Amplitude and Period

Pre-Calculus · Axiom Academy

Two numbers reshape the sine wave: one stretches it tall, the other squeezes it tight. 1. Amplitude: How Tall Is the Wave? The parent wave swings between -1 and 1 , so it reaches a height of 1 above its midline (the center line it oscillates around). That peak height is the amplitude . In the animation, the orange bracket measures from the midline straight up to the crest — and it lands on exactly 1 . amplitude = distance from midline to the peak 2. Amplitude in Action: A Stretches the Wave Watch what A does to the real curve. The faint wave is the parent ; the bright wave is as A grows from 1 up to 2.5 . Every point's height is multiplied by A , so the whole wave stretches taller — the peaks climb, the troughs drop, but the midline and the crossings stay put. The wave is stretched taller — a vertical stretch. swings between -3 and 3 . The wave is squashed shorter — a vertical compression. only reaches . always oscillates between -|A| and |A| . The range is . A changes only height. Each cycle is still wide — stretching up doesn't change the spacing. For , the amplitude is |2| = 2 . The wave reaches 2 at its crest and -2 at its trough — twice as tall as the parent — yet still completes one cycle over . 3. Period: How Wide Is One Cycle?

This is the written version of the interactive lesson above. See the full Pre-Calculus course.