Question

The frequency of a radio wave varies inversely with its wavelength. If a 100-meter wave has a frequency of 3,000 kilohertz, what is the wavelength of a wave that has a frequency of 500 kilohertz? Round your answer to the nearest meter.

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{frequency varies inversely with its wavelength}\qquad f=\cfrac{k}{w} \\\\\\ \textit{we also know that } \begin{cases} w=100\\ f=3000 \end{cases}\implies 3000=\cfrac{k}{100} \\\\\\ 300000=k\qquad thus\qquad \boxed{f=\cfrac{300000}{w}} \\\\\\ \textit{now, when f = 500, what is \underline{w}?}\qquad 500=\cfrac{300000}{w} \\\\\\ w=\cfrac{300000}{500}\implies w=600$