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How a Guitar String Makes Different Notes
Length, tension, and the fretboard
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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.
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.