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 trus ty Physics textbook, you find that the speed of sound in air is 343 m/s.

A) Physic Approach - what equation and physics concepts are being used in this question.

B) Equation - show your work for the equation you will be using in the problem, equation manpulation (Do not plug in numbers)

C) Mathematical Approach - plug in the numbers

D) Check your answer - unit check and short explantion

Explanation / Answer

In a pipe closed at one end and opened at other end

at the closed end node is formed

at the open end antinode is formed

In fundamental mode of vibration

length of pipe = L = wavelength/4

wavelength 1= 4L

frequency f1 = v/wavlength1 = v/4L

--------------------------------

In second harmonic vibration

length of pipe = L = 3*wavelength/4

wavelength 2 = 4L/3

frequency f2 = v/wavelength2 = 3v/4L = 3f1

++++++++++++++

In third harmonic vibration

length of pipe = L = 5*wavelength/4

wavelength 2 = 4L/5

frequency f2 = v/wavelength2 = 5v/4L = 5f1

f1 = 343/(4*0.027) = 3176 Hz

f2 = 3f1 = 9528 Hz

f3 = 5f1 = 15880 Hz

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