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Question

The function given by f(x)=k2x/12f(x)=k 2^{x / 12} can be used to determine the frequency, in cycles per second, of a musical note that is xx half-steps above a note with frequency k.k^*.

Show that the C\mathrm{C} sharp that is 44 half-steps (a "major third") above concert A (see the previous exercise) has a frequency that is about 25%25 \% greater than that of concert A\mathrm{A}.

Solution

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Answered 1 year ago
Answered 1 year ago
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Based on the problem, we let:

k=440 cycles per secondx=4 half-steps\begin{aligned} k&=440 \text{ cycles per second}\\ x&=4 \text{ half-steps}\\ \end{aligned}

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