Lab: Resonance Tubes
- Work in groups of 3!
A resonance tube is like a wind instrument: You excite the air in the tube (we’ll be using a “function
generator” for this purpose—it vibrates a speaker on the end of the tube) and if the frequency of this
“driving” force happens to be roughly equal to the resonant frequency of the tube, you get a nice clear
standing wave in the tube. (This phenomenon is called resonance.)
The generator has a frequency dial that allows you to control the driving frequency. By changing this
frequency, you can find the resonance frequency of the tube. You’ll know that you’ve found the
resonance because the oscilloscope will show a clear wave with a nice big amplitude. If you overshoot
the resonant frequency, the amplitude of the wave starts decreasing again. You can pull on the plastic rod
to change the length of the tube.
The tube is open at the end where you stick the microphone. To get the microphone farther into the tube,
you can clip it to the brass rod.
One word of warning: Do not turn up the amplitude on the function generator too high, or you can
blow out the amplifier.
Activity 1: Determining resonant frequencies
PREDICTIONS
Looking at this tube, would you expect it to be behave more like
(i)
a pipe open at both ends, or
(ii)
closed at one end and open at the other?
[Note: although we didn’t discuss this in class, a pipe with two closed ends would behave
similarly to case (i)]. The goal of this part of the lab will be to determine which of the two
models above applies to this “instrument.” There is no “right” answer to this question; in real
life, an instrument may not conform perfectly to the behavior of an ideal / theoretical pipe.

Calculate the theoretical values of the n = 1 and n = 2 frequencies from the equation for f
that you derived in class. At room temperature the speed of sound will be something like
343 m/s. The length of the tube will be 44 cm. Show your calculations below.
Open at both ends
(or closed at both ends)
n=1
n=2
One end closed; one end open
EXPERIMENT
Adjust the piston so that the length of the pipe is 44 cm. The holes drilled in the pipe should be
closed, and the piston should be positioned just after the 2nd hole. Make sure that the TIME/DIV
dial on the oscilloscope is set to .5 ms.
Put the battery in the microphone, turn it on and stick the mic into the tube. It can’t be at the
edge of the tube; make sure it’s at least 15 cm in.

Find the first resonant frequency (“fundamental”) by starting at f = 50 Hz and dialing up
the adjust button. Record the frequency using appropriate units.
Draw what the wave on the oscilloscope looked like at the 1st resonant frequency:
Draw what the wave looked like when you were 50 Hz below this frequency:
…and 50 Hz above this frequency:

Find the 2nd resonant frequency (n=2).

If this resonance isn’t as strong as the fundamental (ie, much lower in amplitude), try to
find a resonance above it that’s stronger. Record this frequency as well.
ANALYSIS
1. Compare your answers above to the n = 1 and n = 2 frequencies from the chart you made on
page 1.
(a) Which of the two models seems to describe your pipe the best? Or could the pipe be
acting like one end is partially open? Explain your answer.
Discuss your conclusion with the instructor before continuing.
(b) To the extent that your tube behaves like a pipe closed at one end, which end do think
acts like the closed end?
(c) Test your answer above by setting the frequency to the n = 1 value that you found
experimentally. Then open the hole that is right next to the piston. What happens,
and why?
2. In this experiment, do you find that the resonant frequencies are close to where they’re
expected, or consistently a bit too high or too low? Can you think of anything about the
construction of the pipe that could cause the actual resonant frequencies to be shifted
from the theoretical values?
If you don’t get exactly the result you expected from the theoretical calculation, could it be that
the effective length of the tube is actually a bit shorter than it appears—maybe atmospheric
pressure penetrates a few centimeters into the tube, so that the end of the tube isn’t really a
pressure node?
 Using the n = 1 frequency that you measured on the previous page, compute what value
of L satisfies the equation f = (2 n -1 ) v / 4L.

Is the effective length for your tube different from the apparent value?
Activity 2: Nodes
Verify that the frequency dial is at the fundamental resonant frequency (the actual frequency, not
the one you predicted). Predict where the “node(s)” will be for this frequency. (Draw a diagram
of a pipe with one open end and one closed end and label where the nodes will be. You can use
either parallel lines or dots to represent the pressure.)

Where do you predict the node(s) will be at the n = 2 resonance?

Test your predictions. You can locate the nodes by sliding the mike around. Did you
find what you expected?

What do you expect to see happen to the amplitude of the wave if you’re at node?
In the space below, draw 2 pipes (one for n = 1, and one for n = 2) and show where you
found the nodes:

Activity 3: Effect of changing the length of the pipe
Predict what the resonant frequencies will be (n = 1, 2) when the length of the pipe is
significantly lengthened (by at least 15 centimeters.)

Test your prediction by moving the piston. What resonant frequencies do you find? Was
your prediction confirmed?

Calculate the fundamental frequency for this length. How does it compare to the actual
fundamental frequency that you measured?

Keeping the piston where it is, uncover one of the holes in the tube. Find one of the new
resonant frequencies (pick one where you can clearly hear the resonance in addition to
seeing it on the oscilloscope.) What happens if you then cover the hole with your finger?

Relate your observations to how wind instruments are used. What is happening when
you use your fingers to cover the holes in a recorder or other wind instrument?
Activity 4
This experiment uses the brass tube at the front of the room. Before testing it, make some
predictions. (You can do this at your usual station, to avoid crowding around the tube.) For this,
you’ll need the chart of frequencies that correspond to musical notes.
PREDICTIONS – show your calculations!
 What length of pipe (closed at one end, open at the other) would give the frequency that
corresponds to middle C? [C4]

What length of pipe would give the frequency that corresponds to high C? [C5]

What is the difference between the two lengths?

Using a similar calculation, what should be the difference between the two lengths for G3
and G4?
EXPERIMENT
 Test your prediction by looking at the piston on the brass tube. What is the actual
distance between middle C (labeled C) and high C (labeled C’?) Is it close to what you
predicted?

What is the actual distance between G3 (labeled G1) and G4 (labeled G)? Is it close to
what you predicted?

What do you think would happen if you slide out the piston while blowing into the
business end of the pipe? Test your prediction and describe the results.
CONCLUSION
 What is the general rule for how you have to change the length of a pipe if you want the
pitch to go up an octave?

Why do you think this instrument was designed to be adjustable? (Note that the mouth
end can be shortened or lengthened.)
Have the instructor check off your work.