91Ó°ÊÓ

For an open organ pipe, the fundamental frequency can be obtained by using the formula \({f_n} = \frac{v}{{4L}}\left( {2n - 1} \right)\) where v is the speed of sound, n is the number of harmonics, and L is the length of the human ear canal.

Given data:

The length of the human ear canal is \(L = 2.5\;{\rm{cm}}\).

The audible frequency range of sound lies between \(20\;{\rm{Hz}}\) to \(20,000\;{\rm{Hz}}\).

For the first harmonics, the fundamental frequency can be calculated as:

Hence, the fundamental frequency for the first harmonic lies in the audible range.

For the second harmonics, the fundamental frequency can be calculated as:

Hence, the fundamental frequency for the second harmonic lies in the audible range.

For the third harmonics, the fundamental frequency can be calculated as:

Hence, the fundamental frequency for the third harmonic lies in the audible range.

For the fourth harmonics, the fundamental frequency can be calculated as:

Hence, the fundamental frequency for the fourth harmonic does not lie in the audible range.

Now, from figure 12-6, the most sensitive frequency lies between \(3000 - 4000\;{\rm{Hz}}\), corresponding to the fundamental frequency of the ear canal. Another flat region is at around \(1000\;{\rm{Hz }}\) , and this corresponds to the first overtone.