Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.6 - Rational Equations and Problem Solving - Exercise Set - Page 390: 68

Answer

$ 351.3 $ $Hz$; the musical note $F.$

Work Step by Step

Based on the given table, with a musical note of G, the pitch is $392.00$ $Hz.$ Using the given formula, $ h=\dfrac{a}{1-\dfrac{s}{770}} ,$ then \begin{array}{l}\require{cancel} 392=\dfrac{a}{1-\dfrac{80}{770}} \\\\ 392=\dfrac{a}{\dfrac{770}{770}-\dfrac{80}{770}} \\\\ 392=\dfrac{a}{\dfrac{690}{770}} \\\\ 392=a\div\dfrac{690}{770} \\\\ 392=a\cdot\dfrac{770}{690} \\\\ 392=\dfrac{770}{690}a \\\\ \dfrac{690}{770}(392)=\left(\dfrac{770}{690}a\right)\left(\dfrac{690}{770}\right) \\\\ \dfrac{690(392)}{770}=a \\\\ a=351.27272727272727272727272727273 .\end{array} Rounded to the nearest tenth, the pitch the observer hears is $ 351.3 $ $Hz.$ This pitch is closest to the musical note $F.$
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