Will it resonate?

A singer holds one loud note at a wine glass. At most notes, nothing happens. At one particular note, the glass hums and shakes violently.

The glass has a natural frequency. The note is a driving frequency. One comparison settles whether the shaking builds up: do the two match?

The glass's natural frequency is 520 Hz: tapped once, it rings at 520 Hz.

The singer's note drives the glass at the note's own frequency.

Note at 520 Hz against natural 520 Hz: a match, and the glass's amplitude builds up large.

Note at 520 Hz: the driving frequency matches the natural frequency. The glass resonates, and its amplitude builds up large.

Note at 470 Hz: no match. The glass only trembles a little, a small forced vibration with no build-up.

Note at 470 Hz against natural 520 Hz: no match, and the glass only trembles.

That is the whole test. Compare the driving frequency with the natural frequency: a match means resonance; a mismatch means only a small response.

Does the driving frequency match the natural frequency? The match builds up; the mismatch only trembles.

A hallway floor's natural frequency is 12 Hz. A treadmill on it shakes it at 12 Hz. Will the floor resonate?

Driving frequency: 12 Hz. Natural frequency: 12 Hz.

The frequencies match.

Yes. The floor resonates, and its vibration builds up large.

A floor's natural frequency is 12 Hz. A box fan on it shakes it at 20 Hz. Will the floor resonate?

Driving frequency: 20 Hz. Natural frequency: 12 Hz.

The frequencies do not match.

No. There is no build-up: only a small forced vibration.

Quick-fire drill

A crystal glass rings at 600 Hz when tapped. A speaker beside it plays a 600 Hz tone. Will the glass resonate?

A bookshelf's natural frequency is 8 Hz. A printer on it shakes it at 14 Hz. Will the shelf resonate?

A streetlamp pole, gusted once, sways at 2 Hz. Steady wind gusts shake it 5 times each second. Will the pole resonate?

A trampoline's surface, pressed once and released, springs at 3 Hz. Pim bounces on it exactly 3 times each second. Will the trampoline resonate?

A garage door panel rattles at 40 Hz when knocked once. An idling engine next to it vibrates it at 40 Hz. Will the panel resonate?

A thin glass rings at 450 Hz when tapped. A singer beside it holds a note at 380 Hz. Will the glass resonate?

Four tuning forks are each driven by a speaker's tone. Which one resonates?

What decides whether a driven system resonates?

A thin steel panel rings at 220 Hz when tapped once. Which driving frequency would make it resonate?