TwiddleLab / Physics / Waves and Sound

Resonance: Pushing at the Right Time

Lesson 8 of 10 · 7 min · Free, no account needed

What you will learn

• Everything that can swing or vibrate has a natural frequency: its own rhythm when left alone.
• Resonance: pushes in step with that rhythm add up, so small pushes make big swings.
• A swing's rhythm depends on its length, not on who sits on it. Glasses, bridges and radios resonate too.

Start the lesson

How the lesson goes

1. A small kid can push an adult really high on a swing. What's the trick?

2. Push the swing. Can you make it go higher?

   Each push is the same small push.

3. A robot pushes with a steady rhythm. Find the rhythm that gives the biggest swing.

   If the pushes come at the swing's own frequency, each one arrives just as the seat starts forward, so every push adds energy. Any other rhythm sometimes pushes against the motion.

4. Resonance.

   Left alone, a swing goes back and forth at its own natural frequency.

   Push in step with it and each push adds to the last: the swing grows big. That is resonance.

   Useful: a radio tunes to one station, a guitar body makes the string louder. Harmful: a washing machine shaking the floor, a singer's note shattering a glass.

   Simplified: a swing is a pendulum with small swings and a bit of air drag. Then its frequency is √(g/L) ÷ 2π: about 0.35 Hz for 2 m.

5. Game: Swing high. Reach the green flag with at most 10 pushes.

6. A short swing and a long one. Which has the higher natural frequency?

   Swap the kid for an adult too.

   A pendulum's natural frequency is √(g/L) ÷ 2π: only the length (and gravity) appear. A heavier rider needs a bigger pull to speed up, and gravity pulls harder on them by exactly the same factor.

7. Math: find the maximum. Which note would shake this wine glass hardest?

   The glass rings at its own natural frequency. A sound at exactly that frequency pushes it in step every cycle, so its wobble grows until the glass may crack.

8. The pusher stands behind. Where should the hand meet the swing?

   A push adds energy only when it acts in the direction the seat is moving. At the back end the seat is right at the pusher and starts moving forward, so the whole push helps.

9. Race: your pushes from the game against a robot with perfect rhythm.

Previous lesson: Standing Waves: Why Strings Have Notes · Next lesson: The Doppler Effect · Part of the course: Waves and Sound

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