## Related questions with answers

If a human ear canal can be thought of as resembling an organ pipe, closed at one end, that resonates at a fundamental frequency of 3 000 Hz, what is the length of the canal? Use a normal body temperature of $37 ^ { \circ } \mathrm { C }$ for your determination of the speed of sound in the canal.

Solutions

VerifiedIn this problem, the human ear canal is modeled as a pipe with one closed end. The resonant fundamental frequency is $f_{1} = 3000~\mathrm{Hz}$. The temperature of the human body is $T = 37~\mathrm{^{\circ}C}$. We calculate the length of the ear canal.

The speed of the sound:

$v = 331 \ \sqrt{1 + \dfrac{T}{273}} = 331 \ \sqrt{1 + \dfrac{37}{273}} = 353 \ m/s$

Th wavelength:

$\lambda = \dfrac{v}{f} = \dfrac{353}{3000} = 0.118 \ m$

The required length:

$L = \dfrac{\lambda}{4} = \dfrac{0.118}{4} = 0.0295 \ m$

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