When two sound waves of frequencies $f_1$ and $f_2$ ($f_1 \approx f_2$) superpose: $y = 2A\cos(2\pi\frac{f_1-f_2}{2}t)\sin(2\pi\frac{f_1+f_2}{2}t)$. The amplitude modulates at frequency $|f_1-f_2|/2$, but loudness maxima occur at rate $|f_1-f_2|$ (beat frequency). Beats are perceived when $f_{\text{beat}} \leq 7$ Hz. Beats are used to tune musical instruments and to determine unknown frequencies. If wax is added to a fork (loading), its frequency decreases.