Question

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.)

Answer 1

3850 Hz

Step-by-step 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

`f_1 = (v)/(4L)`

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

`f=(348 m/s)/(4(0.0226 m))=3,850 Hz`