Question

sound waves can be ranked by their intensity, \\(i\\), given in the formula below, where \\(r\\) is the distance from the source of a sound with a power output of \\(p\\).

\\p = 4\pi i r^2\\

solve the formula for the distance from the source, \\(r\\).

\\(r = \frac{1}{2}\sqrt{\frac{\pi i}{p}}\\)

\\(r = \frac{1}{4}\sqrt{\frac{p}{\pi i}}\\)

\\(r = \frac{1}{2}\sqrt{\frac{p}{\pi i}}\\)

\\(r = \frac{1}{4}\sqrt{\frac{\pi i}{p}}\\)

Explanation:

Isolate the term containing r

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Solve for r by taking the square root

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Answer:

• \(r = \frac{1}{2} \sqrt{\frac{\pi I}{P}}\)
• \(r = \frac{1}{4} \sqrt{\frac{P}{\pi I}}\)
• \(r = \frac{1}{2} \sqrt{\frac{P}{\pi I}}\) (Correct answer)
• \(r = \frac{1}{4} \sqrt{\frac{\pi I}{P}}\)