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Sound enters the ear, travels through the auditory canal, and reaches the eardrum. The auditory canal is approximately a tube open at only one end. The other end is closed by the eardrum. A typical length for the auditory canal in an adult is about 2.26 cm. The speed of sound is 348 m/s. What is the fundamental frequency of the canal? (Interestingly, the fundamental frequency is in the frequency range where human hearing is most sensitive.)

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skyluke89

Answer:

3850 Hz

Explanation:

The auditory canal is a tube open at only one end, so we can consider it as a closed tube.

The fundamental frequency in a closed tube is given by

[tex]f_1 = \frac{v}{4L}[/tex]

where

v is the speed of sound

L is the length of the tube

Here we have

v = 348 m/s

L = 2.26 cm = 0.0226 m

So the fundamental frequency is

[tex]f=\frac{348 m/s}{4(0.0226 m)}=3,850 Hz[/tex]

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