A tuning fork of 440 Hz sounded with an unknown fork produces 4 beats per second. When a small piece of wax is added to the unknown fork, the beat rate decreases. Determine the unknown fork's original frequency.

Vibrations & Waves Challenge #4 — Beats

The beats of two
tuning forks.

Vibrations & Waves Hard

Problem

A standard 440 Hz tuning fork sounded together with an unknown fork produces 4 beats per second. When a small blob of wax is stuck to the unknown fork, the beat rate decreases. Determine the unknown fork’s original frequency.

Reference fork\( 440\ \mathrm{Hz} \)
Beat rate\( 4 \) beats/s
Wax effectlowers the unknown’s frequency
After waxbeats slow down

The beat count alone leaves two candidates — the wax is what breaks the tie.

Hint: 4 beats/s means the unknown is 436 or 444 Hz. Wax lowers its frequency — if the beats then slow, did the gap to 440 grow or shrink? Only one candidate fits.

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The beats of twotuning forks.

Problem

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The beats of two
tuning forks.