IP Standing Waves in the Human Ear The human ear canal is much like an organ pip

Question

IP Standing Waves in the Human Ear 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 (Figure 1) . A typical ear canal has a length of about 2.4 cm.

a) What are the fundamental frequency and wavelength of the ear canal? Express your answer using two significant figures.

B) Find the frequency and wavelength of the ear canal's thirdharmonic. (Recall that the third harmonic in this case is thestanding wave with the second-lowest frequency.)

canal outer ear Middle ear Inner ear Auditory Oval Semicircular ossicles window canals Nerves (to brain) Cochlea. 2.4 cm Vestibular complex Round window Tympanic Internal Eustachian membrane jugular vein tube

Explanation / Answer

for open pipe fundamentalfrequency f = v/2L

L = 2.4 cm

(a) f = v/2L

velcoity of sound in air v = 343 m/s

f = 343/(2*2.4)

f = 72 Hz

wvaelength lamda = 2L = 2*2.4

lamda = 4.8 cm

(b) f3 = 3*f1 = 3*72

f3 = 220 Hz

lamda = 2L/3 = 2*2.4/3 = 1.6 cm

(c) f3 = 220 Hz, lamda = 1.6 cm

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