Resonance Tube Solutions
1
The Open Pipe
For a pipe of length
L
= 0
.
92
m, what are the resonant frequencies of the pipe
if it is open at both ends?
The pipe supports one half wavelength of the fundamental mode,
L
=
1
2
λ
1
This means that the wavelength of the fundamental mode is twice the length of the
pipe,
λ
1
= 2
L
If the air temperature and pressure remain constant then the speed of sound
v
is
constant,
v
=
λ
1
f
1
v
= 2
L f
1
Solving for the frequency
f
1
of the fundamental mode,
f
1
=
v
2
L
The speed of sound in air at standard temperature and pressure is
v
= 343 m/s.
f
1
=
343 m/s
2
·
0
.
92 m
= 186
.
4 s

1
So the fundamental frequency is
f
1
= 186 Hz
In general the frequencies of all other modes
m
are an integer multiple of this funda
mental frequency,
f
m
=
m f
1
for
m
= 1
,
2
,
3
, ...
.
1
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2
The Stopped Pipe
For a pipe of length
L
= 0
.
92
m, what are the resonant frequencies of the pipe
if it is open at one end and closed at the other?
One end of the pipe is open while the other end is stopped.
The
open
end must be
a pressure
node
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 Fall '09
 Physics, Harmonic Series, Wavelength, Standing wave, fundamental mode

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