Sound enters the ear travels through the auditory canal and reaches the ear drum, 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 2.775 cm. The speed of sound is 343 m/s. What is the fundamental frequency of the canal?
(Interestingly, the fundamental frequency is in the frequency range when human hearing is most sensitive).
To calculate the fundamental frequency of the auditory canal, we need to use the speed of sound and the length of the canal.
The fundamental frequency is the lowest frequency at which a resonance occurs in the auditory canal. In other words, it is the frequency that corresponds to the length of the canal.
The formula for calculating the fundamental frequency of a tube open at one end is given by:
f1 = v / (4L)
Where:
- f1 is the fundamental frequency
- v is the speed of sound
- L is the length of the tube
Given:
v = 343 m/s (speed of sound)
L = 2.775 cm = 0.02775 m (length of the auditory canal)
Plugging the values into the formula, we get:
f1 = 343 / (4 * 0.02775)
Simplifying the equation, we have:
f1 = 343 / 0.111
f1 ≈ 3089 Hz
Therefore, the fundamental frequency of the auditory canal is approximately 3089 Hz.