← Sound, the Doppler effect, and resonance

Forced vibration

A washing machine hits its spin cycle, and the laundry-room floor starts to hum under Pim's feet.

The floor is not choosing how to shake. Something pushes it, over and over, and the pusher sets the rate.

The spinning drum shakes the machine's case 20 times each second, and the case presses on the floor 20 times each second.

The floor answers at exactly that rate: it vibrates at 20 Hz, matching the drum.

floorwashing machinedrum turns at 20 Hzfloor vibrates at 20 Hz
The drum turns at 20 Hz, and the driven floor vibrates at 20 Hz.

Set the drum to a slower cycle, 15 turns each second, and the floor vibrates at 15 Hz.

floorwashing machinedrum turns at 15 Hzfloor vibrates at 15 Hz
Set to a slower cycle, the drum turns at 15 Hz, and the floor follows at 15 Hz.

The floor has its own natural frequency: the frequency it would oscillate at if tapped once and left alone.

Driven like this, the floor vibrates at the pusher's frequency, whatever the floor's own natural frequency is.

An oscillation driven by a repeated external push, at the pusher's frequency, is called a forced vibration.

Every forced vibration runs at the frequency of whatever drives it: the drum's rate, the engine's rate, the pusher's rate.

deskphonephone buzzes at 160 Hzdesktop vibrates at 160 Hz
A different pusher, the same rule: the phone buzzes at 160 Hz, and the driven desktop vibrates at 160 Hz.

A phone on vibrate buzzes 160 times each second on a wooden desk, and the desktop hums along. At what frequency does the desktop vibrate, and what is this kind of oscillation called?

The buzzing phone is the pusher, at 160 Hz.

A driven object vibrates at the pusher's frequency.

The desktop vibrates at 160 Hz, and its oscillation is a forced vibration.

A truck idles at a stoplight, its engine shaking the cab at 30 Hz, and the side mirror trembles. State the mirror's vibration frequency.

The engine is the pusher, at 30 Hz.

The driven mirror vibrates at the pusher's frequency.

The mirror vibrates at 30 Hz.

A box fan rattles a loose vent cover 12 times each second. At what frequency does the vent cover vibrate?

Noll says: 'A floor driven by a washing machine vibrates at the machine's frequency, not at the floor's own natural frequency.' Is Noll correct?

An oscillation driven by a repeated external push, at the pusher's frequency, is called what?

Your turn

A floor polisher runs against a cafeteria table's leg at 45 Hz, and the table trembles. Which statement is correct?

A window hums while a helicopter hovers outside. What sets the frequency of the window's vibration?

A dryer drum turns 18 times each second, and the shelf above it vibrates at 18 Hz. The dryer is switched to a slower cycle, 12 turns each second. What does the shelf do?