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      <text>5.4.4 (Example of trig in music theory)</text>
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      <text><![CDATA[<h3>Example</h3>

<p>Given that a note has a frequency of \(20\)Hz, write down the equation of the corresponding graph that models this note.</p>

<h3>Solution</h3>

<p>We have seen that a single note is modelled by a sine wave and therefor the equation of the graph has the from \(y = \sin bx\). Recall that the value of \(b\) affects the period of the sine wave by the relationship \(\frac{360^\circ}{b}\) and that we know that the period is the reciprocal of the frequency. Hence
\[
\mbox{period} = \frac{1}{\mbox{frequency}} = \frac{1}{20} = \frac{360^\circ}{b}.
\]
Therefore rearranging gives \(b = 7200^\circ\). Hence the equation of the sine wave is 
\[
y = \sin(7200^\circ x)
\]</p>]]></text>
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