Beats
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The bottom window displays f(t) = sin(t) in red and g(t) = A sin(ωt - φ) in yellow. The top window displays their sum, in green. Grab the [ω], A, or φ slider to vary the circular frequency ω, the amplitude A, or the phase lag φ. Position the cursor arrow over the top graphing window to will be displayed. The [zoom] key toggles between a t range of [0,20π] and [0,60π]. The [envelope] key toggles display of an envelope for the sum. An equation for this curve, and its derivation, can be found in the Supplimentary Notes. The [sin(((1+ω)/2)t)] key toggles display of this function in the upper window.
c 2001 H. Hohn |