Chapters
15,16,17,18
Problem 1 (10+10 points)
A scientist is making a mockup model of a human ear using a small can with the top surface
open and the bottom closed. A human ear is especially sensitive to sound whose frequency
is 3,440 Hz. If this is the lowest frequency that the ear is especially sensitive to, (a) what the
height of the mockup model h should be? Assume that the speed of sound is 344 m/s.
(b) What is the next lowest frequency the ear especially sensitive to?
open
closed
Solution
:
(a) This is an example of standing waves in a stopped pipe. When
the incoming sound wave’s frequency coincides with or is very
close to the frequencies of standing waves the ear is especially
sensitive to the sound as resonance occurs (4 points). Therefore
the fundamental frequency f
1
=v/(4h) where v is the speed of
sound (3 points). From 3440 s
1
= (344 m/s)/(4h), h=1.00/40.0=
0.025 m (3 points).
(b) The nth harmonic frequency is described by:
f
n
=nv/(4h) where n=1,3,5,…(odd integer) (5 points).
A harmonics
with an even integer n does not exist. Therefore the next lowest
frequency is when n=3. f
3
=3v/(4h)=3(344 m/s)/(4 x 0.025 m) =
10,300 Hz (5 points).
h
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 Summer '08
 Staff
 Physics, 1m, 3 pints, 5.00 k

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