The human ear canal is much like an organ pipe that is closed at one end (at the
ID: 2018997 • Letter: T
Question
The human ear canal is much like an organ pipe that is closed at one end (at the tympanic membrane, or eardrum) and open at the other (see the figure below). Suppose that a man's eardrum is of length L = 2.69 cm. uploaded image (Note: The cochlea is the primary sound sensor of the ear. However, frequencies which resonate in the ear canal are amplified-- therefore humans are most sensitive to them over other audible frequencies.) (a) What is the fundamental frequency and wavelength of the ear canal? ?kHz ?cm (b) Find the frequency and wavelength of the ear canal's third harmonic. (Recall that the third harmonic in this case is the standing wave with the second-lowest frequency.) ?kHz ?cm (c) Suppose a person has an ear canal that is longer than 2.69 cm. Is the fundamental frequency of that person's ear canal greater than, less than, or the same as the value found in part (a)?Explanation / Answer
a) The fundamental frequency of the ear canal is
f1 = v / 4L
Where v = 343 m/s
L = 2.69 cm= 2.69 * 10^-2 m
==> f1 = 343 / (4 * 2.69 *10^-2)
= 3.1877kHz
Wave length ?1 = 4 L = 4 *2.69cm = 10.76 cm
b)
The third fundamental frequency of the ear canal is
f3 = 3v / 4L
Where v = 343 m/s
L = 2.69 cm= 2.69 * 10^-2 m
==> f3 = (3* 343) / (4 * 2.69 *10^-2)
= 9.563 kHz
Wave length 3 = 4 L/3 = 4 *2.69cm/3 = 3.5866 cm
(c) Shorter
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