Phy222 Experiment 1
Air Column Resonance and the Speed of Sound
Name: ___________________________
Date: _______________
Lab Partners: ______________________________________________
Introduction: Objects vibrate at one or more frequencies called natural, or resonance, frequencies. When a
source of vibration causes the object to vibrate at one of its resonance frequencies the energy transferred from
the source to the object is at a maximum for a given amplitude of the source. In other words, if the source
changed its frequency of vibration to a value either higher or lower than the resonance frequency of the object
while keeping its amplitude constant, the energy transferred to the object would decrease. Also, if the source
increased its amplitude while vibrating at the object’s resonance frequency the energy transferred would
increase.
In this lab the source of vibration will be a tuning fork and the object will be a column of air. The height of the
column of air is adjustable by changing the water level in a vertical plastic pipe. As the length of the column
changes so too does the column’s resonance frequencies. You will be trying to match the resonance frequencies
of the column with the vibrational frequency of the tuning fork.
When a column of air vibrates at its resonance frequency a standing wave of sound is set up inside the column.
Like a standing wave on a string there are displacement nodes and anti-nodes where the medium either doesn’t
move, or moves with largest amplitude. The difference between the wave on a string and the air column is that
the wave on a string is transverse while the wave in air (sound) is longitudinal. There is a displacement node at
the bottom of the column because the water there prevents air from moving. However, there is an anti-node at
the top of the column because it is there that the air can move the easiest. (The actual location of the top antinode is slightly above the top of the plastic column.)
The shortest distance between a node and anti-node on a standing wave is one-quarter wavelength. The distance
between a node and the second anti-node is three-quarters of the wavelength. Similarly, the distance to the next
few anti-nodes is 5/4 , 7/4 . 9/4 , etc.
For an air column of a fixed length, L, there are several resonance frequencies, fm, with wavelengths, n, such
that a node is at the bottom and an anti-node is at the top. The first wavelength is the one where only a quarter
of the wave fits within the column, L = ¼ 1, or 1 = 4L. The next wavelength is the one where ¾ of the wave
fits within the column so that L = ¾ 3, or 3 = 4L/3. In general, m = 4L/m where m = 1, 3, 5, 7, … Thus the
resonance frequencies are
fm = mv/4L,
(1)
where m = 1, 3, 5, …, and v is the speed of sound in air. If you obtained a tuning fork tuned to one of the
frequencies given by equation (1) and you struck the tuning fork while holding it over the air column, you
would create a standing sound wave in the air column of length L. You would hear a much louder tone than if
the tuning fork’s frequency did not match equation (1).
Instead of keeping the length of the column fixed and looking at different frequencies we will pick a frequency,
f, and vary the length L so that equation (1) is satisfied. If we start with the water level near the top of the plastic
pipe (so that our air column’s length is short) and strike a tuning fork of frequency f above the column then we
could slowly lower the water level and listen for an increase in the loudness of the tone. We could then carefully
adjust the water level so that we find precisely the correct length, L1, of the air column at which we hear the first
loud tone. This length, L1, would then be equal to ¼ , or in terms of equation (1) f = v/4L1. We would then
lower the water level again until a second loud tone is heard. This new length, L2, would be equal to ¾ , or in
1
terms of equation (1), f = 3v/4L2. Remember that we are keeping the frequency, and thus the wavelength,
constant while we change the length.
Recall that the anti-node at the top of the pipe really is located slightly above the pipe. Therefore, all of the
equations above are slightly in error. However, for all of the different resonance lengths, L1, L2, etc, the antinode at the top is the same distance, E (called the end correction), above the pipe. Thus we should really write
L1 + E = ¼ , and L2 + E = ¾ , etc. If we do not know the small distance E then we can not use the measured
values of length to calculate the wavelength, . But, if we look at the difference between L1 and L2 we can
calculate the wavelength.
L2 – L1 = (3/4  – E) – (1/4  – E) = ½ 
Similarly, if we continue to lower the water level and measure new lengths, L3, L4, etc, at which resonance
occurs we will always find that the difference between adjacent lengths is ½ .
To summarize; by measuring several lengths, and calculating their differences, we can calculate the wavelength
of the standing sound wave. Combining this with the known frequency we can calculate, or measure, the speed
of sound in air.
We can then compare our measure speed of sound with result of the equation:
vs = (331.5 + 0.6 T) m/s,
(2)
where T is the air temperature in degrees Celsius.
Part I: Tuning Fork with Known Frequency: Measure and record the air temperature in the room.
The air column apparatus (see figure 1) consists of a tall plastic tube and an aluminum can, known as the
reservoir, connected to the bottom of the plastic tube by a rubber hose. Measure the inside diameter of the
plastic tube with a vernier caliper and record this in the data section.
Raise the reservoir as high as it will go and then fill the plastic tube
with water to about an inch or so from the top. Once filled, you will
notice that as you lower the reservoir the water level in the plastic tube
lowers as well.
Wrap four rubber bands around the plastic tube spaced about 5 to 10
cm apart. You will use these to mark the locations where the water
level is when resonance is heard.
Obtain a tuning fork whose frequency is greater than 500 Hz. Record
the frequency of this fork in Table 1. Use a rubber mallet (see figure
2), or the palm of your hand to strike the tuning fork so you hear a nice
clear tone. You may hear a tinny tone in addition to the expected tone.
To remove this tinny tone you may touch the tuning fork about 1/3 of
the way up from the base.
Figure 1
2
With the water level at its maximum height hold the
vibrating tuning fork over the air column. (How do you
orient the fork for maximum effect?) Practice lowering
the reservoir and listening for increases in loudness of
the tone. When you are confident that you know what
you are listening for start over and carefully measure
(using the rubber bands as markers) the locations of the
water level when resonance is heard. Try to locate the
resonance lengths L1, L2, etc, as precisely as you can.
Measure the lengths L1, L2, L3, etc. and record them in
Table 1. Using these lengths calculate the differences in
length, L. Calculate the average L and then the
average .
Using the known frequency and the average
wavelength, calculate the speed of sound.
Figure 2
Repeat the above procedures for a second tuning fork
with a significantly different frequency.
Calculate the average of the calculated speeds of sound from fork 1 and fork 2 and compare this average to that
obtained from equation (2).
Part II: A Tuning Fork With Unknown Frequency: Obtain a tuning fork whose frequency marking
has been covered up. No peeking! Follow the procedures in part I to determine the locations of the resonances
to find the average wavelength. Use this average wavelength along with the average speed of sound from part I
to determine the frequency of the tuning fork. Compare this measured frequency with the accepted value.
3
Data
Temperature of Air = ________________ (°C)
Inside Diameter of Tube = _______________ (cm)
Tuning Fork 1
Tuning Fork 2
Frequency = _____________
Frequency = ____________
Resonance
Position
Resonance
Position
L
L
L1
L2
L3
L4
L5
Average L
Average 
Table 1
Speed of sound from Fork 1 = __________________
Speed of sound from Fork 2 = __________________
Average speed of sound = _____________________
Speed of sound from equation (2) = _____________
Percent Error = _____________________________
Show Calculation Below:
4
Unknown Tuning Fork
Resonance
Position
L
L1
L2
L3
L4
L5
Average L
Average 
Table 2
Experimental Value of Unknown Frequency = _____________
Accepted Value of Frequency = ________________
Percent Error = _____________
5
Questions
1.
Discuss some of the largest sources of error, and their effect on the results, and state whether each was
random or systematic.
2.
Suppose the water level is at length L1 for the first resonance of the first tuning fork.
a) Could another tuning fork with a frequency lower than that of the first tuning fork produce a
resonance? Explain your answer and if it is yes, then calculate the frequency of the new tuning fork.
b) Could another tuning fork with a higher frequency produce a resonance? Explain your answer and if
it is yes, then calculate the frequency of the new tuning fork.
3.
From your data explain how you would calculate the end correction, E, for the top anti-node. Calculate
E and compare to the theoretical value obtained from E = 0.4 * I.D., where I.D. is the inside diameter of the
tube.
6