Signal Sampling Detective
Compare a hidden wave with the dots measured by a sensor. Use a compatible wave to discover why sampling rate matters.
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Try the experiment, then check the ideas behind it. Stars track these answers; they do not measure your experiment.
Progress stays in this browser only. First-try answers earn 100 points, second tries 75, and later tries 50. One star per completed checkpoint. The timer is optional and never affects points.
Theory and model assumptions
y(t) = A sin(2πft + φ); samples occur at t = n/fₛ. f_fold = f − round(f/fₛ)fₛ. The signed folded sine has identical samples. Recovery needs fₛ > 2f and a known band limit. The plotted folded curve is a compatible sinusoid, not a general reconstruction algorithm.
Teacher guidance
Start at 7 Hz and 10 samples/s: the folded frequency is −3 Hz. The minus sign changes the wave direction/phase; its magnitude is 3 Hz. Compare 14 and 15 samples/s for a 7 Hz source. Exact Nyquist equality is phase-degenerate. The budget task works at 19 samples/s: 39 measurements including both endpoints.
Expected time: 15–25 minutes.