Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.5 Exercises - Page 956: 44

Answer

$4.65 Hz/s$ and $576.6$ Hz

Work Step by Step

The perceived frequency is given by: $=[\dfrac{332+34}{332-40}] (460)=576.6$ Hz Take the derivative: $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f] =[\dfrac{(C-f_s)(C+V_0)'-(C+V_0)(C-V_s)}{(C-f_s)^2}]f$ Re-write as: $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f] =\dfrac{(C-f_s)(V_0)'+(C+V_0)(V_s)}{(C-f_s)^2}f$ After plugging in the given values, we get: $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f]=\dfrac{(332-40) \times (1.2)+(332+34) \times (1.4)}{(332-40)^2} \times 460=4.65 Hz/s$
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