Definition

Amplitude is how tall a wave is, measured from the middle line up to the crest, with big amplitude meaning a big, strong wave and small amplitude a gentle one; for sound, amplitude is loudness, and for light it is brightness, since amplitude tells how much energy a wave carries. It is the maximum distance particles move from their rest position, independent of wavelength and frequency, and a wave with larger amplitude carries more energy. Amplitude $A$ is the coefficient in $y(x,t) = A\sin(kx - \omega t)$, and energy transported by a mechanical wave is proportional to $A^2$: a string wave carries power $P = \tfrac{1}{2}\mu\omega^2A^2v$, and sound intensity is $I = \tfrac{1}{2}\rho v \omega^2 s_{\max}^2$, which spans so many orders of magnitude that sound level is defined logarithmically, $\beta = 10\log_{10}(I/I_0)$ decibels with $I_0 = 10^{-12}\ \text{W/m}^2$, and in superposition amplitudes add rather than intensities, producing interference maxima of $2A$ and minima of zero.