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