[tex]\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------[/tex]
[tex]\bf \textit{frequency varies inversely with its wavelength}\qquad f=\cfrac{k}{w}
\\\\\\
\textit{we also know that }
\begin{cases}
w=100\\
f=3000
\end{cases}\implies 3000=\cfrac{k}{100}
\\\\\\
300000=k\qquad thus\qquad \boxed{f=\cfrac{300000}{w}}
\\\\\\
\textit{now, when f = 500, what is \underline{w}?}\qquad 500=\cfrac{300000}{w}
\\\\\\
w=\cfrac{300000}{500}\implies w=600[/tex]
