The human ear canal is much like an organ pipe that is closed at one end (at the

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 person's ear canal is of length L = 2.83 cm.

(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 next harmonic.
___ kHz
___ cm

(c) Suppose a person has an ear canal that is longer than 2.83 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)?
greater or lesser ???

Explanation / Answer

a) fundamental frequency of closed organ pipe= v/4l

= 340/4*0.0283

= 3003.53Hz

wavelength= 4l = 4*2.83=11.32cm

b) 2nd harmonic = 3* (v/4l) = 3003.53*3 = 9010.59Hz

wavelength =4l/3= 11.32/3 = 3.77cm

c) f = v/4l inversely propotional to l

hence if its longer that 2.83

fundamental frequency decreases

lesser

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