Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 12 - Sound - Problems - Page 355: 44

Answer

$f_1=3430Hz$ $f_3=10300Hz$ $f_5=17200Hz$

Work Step by Step

Model the ear canal as a closed pipe of length 0.025m. See figure 12-12. For a pipe that is closed at one end, the fundamental frequency is $f_1=\frac{v}{4 \mathcal{l}}$, and only the odd harmonic frequencies are present. $f_1=\frac{343 m/s}{4 (0.025m)}=3430Hz$ $f_3=3f_1=10300Hz$ $f_5=5f_1=17200Hz$ In the figure, we see that the ear is most sensitive to frequencies between 3-4 kHz, which is approximately the fundamental resonant frequency of the ear canal. There is again a region of enhanced sensitivity just above 10,000 Hz, corresponding to the first overtone of the ear canal.
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