Physics

The wave equation $y = a \sin(bt - cx)$ encodes all the wave's properties in its coefficients. Recognize that $b$ is the angular frequency $\omega$ and $c$ is the wave number $k$—then use the fundamental relationships: frequency comes directly from $\omega$, wavelength from $k$, wave speed from their ratio, and maximum particle speed from how fast the medium oscillates vertically (the amplitude times angular frequency). Matching requires converting between angular and ordinary quantities using $2\pi$.

The wave equation $y = a \sin(bt - cx)$ encodes all the wave's properties in its coefficients. Recognize that $b$ is the angular frequency $\omega$ and $c$ is the wave number $k$—then use the fundamental relationships: frequency comes directly from $\omega$, wavelength from $k$, wave speed from their ratio, and maximum particle speed from how fast the medium oscillates vertically (the amplitude times angular frequency). Matching requires converting between angular and ordinary quantities using $2\pi$.