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📘 Lesson 4 of 7 · Waves

📳 Resonance

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.

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01 Key Concepts

Natural 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).

Resonance 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.

Everyday 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.

Resonance 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.

Damping 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.

02 Solved Examples

Example 1 Why does pushing a playground swing at the same rhythm as its natural back-and-forth motion make it swing higher and higher?
  1. Each push adds energy at exactly the right moment in the swing's motion, aligning with the swing's natural frequency.
  2. This repeated, well-timed energy addition builds amplitude over time -- the defining feature of resonance.
Answer: The pushes match the swing's natural frequency, causing resonance and growing amplitude
Example 2 A singer shatters a wine glass by singing a sustained note. What physical principle explains this?
  1. The singer's note matches the glass's natural resonant frequency.
  2. Sound energy builds up in the glass's vibrations until the amplitude becomes large enough to break it.
Answer: Resonance -- the sound wave's frequency matches the glass's natural frequency, building destructive vibration amplitude
Example 3 Why must engineers be careful about a bridge's natural frequency matching the rhythm of pedestrians walking across it?
  1. If many pedestrians happen to walk in step near the bridge's natural frequency, their combined force could act like a resonance-driving force.
  2. This could cause the bridge to oscillate with dangerously increasing amplitude.
Answer: To avoid resonance, which could cause dangerous, uncontrolled oscillations in the bridge structure

03 Practice Questions

1What is 'natural frequency'?
The frequency a system naturally oscillates at when disturbed and left alone
2What condition causes resonance?
A driving force matching the system's natural frequency
3What effect does resonance have on oscillation amplitude?
It causes amplitude to grow significantly larger than the driving force alone would produce
4What limits how large resonant oscillations can grow in real systems?
Damping (energy loss from friction or resistance)
5Give a real-world example of resonance.
Any valid example, e.g. pushing a swing, a radio tuner, or a shattering wine glass

📄 Resonance — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet