EXPERIMENTS PHYSICS 132
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Experiment 13
Sound Resonance In Air Columns
In this experiment you set up resonant
standing wave vibrations in an air column. A
speaker emitting sound at a fixed frequency is
placed near the air column and the column length
is adjusted. Standing waves are set up in the air,
analogous to the standing waves in a stretched
string. One result of the lab is a determination of
the speed of sound in air.
Preliminaries.
This experiment investigates the resonance
conditions of a simple system consisting of a
column of air closed at one end and driven at the
other by an external speaker.
on average, there is no net molecular motion are
the displacement nodal planes or simply
displacement nodes, while the points where
molecules undergo maximum oscillation about
their equilibrium positions are called displacement
antinodes.
Note:
The displacement designation is to
specify that the wave being considered is
parameterized by molecular displacement
from equilibrium. It is also common in the
study of sound waves to consider pressure
waves, which are related to the density of
gas molecules. The nodes of the pressure
wave correspond to the antinodes of the
microphone
node
antinode
waves
speaker
plug
here
ULI
(magnet)
adjusting
computer
sleeve (magnet) Function
generator
Figure 1. Schematic for Standing Sound Waves
Experiment
Any vibrating object that can compress and
rarifyagascanproducetravelingsoundwavesin
that gas. These waves are longitudinal waves,
where the transporting medium oscillates in the
same direction as the wave velocity (i.e.
molecular motion is parallel to the direction of
waveenergyflow).Inthisexperiment,aspeaker
sendstravelingwavesfromtheopenenddowna
columnofgas(air).SeeFigure1.Ifthelengthof
the column is adjusted properly by moving the
adjustingsleeve,aloudsoundcharacteristicofa
standingwaveisheard.
The standing wave pattern is fixed in space, as
shown in Figure 2. The planes in the tube where,
displacement wave, and vice versa.
Figure 2. Example of a Standing Wave Pattern
Since gas molecules are not free to
longitudinally oscillate at the surface of the plug,
any standing wave produced in the tube must have
a node at the plug surface, as shown in Figure 3.
Although the antinodes are found one quarter of a
wavelength from the nodes, they are not simply
related to the physical properties of the tube.
There is an antinode close to the physical openend of the tube. The distance between the
antinode and the physical open tube end is the end
correction, labeled in Figure 3. is positive if
the antinode is outside the tube, as shown.
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PHYSICS EXPERIMENTS 132
sinusoidal waveform. As the plug is moved,
L1
D
nodes
Figure 3. The Standing Wave in the Tube
Adjustmentofthepositionofthepluginorder
to produce a loud sound characteristic of a
standing wave determines the node positions,
allowing thewavelength ofthesoundwaveto
bedetermined.Thefrequencyfofthewavefrom
thespeaker(source)canthenbeusedtocalculate
thespeedofsoundvinthegasaccordingto
v = fl
(eq. 1)
Thereisalsoatheoreticalexpressionforthe
speedofsoundinair,basedonthekinetictheory
ofgases.Thisrelationship(foraironly)is
changing the effective length of the tube, the
amplitude of the microphone signal varies.
Resonance occurs when the output amplitude
passesthroughalocalmaximum.
Procedure
Measureandrecordthetubediameter D
androomtemperatureTC.
Connect the speaker to the LO/GND
terminalsofthefunctiongenerator. Turn
on the function generator. Adjust the
waveformselectorsothatasinewaveis
generated. The function generator starts
withadefaultfrequencyof1000Hz.This
isagoodfrequencyforthesizeofthetube
beingused,althoughthefrequencymaybe
adjusted to any value. Record the
frequencyf.
v = ( 331 + 0.606TC ) m / s
(eq. 2)
where TC isthetemperature oftheairmedium,
expressedinCelsiusdegrees.
The end correction may be measured as shown
in Figure 3.
= /4 L1
(eq. 3)
where L1 is the distance from the first to node the
physical open end of the tube. The end correction
is approximately given by a theoretical analysis
beyond the scope of this course as
= 0.305 D
(eq. 4)
where D is the tube diameter.
Inthisexperiment,thepresenceofastanding
waveisdetectedbyamicrophoneplacedinthe
tube. The output from the microphone is
displayed on a computer. This output is a
The microphone should be attached to the
computer through an interface box. Turn
on the computer and double click on the
Sound icon. It starts up and a set of axes
appears. Everything is working as it
should if the Collect arrow in the upper
right of the screen is green. Place the
microphone anywhere in the open end of
the tube. Its precise placement is not
PHYSICS EXPERIMENTS 132
critical. Hold the speaker slightly away
from and off to the side of the tube end.
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Click on the (green) collect button. The
computer displays the microphone output,
continually refreshing the screen. Start
with the plug at the open end of the
column. Move the plug into the tube until
the amplitude of the microphone signal
gets larger. Eventually, as the plug is
moved farther from the open end, the
amplitude of the microphone signal drops.
Move the plug back. Find the position of
the plug at the exact location of the node
where the amplitude of the signal is a
distinct, clear maximum. Measure the
distance L1 of the face of the plug from
the open end of the tube.
Note:
The computer is trying to collect and
display a lot of data from the microphone.
It takes a while to do this. The data
refresh rate, the rate at which the computer
updates the microphone output, is low.
Rapid changes in the microphone output
can be missed. Therefore, the plug must
be moved very slowly so that the computer
can keep up. Make sure the plug is moved
slowly enough so that that the variation of
amplitude observed on the computer
display is smooth.
Continue moving the plug down the tube.
Determine all the nodal positions by
determining where the amplitude of the
signal is a distinct, clear maximum.
Record the distances L of the nodes from
the open end of the tube.
Calculate the internodal distance, , from
each node to the node immediately before
it by subtracting nodal positions. The
internodal distances should all be the same
(or, at least, close. Why?). Determine the
best value of internodal distance by
computing the average.
Calculate the wavelength of the wave
from the average internodal distance using
Figure 2.
Calculate the experimental wave speed v
of the sound wave from eq. 1.
Calculate the theoretical wave speed from
eq. 2.
The experimental calculation of wave
speed should agree with the theoretical
determination of the wave speed.
Determine the percent difference of the
experimental value from the theoretical
value.
Calculate the end correction from eq. 3.
Calculate the theoretical end correction
from Eq. 4.
The experimental calculation of end
correction should agree with the
theoretical determination. Determine the
percent difference of the experimental
value from the theoretical value.
Questions (Answer clearly and completely).
1. How is the distance between adjacent nodes
relatedtothewavelength?
2 Canasoundwavereflectbackfromanopen
(unplugged)tubeend?
3. Astheplugismovedfromonestandingwave
positiontoanother,howdoesthewavefrequency
change?Howdoesthewavewavelengthchange?
Howdoesthewavespeedchange?
4. What value do you determine experimentally
for the wave speed? What value do you determine
theoretically for the wave speed? What is the
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percent difference of the experimental value from
the theoretical value?
5. What value do you determine experimentally
for the end correction? What is the percent
difference of this value from the theoretical value?
6. If the experiment were to be redone at the same
frequency with the speaker held firmly against the
end of the tube, what would change: the locations
of the cap at resonance? the internodal distance?
the wave speed in the tube?
PHYSICS EXPERIMENTS 132