Beats

Beat occur when two harmonic signals with nearly the same frequency are added together. The $x$-position of the black dot below is the sum of two cosine terms. The black point is the sum of the projections of the red and blue phasors onto the $x$-axis. When the two frequencies are nearly the same, the resulting interference is called beats. The perioid of the interference pattern is the time it takes for the faster phasor to travel $2\pi$ further than the slower phasor, $(\omega_2 - \omega_1)T=2\pi$.

Your browser does not support the canvas element.    \[ \begin{equation} \large x(t) = A_1\cos(\omega_1t)+A_2\cos(\omega_2t). \end{equation} \]

$A_1=$1 [m]

$A_2=$1 [m]

$\omega_1=$1 [rad/s]

$\omega_2=$1 [rad/s]

Beats are often used to tune a piano or guitar. A note is played on the instrument while simultaneously striking a tuning fork. The sound gets louder and softer because of the beats and the instrument is tuned to increase the period of the beats so that the two frequencies get closer together.