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The wavelength, W, of a wave varies inversely as its frequency, F. A wave with a frequency of 100 kHz has a length of 308 meters. What is the frequency of a wave with a length of 201 meters? Round your answer to the nearest tenth.

The equation of variation is \(\displaystyle W = \frac{k}{F}\). Substituting gives \(\displaystyle W = \frac{k}{100}\) and solving for \(\displaystyle k\) gives \(\displaystyle 30800\). This gives the variation equation \(\displaystyle W = \frac{30800}{F}\). Using the given wave length gives the equation \(\displaystyle 201 = \frac{30800}{F}\). Solving for \(\displaystyle F\) gives \(\displaystyle F = \frac{30800}{201}=153.2\) meters.

Download \(\LaTeX\) 

\begin{question}The wavelength, W, of a wave varies inversely as its frequency, F. A wave with a frequency of 100 kHz has a length of 308 meters. What is the frequency of a wave with a length of 201 meters?  Round your answer to the nearest tenth. 
    \soln{9cm}{The equation of variation is $W = \frac{k}{F}$. Substituting gives $W = \frac{k}{100}$ and solving for $k$ gives $30800$. This gives the variation equation $W = \frac{30800}{F}$. Using the given wave length gives the equation $201 = \frac{30800}{F}$. Solving for $F$ gives $F = \frac{30800}{201}=153.2$ 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 100 kHz has a length of 308 meters. What is the frequency of a wave with a length of 201 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}{100} " src="/equation_images/%20%5Cdisplaystyle%20W%20%3D%20%5Cfrac%7Bk%7D%7B100%7D%20" alt="LaTeX:  \displaystyle W = \frac{k}{100} " data-equation-content=" \displaystyle W = \frac{k}{100} " />  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 30800 " src="/equation_images/%20%5Cdisplaystyle%2030800%20" alt="LaTeX:  \displaystyle 30800 " data-equation-content=" \displaystyle 30800 " /> . This gives the variation equation  <img class="equation_image" title=" \displaystyle W = \frac{30800}{F} " src="/equation_images/%20%5Cdisplaystyle%20W%20%3D%20%5Cfrac%7B30800%7D%7BF%7D%20" alt="LaTeX:  \displaystyle W = \frac{30800}{F} " data-equation-content=" \displaystyle W = \frac{30800}{F} " /> . Using the given wave length gives the equation  <img class="equation_image" title=" \displaystyle 201 = \frac{30800}{F} " src="/equation_images/%20%5Cdisplaystyle%20201%20%3D%20%5Cfrac%7B30800%7D%7BF%7D%20" alt="LaTeX:  \displaystyle 201 = \frac{30800}{F} " data-equation-content=" \displaystyle 201 = \frac{30800}{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{30800}{201}=153.2 " src="/equation_images/%20%5Cdisplaystyle%20F%20%3D%20%5Cfrac%7B30800%7D%7B201%7D%3D153.2%20" alt="LaTeX:  \displaystyle F = \frac{30800}{201}=153.2 " data-equation-content=" \displaystyle F = \frac{30800}{201}=153.2 " />  meters. </p> </p>