Amplitude (of a Wave)

Amplitude is the maximum deviation of a periodic function from its mean (centre) value. For the sinusoid $y = A \sin(Bx + C) + D$, the amplitude is $|A|$ — the wave oscillates between $D + |A|$ and $D - |A|$.

For pure $\sin$ and $\cos$, amplitude is $1$. Multiplying by $A$ scales the wave vertically: $y = 3\sin x$ swings between $-3$ and $+3$.

Amplitude is one of four parameters of a transformed sinusoid:

• Amplitude $|A|$: vertical stretch.
• Period $\frac{2\pi}{|B|}$: horizontal stretch.
• Phase shift $-C/B$: horizontal slide.
• Vertical shift $D$.

Physical meaning: sound waves → loudness; light waves → brightness; pendulum / spring → max displacement; AC current → peak voltage.