Question

Problem 14.71 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.

Part A What are the fundamental frequency and wavelength of the ear canal? Express your answer using two significant figures. f1 =_______ Hz

Part B Express your answer using two significant figures. λ1 = _____cm

Part C Find the frequency and wavelength of the ear canal's third harmonic. (Recall that the third harmonic in this case is the standing wave with the second-lowest frequency.) Express your answer using two significant figures. f3 =_______ Hz

Part D Express your answer using two significant figures. λ3 =_____ cm

Part E Suppose a person has an ear canal that is shorter than 2.4 cm. Is the fundamental frequency of that person's ear canal greater than, less than, or the same as the value found in part A? Explain.

Answer 1

This numercal can be realted with the problem of Organ pipe which is One end closed.

Given: Length of ear canal L=2.4cm

In the first part of the question we are told to find the Fundamental frequency which corresponds to First harmonic(n=1);

Using the formula

​

v=velocity of sound in dry air = 343m/s

L=2.4*10^-2 m

= 35.7 *

= 3.6 * Hz {Since we are told to round of the answer in two significant figure}

= 3.6 Khz

Corresponding Wavelength

Substituting the values we get

= 9.6Cm

Answer for the first part

i.e Fundamental frequency corresponding to First Harmonic

f₁ = 3.6 Khz

NOTE IN The situation related to ORGAN PIPES WITH ONE END CLOSED SECOND HARMONIC IS NOT PRESENT => n can not be equal to 2

n=3, v= 343 m/s, L=2.4 * 10^-2 cm

Substituting the value we get

=11 Khz {we are told to express the answer in two significant digit}

and similiarly,

Substituting the values we get,

Solution for the part two of the question is

From the formulla you must have observed that Fundamental frequency is INVERSLY Propotional to the Length of ear canal,

Hence if the length of the ear canal is shorter than 2.4cm than Fundamental frequency will be GREATER than

3.6 Khz( answer obtained in first part)