
Key Facts
- Higher frequency means higher pitch.
- For a stretched string, f1 = v/(2L), where f1 is the fundamental frequency, v is wave speed, and L is vibrating length.
- Wave speed on a string is v = sqrt(T/mu), where T is tension and mu is mass per length.
- Shortening the vibrating length L raises the fundamental frequency.
- Increasing string tension T raises wave speed and raises frequency.
- A heavier string with larger mu vibrates more slowly and produces a lower frequency if length and tension stay the same.
Vocabulary
- Frequency
- Frequency is the number of vibrations or wave cycles each second, measured in hertz.
- Pitch
- Pitch is how high or low a sound seems to a listener, and it mainly depends on frequency.
- Fret
- A fret is a metal strip on a guitar neck that sets a new endpoint for a vibrating string when the string is pressed against it.
- Fundamental frequency
- The fundamental frequency is the lowest natural frequency of a vibrating string and is usually heard as the main note.
- Standing wave
- A standing wave is a vibration pattern that appears to stay in place because waves reflect and interfere on the string.
Common Mistakes to Avoid
- Thinking the whole string always vibrates, but when a finger presses a fret only the section between that fret and the bridge vibrates strongly.
- Saying thicker strings always make higher notes, but greater mass per length lowers wave speed and usually lowers the frequency.
- Confusing loudness with pitch, but plucking harder mainly increases amplitude and volume, not the note frequency.
- Forgetting that tension matters, but tuning works because changing tension changes wave speed and therefore frequency.
Practice Questions
- 1 A string has wave speed 120 m/s and a vibrating length of 0.60 m. What is its fundamental frequency using f1 = v/(2L)?
- 2 A guitar string is shortened from 0.64 m to 0.32 m while wave speed stays the same. If the original fundamental frequency was 110 Hz, what is the new fundamental frequency?
- 3 A guitarist presses a string closer to the bridge instead of closer to the nut. Explain what happens to the vibrating length, frequency, and pitch.