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. typically this canal is approximately 2.4 cm long.

A) at what frequencies would it resonate in its first two harmonics?
express your answers using two significant figures separated by a comma.

B) what are the corresponding sound wavelengths in part A?
express your answers using two significant figures separated by a comma.

Explanation / Answer

Part A)

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

Assuming that your book uses 340 m/s for the standard speed of sound in air, for the first two harmonincs we get...

f1 = (1)(340)/(4)(.024)

f1 = 3542 Hz

f3 = (3)(340)/(4)(.024)

f3 = 10625 Hz

Part B)

Use the formula v = f to find the wavelength

1 = 340/3542 = .096 m which is 9.6 cm

3 = 340/10625 = .032 m   which is 3.2 cm

Note: These answers are correct for the speed of sound of 340 m/s. If your book uses a different standard value, the answers will be slightly off. Since you did not include that value in the question, I just had to make the assumption. Follow the procedure and the calculations with the value your book uses if needed, however, please rate my correct work with the value I used. If the answers are not exact it is due to not having all of the proper information in the question.

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