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: 67

Answer

lower; musical note $D$

Work Step by Step

Based on the given table, with a musical note of E, the pitch is $329.63$ $Hz.$ Using the given formula, $ h=\dfrac{a}{1-\dfrac{s}{770}} ,$ then \begin{array}{l}\require{cancel} 329.63=\dfrac{a}{1-\dfrac{50}{770}} \\\\ 329.63=\dfrac{a}{\dfrac{770}{770}-\dfrac{50}{770}} \\\\ 329.63=\dfrac{a}{\dfrac{720}{770}} \\\\ 329.63=a\div\dfrac{720}{770} \\\\ 329.63=a\cdot\dfrac{770}{720} \\\\ 329.63=\dfrac{770}{720}a \\\\ \dfrac{720}{770}(329.63)=\left(\dfrac{770}{720}a\right)\left(\dfrac{720}{770}\right) \\\\ \dfrac{720(329.63)}{770}=a \\\\ a=308.22545454545454545454545454545 .\end{array} With $a\approx308,$ then the actual pitch the observer hears is lower than the real pitch. The actual pitch heard is closer to the musical note $D.$
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