BEATS

The bottom window displays $$f(t) = \sin(t)$$ in red and $$g(t) = A \sin(\omega t - \phi)$$ in yellow. The top window displays their sum, in green.

Grab the $$[\omega], [A],$$ or $$[\phi]$$ slider to vary the circular frequency $$\omega$$, the amplitude $$A$$, or the phase lag $$\phi$$.

Position the cursor arrow over the top graphing window to will be displayed.

The [Zoom] key toggles between a $$t$$ range of $$[0,20\pi]$$ and $$[0,60\pi]$$.

The [Envelope] key toggles display of an envelope for the sum. An equation for this curve, and its derivation, can be found in the Supplementary Notes.

© 2001 H. Hohn and H. Miller