The human outer ear contains a more or less cylindrical cavity called the audito

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 2.5 cm long. The speed of sound in air is 344 m/s.

Part 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.

Part B

What are the corresponding sound wavelengths in Part A?

Express your answers in centimeters to two significant figures separated by a comma.

Explanation / Answer

( A) For a closed resonance tube, the formula to apply is f = nv/4L    where n = 1, 3, 5, ...

f1 = (1)(344)/(4)(.025)

f1 = 3440 Hz

f1=3.4KHz   two sig fig

f3 = (3)(344)/(4)(.025)

f3 = 10320Hz

f3=1.0x101KHz

(B) v = f

1 = 344/3440= 0.1m

1=1.0 x101cm

3 = 344/10320= .033 m   

3=3.3 cm

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