Question

The human outer ear contains a more or less cylindrical cavity called the auditory canal that behaves like a resonant tube to aid in the hearing process. One end terminates at the eardrum (tympanic membrane), while the other opens to the outside. (See (Figure 1).) Typically, this canal is approximately 2.3 cm long. The speed of sound in air is 344 m/s.

A) At what frequencies would it resonate in its first two harmonics? Express your answers in kilohertz to two significant figures separated by a comma.

Answer 1

frequency in closed tube

f = n v / ( 4 L)

where, n = 1 3,5,7.. .

so 1st harmonic

f1 = 1* 344 / ( 4* 2.3*10^-2)

f1 = 3.7 kHz

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2nd harmonic

f2 = 3 * f1 = 11 kHz

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