You have a summer job in a biomedical engineering laboratory studying the techno

Question

You have a summer job in a biomedical engineering laboratory studying the technology to enhance hearing. You have learned that the human ear canal is essentially an air filled tube approximately 2.7 cm long which is open on one end and closed on the other. You wonder if there is a connection between hearing sensitivity and standing waves so you calculate the lowest three frequencies of the standing waves that can exist in the ear canal. From your trusty Physics textbook, you find that the speed of sound in air is 343 m/s.

Explanation / Answer

The formula for an air column closed at one end is

fn = nv/4L (n = 1, 3, 5, ...) so...

f1 = (1)(343)/(4)(.027)

f1 = 3179 Hz

f3 = (3)(343)/(4)(.027)

f3 = 9528 Hz

f5 = (5)(343)/(4)(.027)

f5 = 15880 Hz

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