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Beats arise from superposition of two sound waves with slightly different frequencies $f_1$ and $f_2$. The resultant amplitude modulates at the beat frequency $f_{\text{beat}} = |f_1 - f_2|$, producing periodic waxing and waning of loudness. Beats are perceptible only when $f_{\text{beat}} \leq 7$ Hz; beyond this, the fluctuations are too rapid for the ear to resolve.

The primary application of beats is determining an unknown frequency. Given a known fork ($f_1$) and beat count ($n$), the unknown $f_2 = f_1 \pm n$. To resolve the ambiguity: load the unknown fork with wax (decreasing $f_2$). If beats increase, $f_2$ was below $f_1$ (moved further away). If beats decrease, $f_2$ was above $f_1$ (moved closer). Filing the fork increases its frequency — the same logic applies in reverse.

For musical instrument tuning: zero beats between two strings means perfect unison. Piano tuners adjust string tension until beats with a reference fork disappear. In sonometer problems, increasing tension increases wire frequency — combine this with the beat change direction to determine whether the wire was originally above or below the reference frequency.