Estimating Ear Canal Length & Frequency Sensitivity

[duoheer]

Homework Statement

I read this question online.
Estimate the length of your ear canal. Regard the canal as a narrow tube that is open at one end and closed at the other, at approximately what fundamental frequency would you expect you hearing to be most sensitive? Explain why you can hear especially soft sounds just around this frequency.
thx

Homework Equations

The Attempt at a Solution

 

[Shooting Star]

The human ear is most sensitive to the human speech bandwidth, which is from 500-4000 Hz, particularly at about 4,000 Hz.

The ear canal can be treated as open pipe resonating at that frequency, and the length estimated by f=v/(2L).

 

[ogb p]

I would approach this question by first considering the anatomy and physiology of the ear. The ear canal is a narrow tube that connects the outer ear to the middle ear and is approximately 2.5 cm in length in adults. This length may vary slightly from person to person, but it is a good estimate to start with.

To determine the fundamental frequency at which our hearing would be most sensitive, we need to understand the functioning of the inner ear, specifically the cochlea. The cochlea is a spiral-shaped structure that contains tiny hair cells responsible for converting sound waves into electrical signals that are then sent to the brain for interpretation. These hair cells are organized according to frequency, with the high-frequency sounds being detected near the entrance of the cochlea and the low-frequency sounds being detected near the apex.

Based on this information, we can estimate that the fundamental frequency at which our hearing would be most sensitive would be around 2000 Hz, which is in the middle to high range of human hearing. This is because the length of the ear canal is optimal for amplifying and directing sound waves towards the hair cells that are most sensitive to this frequency. Additionally, the hair cells in this region of the cochlea are densely packed and have a high sensitivity to vibrations, making them more likely to respond to soft sounds.

Furthermore, the ear canal also acts as a resonant chamber, amplifying certain frequencies and making them easier to detect. This is especially true for frequencies that are close to the resonant frequency of the ear canal, which is around 3000 Hz. So, soft sounds near this frequency would be amplified and easier to detect by the hair cells in the cochlea.

In conclusion, the length of the ear canal and the organization of the hair cells in the cochlea play significant roles in determining the fundamental frequency at which our hearing would be most sensitive. By understanding the anatomy and physiology of the ear, we can estimate this frequency to be around 2000 Hz and explain why we can hear soft sounds just around this frequency.