The human ear canal is much like an organ pipe that is closed at one end (at the
ID: 1399949 • Letter: T
Question
The human ear canal is much like an organ pipe that is closed at one end (at the tympanic membrane, or eardrum) and open at the other (see Figure 14-35). Suppose that a man's ear canal has a length L = 2.75 cm.
(a) What is the speed of sound in the ear canal? Assume a normal body temperature of 37°C.
_____ m/s
(b) What is the fundamental frequency of the ear canal?
_____ Hz
(c) What is the wavelength and frequency of its first overtone (next available harmonic)?
_____ cm
_____ Hz
(d) Find the length of an ear canal whose fundamental frequency is 600 Hz. (Elephants have ear canals of about 20 cm in length and are more sensitive to the lower frequencies.)
_____ cm
Explanation / Answer
a) we know speed of sound at T temperature,
v = vo + 0.6*T
= 331 + 37*0.6
= 353.2 m/s
b) here year acts as closed tube.
so, fundamental frequency, fo = v/(4*L)
= 353.2/(4*0.0275)
= 3211 Hz
c) for first overtone, wavelength lamda = 4*L/3
= 4*0.0275/3
= 0.0367 m
frequency, f = v/lamda
= 353.2/0.0367
= 9633 Hz
d) fo = v/(4*L)
==> L = v/(4*fo)
= 353.2/(4*600)
= 0.1472 m
= 14.72 cm
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