26.(I) What would you estimate for the length of a bass clarinet,assuming that it is modeled as a closed tube and that thelowest note that it can play is a whose frequency is 69 Hz?
27.(I) The A string on a violin has a fundamental frequency of440 Hz. The length of the vibrating portion is 32 cm, and ithas mass 0.35 g. Under what tension must the string be placed?
28.
(I) An organ pipe is 116 cm long. Determine the fundamental
and first three audible overtones if the pipe is (
a
) closed
at one end, and (
b
) open at both ends.
29.(I) (a) What resonant frequency would you expect fromblowing across the top of an empty soda bottle that is 24 cmdeep, if you assumed it was a closed tube? (b) How wouldthat change if it was one-third full of soda?
30.(I) If you were to build a pipe organ with open-tube pipesspanning the range of human hearing (20 Hz to 20 kHz),what would be the range of the lengths of pipes required?
31.(II) A tight guitar string has a frequency of 540 Hz as itsthird harmonic. What will be its fundamental frequency ifit is fingered at a length of only 70%of its original length?
32.
(II) Estimate the frequency
of the “sound of the ocean”
when you put your ear very
near a 15-cm-diameter sea-
shell (Fig. 12
–
35).
D
41.(II) How many overtones are present within the audiblerange for a 2.18-m-long organ pipe at 20°C (a) if it is open,and (b) if it is closed?
42.
(II) Determine the fundamental and first overtone frequen-
cies when you are in a 9.0-m-long hallway with all doors
closed. Model the hallway as a tube closed at both ends.
43.
(III) When a player’s finger presses a guitar string down
onto a fret, the length of the vibrating portion of the string
is shortened, thereby increasing the string’s fundamental
frequency (see Fig.12
–
36). The string’s tension and mass per
unit length remain unchanged. If the unfingered length of
the string is
determine the positions
x
of the
first six frets, if each fret raises the pitch of the fundamental
by one musical note compared to the neighboring fret. On
the equally tempered
chromatic scale,
the
ratio of frequencies
of neighboring notes
is 2
1
12
.
l
=
75.0
cm,
l
75.0 cm
x
FIGURE 12–36
Problem 43.
FIGURE 12–35
Problem 32.
33.
(II) An unfingered guitar string is 0.68 m long and is tuned
to play E above middle C (330 Hz). (
a
) How far from the
end of this string must a fret (and your finger) be placed to
play A above middle C (440 Hz)? (
b
) What is the wave-
length on the string of this 440-Hz wave? (
c
) What are the
frequency and wavelength of the sound wave produced in
air at 22°C by this fingered string?
34.
(II) (
a
) Determine the length of an open organ pipe that
emits middle C (262 Hz) when the temperature is 18°C.
(
b
) What are the wavelength and frequency of the funda-
mental standing wave in the tube? (
c
) What are
and
f
in
the traveling sound wave produced in the outside air?

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