= Vacuum frequency-wavelength relation
{title2=$\nu\lambda=c$}
A <monochromatic wave> in vacuum has <frequency> $\nu$ and <wavelength> $\lambda$ related by $\nu\lambda=c$, where $c$ is the <speed of light>. During one <oscillation period> $T=1/\nu$, a constant-<wave phase> surface travels one <wavelength>, so $\lambda=cT$. Equivalently, the <plane electromagnetic wave> relation $\omega=ck$ with <angular frequency> $\omega=2\pi\nu$ and <wavenumber> $k=2\pi/\lambda$ gives the same result.
As a calculated example, a vacuum <radio wave> with $\nu=300\,\mathrm{MHz}=3.00\times10^8\,\mathrm{Hz}$ has $\lambda=0.999308\,\mathrm m$ using $c=299792458\,\mathrm{m/s}$. Doubling <frequency> halves <wavelength>, independently of <wave amplitude> and <wave intensity>. The <frequency spectrum> of a pulse contains multiple <frequencies>; the relation applies to each vacuum component, rather than assigning one exact <wavelength> to the whole pulse. In a homogeneous medium replace $c$ by the appropriate <phase velocity>; the vacuum equation does not assert that all media have the same <wavelength> at a given <frequency>.
Back to article page
