Compressed Waves

Trigonometry · Axiom Academy

Discover why sin(2x) = ½ has twice as many solutions as sin(x) = ½. Watch waves compress and solutions multiply! Let's compare two sine waves: sin(x) and sin(2x). Move the slider to explore how they differ. Adjust the compression factor (b) in sin(bx) and watch what happens to the wave! Side-by-Side: Solutions Revealed Watch how solutions multiply as we compress the wave. Understanding Wave Compression For sin(bx), the period is 2π/b. As b increases, the period decreases, causing the wave to repeat more frequently. More repetitions mean more solutions. In any fixed interval, a compressed wave intersects a horizontal line more times. The coefficient b is called the frequency. It determines how many complete oscillations occur in a standard interval. Wave compression appears in sound (higher pitch = higher frequency), light (color), and signal processing.

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