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Waves · Quick Reference
Resonance Cheat Sheet
In one line: resonance occurs when a system is driven at its natural frequency, causing oscillations to build dramatically in amplitude — the same principle that lets you push a swing higher and higher with well-timed pushes.
Key Ideas
1Natural Frequency. The frequency at which a system tends to oscillate when disturbed and left alone, determined by its physical properties (like mass, stiffness, or length).
2Resonance Condition. Occurs when a system is driven by an external periodic force matching its natural frequency, causing the amplitude of oscillation to grow much larger than the driving force alone would suggest.
3Everyday Examples of Resonance. Pushing a playground swing at just the right rhythm, a singer shattering a glass by matching its natural frequency, or a radio tuner selecting a specific broadcast frequency.
4Resonance and Structural Engineering. Engineers must carefully avoid designing structures (like bridges) with natural frequencies that could be matched by common external forces (like wind or foot traffic), which could otherwise cause catastrophic resonant oscillations.
5Damping and Resonance. Damping (energy loss from friction or resistance) limits how large resonant oscillations can grow -- without any damping, resonance could theoretically build amplitude without bound.
Worked Examples
Why does pushing a playground swing at the same rhythm as its natural back-and-forth motion make it swing higher and higher?
The pushes match the swing's natural frequency, causing resonance and growing amplitude
A singer shatters a wine glass by singing a sustained note. What physical principle explains this?
Resonance -- the sound wave's frequency matches the glass's natural frequency, building destructive vibration amplitude
Why must engineers be careful about a bridge's natural frequency matching the rhythm of pedestrians walking across it?
To avoid resonance, which could cause dangerous, uncontrolled oscillations in the bridge structure
Practice Yourself
What is 'natural frequency'?
The frequency a system naturally oscillates at when disturbed and left alone
What condition causes resonance?
A driving force matching the system's natural frequency
What effect does resonance have on oscillation amplitude?
It causes amplitude to grow significantly larger than the driving force alone would produce
What limits how large resonant oscillations can grow in real systems?
Damping (energy loss from friction or resistance)