Chapter 12 Solution
QTD6.
The air column of a clarinet is essentially a closed cylinder (odd harmonics of v/4L), that
of a flute an open cylinder (all harmonics of v/2L), so the acoustical resonances are much
different. Also, the qualities of an airreed are much different than a clarinet reed
emphasizing different harmonics.
EX1.
(a) The lowest resonance frequency of a closed pipe is
Hz
m
s
m
L
v
f
128
67
.
0
4
/
434
4
=
⋅
=
⋅
=
(b) The frequency of D
3
is 146.83Hz (P183).
(
29
%
15
15
.
0
128
128
8
.
146
=
=

=
∆
Hz
Hz
f
f
Hence, the frequency of D
3
is 15% greater.
(c) Flare of bell shortens the effective pipe length.
EX5
(a) The lowest resonance frequency of an open pipe is
Hz
m
s
m
L
v
f
83
.
285
60
.
0
2
/
434
2
=
⋅
=
⋅
=
(b) The frequency of F
4
is 349.23Hz (P183).
(
29
%
14
14
.
0
408
408
23
.
349
=
=

=
∆
Hz
Hz
f
f
Hence, the frequency of F
4
is 14% lower.
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View Full DocumentChapter 13 Solution
RQ1.
The frequencies of a bar are proportional to 1/L
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 Fall '09
 Standing wave, Resonator, Acoustic resonance, lowest resonance frequency

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