Resonance
Resonance means: a body capable of sounding vibrates along when it is excited from outside in step with its natural frequency or an overtone. Older texts say “sympathetic vibration”. The guitar body, the piano soundboard and the strings that ring along by themselves at a note are examples.
- Condition
- excitation near the natural frequency or an overtone
- Also
- sympathetic vibration
- Example
- open A string vibrates along when another string plays A
- Use
- body and soundboard make the string sound loud
Vibrating along in step
Every body capable of vibrating has a natural frequency. If it is set off from outside in the right rhythm, it vibrates along, even if the push is weak. The push need only match the natural frequency or one of its partials. It is the same with a child on a swing: if you push at the right moment, you can get it swinging high with small pushes.
Which strings vibrate along when A sounds?
A struck low A (110 Hz) contains the partials A, A, E, A, C♯. A string or body with one of these natural frequencies vibrates along; here are the fundamental A, the A an octave higher (marked, 220 Hz), the E (330 Hz) and the A two octaves higher (440 Hz).
Which strings ring along?
The table shows the first partials of an A at 110 Hz. A second string vibrates along if one of its frequencies coincides with one of these partials. That is why a string an octave away reacts at once and clearly, one a fifth away more weakly and one a third away hardly, above all because in equal temperament it does not hit exactly, compare the overtone series. If the string is detuned, the vibrating along stops.
| Partial | Frequency at fundamental 110 Hz | Note | Vibrates along? |
|---|---|---|---|
| 1 | 110 Hz | A | yes, same natural frequency |
| 2 | 220 Hz | A | yes, octave |
| 3 | 330 Hz | E | yes, but weaker |
| 4 | 440 Hz | A | yes, two octaves |
| 5 | 550 Hz | C♯ | only weakly, in equal temperament the third deviates by 14 cents |
Body and soundboard
A string alone is quiet, because it hardly moves any air. Guitar body, violin belly and piano soundboard are themselves capable of vibrating and take over the vibration of the string via bridge or saddle. Because they move larger surfaces, the sound becomes loud. Resonance applies here too: the body has natural frequencies that reinforce some notes more strongly than others. That makes up part of the character of every instrument.
Common mistakes
- Confusing resonance with reverberation: reverberation is reflection in the room, resonance the vibrating along of a body.
- Assuming every string vibrates along: only suitable frequencies excite it.
- Taking resonance for loudness: it reinforces certain frequencies more strongly than others.
Continue on Maikstrings
Related terms
Natural frequencyVibrationHarmonic seriesPartialTuning forkBeatingWaveInterferenceStandard pitch
Editor: Maik Krohm · reviewed on 3 October 2026
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