What is amplitude?
Amplitude is the distance from the midline of a wave to its peak — how tall the wave is. For y = A·sin(Bx), the amplitude is the absolute value of A. It is a pure number, the same whether the x-axis is in degrees or radians.
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Period & amplitude
Find the amplitude and period of a wave y = A sin(Bx): the amplitude is the absolute value of A and the period is 360 degrees (or 2π radians) divided by the absolute value of B, shown with a wave that stretches or compresses as you change A and B, with the x-axis in degrees or radians.
amplitude = |A| · period = 360°/|B| = 2π/|B|
Angle unit
Frequently asked questions
What is the period?
The period is the horizontal length of one complete cycle before the wave repeats. For y = A·sin(Bx) it is 360°/|B|, or 2π/|B| in radians — the same physical width, just labelled in different units.
Can you give a worked example?
For y = 3·sin(2x), the amplitude is 3 and the period is 360°/2 = 180° (equivalently 2π/2 = π radians). The wave is three units tall and completes a full cycle every 180°. Flip the Degrees/Radians toggle to see the x-axis marked in multiples of π.
How are amplitude and frequency related?
Amplitude (height) and frequency (cycles per unit) are independent. B controls frequency and period; A controls amplitude. Doubling B halves the period without touching the height.
Where is this used in real life?
Amplitude and period describe sound (loudness and pitch), light, radio waves, springs and pendulums, AC electricity, and any repeating signal studied in physics and engineering.