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The wavelength, W, of a wave varies inversely as its frequency, F. A wave with a frequency of 400 kHz has a length of 323 meters. What is the frequency of a wave with a length of 237 meters? Round your answer to the nearest tenth.

The equation of variation is \(\displaystyle W = \frac{k}{F}\). Substituting gives \(\displaystyle W = \frac{k}{400}\) and solving for \(\displaystyle k\) gives \(\displaystyle 129200\). This gives the variation equation \(\displaystyle W = \frac{129200}{F}\). Using the given wave length gives the equation \(\displaystyle 237 = \frac{129200}{F}\). Solving for \(\displaystyle F\) gives \(\displaystyle F = \frac{129200}{237}=545.1\) meters.

Download \(\LaTeX\) 

\begin{question}The wavelength, W, of a wave varies inversely as its frequency, F. A wave with a frequency of 400 kHz has a length of 323 meters. What is the frequency of a wave with a length of 237 meters?  Round your answer to the nearest tenth. 
    \soln{9cm}{The equation of variation is $W = \frac{k}{F}$. Substituting gives $W = \frac{k}{400}$ and solving for $k$ gives $129200$. This gives the variation equation $W = \frac{129200}{F}$. Using the given wave length gives the equation $237 = \frac{129200}{F}$. Solving for $F$ gives $F = \frac{129200}{237}=545.1$ meters. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>The wavelength, W, of a wave varies inversely as its frequency, F. A wave with a frequency of 400 kHz has a length of 323 meters. What is the frequency of a wave with a length of 237 meters?  Round your answer to the nearest tenth. </p> </p>
HTML for Canvas
<p> <p>The equation of variation is  <img class="equation_image" title=" \displaystyle W = \frac{k}{F} " src="/equation_images/%20%5Cdisplaystyle%20W%20%3D%20%5Cfrac%7Bk%7D%7BF%7D%20" alt="LaTeX:  \displaystyle W = \frac{k}{F} " data-equation-content=" \displaystyle W = \frac{k}{F} " /> . Substituting gives  <img class="equation_image" title=" \displaystyle W = \frac{k}{400} " src="/equation_images/%20%5Cdisplaystyle%20W%20%3D%20%5Cfrac%7Bk%7D%7B400%7D%20" alt="LaTeX:  \displaystyle W = \frac{k}{400} " data-equation-content=" \displaystyle W = \frac{k}{400} " />  and solving for  <img class="equation_image" title=" \displaystyle k " src="/equation_images/%20%5Cdisplaystyle%20k%20" alt="LaTeX:  \displaystyle k " data-equation-content=" \displaystyle k " />  gives  <img class="equation_image" title=" \displaystyle 129200 " src="/equation_images/%20%5Cdisplaystyle%20129200%20" alt="LaTeX:  \displaystyle 129200 " data-equation-content=" \displaystyle 129200 " /> . This gives the variation equation  <img class="equation_image" title=" \displaystyle W = \frac{129200}{F} " src="/equation_images/%20%5Cdisplaystyle%20W%20%3D%20%5Cfrac%7B129200%7D%7BF%7D%20" alt="LaTeX:  \displaystyle W = \frac{129200}{F} " data-equation-content=" \displaystyle W = \frac{129200}{F} " /> . Using the given wave length gives the equation  <img class="equation_image" title=" \displaystyle 237 = \frac{129200}{F} " src="/equation_images/%20%5Cdisplaystyle%20237%20%3D%20%5Cfrac%7B129200%7D%7BF%7D%20" alt="LaTeX:  \displaystyle 237 = \frac{129200}{F} " data-equation-content=" \displaystyle 237 = \frac{129200}{F} " /> . Solving for  <img class="equation_image" title=" \displaystyle F " src="/equation_images/%20%5Cdisplaystyle%20F%20" alt="LaTeX:  \displaystyle F " data-equation-content=" \displaystyle F " />  gives  <img class="equation_image" title=" \displaystyle F = \frac{129200}{237}=545.1 " src="/equation_images/%20%5Cdisplaystyle%20F%20%3D%20%5Cfrac%7B129200%7D%7B237%7D%3D545.1%20" alt="LaTeX:  \displaystyle F = \frac{129200}{237}=545.1 " data-equation-content=" \displaystyle F = \frac{129200}{237}=545.1 " />  meters. </p> </p>