OpenClosed
and OpenOpen Resonance Pipe Experiments
Scott Hildreth
Background
We have discussed the physics of soundwave superposition in
“resonance pipes”, where particular frequencies of sound will create standing
waves and intensify the resulting sound we hear depending upon the length of
the pipes. For openclosed pipes, the resonance conditions are displacement nodes at the closed end, where the air
molecules in the pipes are not moving, and displacement antinodes at the open end where the air molecules do move forwards
and backwards at maximum amplitude longitudinally. The pressure variation in
the pipes for standing waves has nodes of no pressure variation at the open end
(atmospheric pressure), and antinodes of maximum pressure variation over and
under the atmospheric pressure at the closed end. The first three resonances for openclosed
pipes are shown below; the fundamental frequency is the lowest that creates a
resonance in the pipe, and each successive overtone (“harmonic”) is an
oddinteger multiple of that fundamental frequency.
For openopen pipes, the resonance conditions are similar, but since both ends are open, the standing wave pattern within the pipes is slightly different, and consequently the resonant frequencies are also different:
Experiment Part A:
Open – Closed Resonance
Experiment A:
OpenClosed Resonance Pipes
Inside Diameter of Resonance Tube: ___________ Temperature:____________

Tuning Fork #1 Frequency =
__________ 
Tuning Fork #2 Frequency =
__________ 
Variable Tuning Fork Frequency =
__________ 

Ln 
Resonance Position 
L_{n} – L_{(n1)} 
Resonance Position 
L_{n} – L_{(n1)} 
Resonance Position 
L_{n} – L_{(n1)} 
L1 






L2 






L3 






L4 






L5 






Average DL 

Average DL 

Average DL 


Average l 

Average l 

Average l 


End Correction 





Calculations:
Velocity of sound from Tuning Fork #1: _________ +/ _____ m/s
Velocity of sound from Tuning Fork #2: _________
+/ _____ m/s
Average Velocity of Sound: _________ +/ _____ m/s
Expected Velocity of Sound based on T: _________ m/s
Percent Error in Velocity of Sound _________ %
Experimental
frequency of variable tuning fork: _________ Hz +/ _____ Hz
Actual frequency as measured by oscilloscope: _________ Hz +/ _____ Hz
Percentage error in experimental vs. actual frequency: _________ %
Average Experimental End correction: _________ +/ _____ m
Predicted End
Correction: _________
to _________
0.3 x Inside Diameter to 0.4 x Inside Diameter
Experiment Part B:
Open – Open Tube Resonance
Record: Approximate frequencies for relative maxima, from 100 Hz to
2000 Hz, based on frequency generator dial.
Question: How many significant
digits in your observation are reasonable here?
Why?
Questions:
a) Did you notice apparent resonances at other lengths in addition to those
predicted by theory? What could cause
these resonances to occur?
b)
Explore and
record resonances in openopen pipes using the available tuning forks. For which fixed frequency forks do the short
and long tubes evidence the greatest resonance?
Why? Can you create a resonance
with the variablefrequency tuning fork set to a different value?
Experiment B: OpenOpen
Resonance Pipes
Inside Diameter of Resonance Tube: ___________ Temperature:____________

30 cm tube 

Resonance # 
Approximate Resonant frequency 
Oscilloscope Period 
Oscilloscope Resonant frequency 
Calculated Resonant Wavelength 
Theoretical Resonant Frequency 
Theoretical Resonant Wavelength 
L1 






L2 






L3 






L4 






L5 







60 cm tube 

Resonance # 
Approximate Resonant frequency 
Oscilloscope Period 
Oscilloscope Resonant frequency 
Calculated Resonant Wavelength 
Theoretical Resonant Frequency 
Theoretical Resonant Wavelength 
L1 






L2 






L3 






L4 






L5 







90 cm tube (put 60 and 30 together!) 

Resonance # 
Approximate Resonant frequency 
Oscilloscope Period 
Oscilloscope Resonant frequency 
Calculated Resonant Wavelength 
Theoretical Resonant Frequency 
Theoretical Resonant Wavelength 
L1 






L2 






L3 






L4 






L5 





