Resonance happens when an object vibrates strongly because it is driven at or near one of its natural frequencies. In music, resonance is what lets a small motion, such as a plucked guitar string, become a much louder and richer sound. The string alone moves very little air, but the guitar body vibrates with it and pushes on a larger volume of air.
This is why the shape and material of an instrument matter so much to its tone.
Key Facts
- Resonance occurs when driving frequency is close to natural frequency.
- For a stretched string fixed at both ends, f1 = v/(2L).
- Wave speed on a string is v = sqrt(T/mu), where T is tension and mu is mass per unit length.
- String harmonics follow fn = n f1 for n = 1, 2, 3, ...
- Larger vibration amplitude usually means louder sound because more energy is transferred to the air.
- A resonator, such as a guitar body, transfers vibration from the string to the surrounding air more effectively.
Vocabulary
- Resonance
- Resonance is the large-amplitude vibration that occurs when a system is driven near one of its natural frequencies.
- Natural frequency
- A natural frequency is a frequency at which an object tends to vibrate freely after being disturbed.
- Amplitude
- Amplitude is the maximum displacement of a vibrating object from its rest position.
- Harmonic
- A harmonic is a standing-wave frequency that is an integer multiple of the fundamental frequency.
- Soundboard
- A soundboard is the vibrating surface of an instrument that helps transfer energy from strings to the air.
Common Mistakes to Avoid
- Thinking resonance creates energy from nothing. Resonance increases amplitude by efficiently transferring energy from a driver into a vibrating system.
- Confusing pitch with loudness. Pitch depends mainly on frequency, while loudness depends mainly on amplitude and sound intensity.
- Assuming the guitar string alone makes most of the sound. The string has a small surface area, so the guitar body and soundboard are needed to move much more air.
- Using f = v/L for the fundamental of a string fixed at both ends. The correct fundamental relation is f1 = v/(2L) because the string length holds half of a wavelength.
Practice Questions
- 1 A guitar string is 0.65 m long and the wave speed on it is 260 m/s. What is its fundamental frequency?
- 2 A string has a fundamental frequency of 110 Hz. What are the frequencies of its 2nd, 3rd, and 4th harmonics?
- 3 A tuning fork near a guitar causes one string to vibrate loudly even though it is not touched. Explain why this happens and what must be true about the fork frequency and the string.