Chabot College Physics

Open-Closed and Open-Open Resonance Pipe Experiments

Scott Hildreth

 

 

Background

 

We have discussed the physics of sound-wave 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 open-closed 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 open-closed pipes are shown below; the fundamental frequency is the lowest that creates a resonance in the pipe, and each successive overtone (“harmonic”) is an odd-integer multiple of that fundamental frequency.


For open-open 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

 

  1. Using the water column resonance tubes provided, measure the inside diameter of the tube with a caliper, along with the room temperature.  Note that the tubes are glass, and breakable!  Please take care when measuring the tubes.

    Record: Inside Pipe Diameter +/- uncertainty; Room air temperature +/- uncertainty

  2. Raise the water level in the tube by sliding the reservoir can upwards.  Practice moving the sliding can up and down smoothly, and notice how the water level in the tube follows.  Check for leaks in the hose at the bottom of the apparatus, too, and adjust water levels in the can so that you can have a large range in the water column of open-pipe lengths.

    Question: Why does the water level in the tube go up?  Consider what we learned from Bernoulli’s principle!

  3. With the water level near the top of the column, take a tuning fork of known frequency and set it oscillating by striking it with the rubber mallet.  Safety Note!  Do this away from the glass tube – do not strike the tuning fork near the tube risking hitting it with the hammer, or hitting the tuning fork into the side of the tube.  Also, do not strike the tuning fork on a hard object, like the table or your lab partner’s head!  You can damage the fork (let alone your partner.)

    Bring the ringing tuning fork quickly near to the top of the open resonance pipe; hold it so that the sound is directed down the tube.

    Question: In what direction should you hold the fork over the tube?  Should the tines be held parallel to the radial axle of the tube (so the fork is “pointing” down towards the water?)  Should the tines be held aligned vertically with the tube?  Or should the tines be held orthogonal to the tube?  Why?




 

 

 

 

 

 

 

 

 

 

  1. As the tuning fork vibrates, quickly lower the reservoir can, watch the water in the column fall, and listen for a sign of resonance.  Successive resonances will occur as the descending water level approaches, reaches, and passes the locations where standing waves can be set up in the pipe based upon the frequency of the fork.  Note the positions of the resonances, and determine the distances from the top of the resonance tube to those positions.

    Record: Frequency of tuning fork #1, positions of resonances and uncertainties.



  2. Repeat this process for a second tuning fork of a known frequency.

    Record: Frequency of tuning fork #2, positions of resonances and uncertainties.

  3. Calculate the average difference between successive resonances (L2-L1, L3-L2, etc.)  and from this, the average wavelength for each fork.  Look again at the pattern of standing waves for open-closed pipes to understand how the measured distances of the air columns relates to the wavelengths. 

    Using the known frequencies of the forks, calculate the speed of sound for each trial, and compute the average value of the speed of sound for the experiment, including the uncertainty. 

  4. Compare the value of the speed of sound from step 6 with the expected value of the speed of sound, based on the temperature dependence equation:

    vs =  (331.5 + 0.6 Tc) meters/sec

    Questions: What is the overall percentage error of the experiment?  How do you account for the error in your value for the speed of sound?  Are your identified experimental uncertainties sufficient to explain your results? 

  5. Now use a variable frequency tuning fork, set to one of the same notes as either of the forks used above.  Repeat the experiment, and determine the experimental frequency of the fork assuming the speed of sound is given by the value in step 7.   Check that frequency with the oscilloscope.

    Questions: What is the experimental uncertainty in your variable fork?  How do you estimate that uncertainty?  What was the oscilloscopes measured frequency?  And the stated frequency on the variable tuning fork user’s guide?  How did these values compare?

  6. The “end correction” for the open-closed pipe is typically regarded as 0.3 to 0.4 times the inside diameter of the pipe.  Calculate the experimental end correction for the pipe based on the experimental wavelengths for each trial, and the length of the fundamental wavelength (the first resonance.)  How do you do this?

    Compute the average end correction, and compare with the theoretical prediction. 

    Question: How does your computed average value of the end correction compare with the theoretical value?  What is your uncertainty in calculating the end correction you obtained?


  7. Additional Questions

    1. Suppose the temperature in the room were higher than what you measured.  How does this affect the results of your experiment?  Why?

    2. With the water in the resonance tube at the level for the first resonance of the first fork, does the second fork produce a resonance as well?  Why?  What frequency of tuning forks would produce a resonance.  Design an experiment using available forks to test out this theory, record your data, and explain your results.


Experiment A: Open-Closed Resonance Pipes

 

 

Inside Diameter of Resonance Tube: ___________                  Temperature:____________

 

 

Tuning Fork #1

 

Frequency = __________

Tuning Fork #2

 

Frequency = __________

Variable Tuning Fork

 

Frequency = __________

Ln

Resonance Position

Ln – L(n-1)

Resonance Position

Ln – L(n-1)

Resonance Position

Ln – L(n-1)

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

 

  1. Measure the lengths of the long and short plastic resonance tubes provided , and the inside diameter of the tubes with a caliper, and the room temperature. 

    Record: Pipe Lengths; Inside Diameter; Room air temperature; (all +/- uncertainty)

  2. Set up the speaker, microphone, frequency generator, and oscilloscope to match the example, with the speaker and microphone about ½ cm from the opening of the tube itself. Start with the short tube.  You’ll measure both applied voltage to the speaker on Channel 1, and received voltage at the microphone on Channel 2 using the oscilloscope. Set the time division selector to 1 millisecond per division to start.  Vary the voltage settings for each channel so that you can see the sinusoidal traces reasonably well.  Set the frequency generator to produce 1 KHz sine waves.

  3. Vary the frequency generator, starting from the lowest frequency to the highest, and record the approximate frequencies when the received signal (Channel 2) reaches a maximum.  Note the uncertainty in your dial reading will be based on the frequency generator dial markings.

 

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?

  1. Once you have located a maximum in the signal, determine the actual period of the signal by counting how many divisions lie between successive maxima on the oscilloscope trace.  Remember that if you change the time selector dial from 1 ms/div to another value, the elapsed time between maxima will be affected as well. 

    Record: Periods of signals at resonance, and uncertainties.

  2. From these values, calculate the measured frequencies of the source at the point of a maximum.

    Record: Frequencies of signals at resonance, and uncertainties.

  3. Repeat the experiment with the long tube, and then put them together to form an even longer tube.

  4. Using the speed of sound as 343 m/s at room temperature, calculate and record the theoretical resonant frequencies for the open-open tubes, and the wavelengths.  Compare these to your experimental values.  Discuss the accuracy of your results, and why you obtained the results.


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 open-open 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 variable-frequency tuning fork set to a different value?


 

Experiment B: Open-Open 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