longitudinal standing waves in an air column
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Physics 213 Laboratory
Longitudinal Standing Waves in an Air Column
Purpose: We shall determine the velocity of sound in air by studying longitudinal
standing waves in an air column.
Theory: In the text it isshown that if two travelling
waves of identical
wavelength move in
opposite directions, (seefigure to the right) they add
to form a standing wave.
Each node to nodedistance in the standing
wave is half as long as the
wavelength of the travellingwave.
In the experiment, aresonance (standing wave)
is set up in an air column in
a vertical glass tube. !he top of the tube is open. " water surface of ad#ustable heightforms the bottom of the air column$ this causes the air column to be closed at the bottom
and open at the top. %tanding waves can only
exist in the air column when there is a node atthe closed end and an antinode at the open
end. &ossible standing waves are shown in thediagram to the left.
%ince each nodetonode distance is half the
wavelength of the travelling waves,standingwaves can only be set up if the length of the
air column is ' , or * ,or + , or ,etc.
of a wavelength. In the experiment a tuningfor- of -nown freuency is held above the air
column, and the water level is moved up or
down, thus changing the length of the air
column. Whenever the length becomes eualto one of these values, a standing wave is set up and causes the sound to become much
louder.
!he listener observes the water levels which produce standing waves. !hese
levels are exactly '/ wavelength apart so the wavelength can be determined. !hen from
0elocity 1 (wavelength)(freuency)
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the velocity of sound in air can be calculated.
!heoretically the velocity of sound in a gas is proportional to the suare root of
the absolute temperature, so it can be calculated from
0%ound at !(o
2) 1 0%ound at /*32 o
2 ! /*
where 0%ound at /*3
2 is **'. meterssecond (in air)
4ote: 5etailed analysis shows that the antinode at the open end of the tube is
actually located slightly outside the tube by a distance of (.*)(diameter of tube.)
Procedure: !he apparatus used includes a resonance tube and holder, +33 and '333 hert6
tuning for-s, rubber mallet, meter stic-, large aluminum bea-er, thermometer, and water.
'. &ut enough water in the resonance apparatus to enable the water level to bevaried over the length of the tube.
/. 7sing the +33 hert6 tuning for-, stri-e the for- with the mallet and hold the for- over the open end of the tube. 0ary the water level to locate the positions that
produce a resonance. !he sound gets much louder at the resonance position.
8ou can expect the first resonance position between '+ and /3 centimetersfrom the top of the tube. 9thers should be at about *, +, and times this
distance. ocate each resonance as accurately as possible and record these
positions.
*. ;epeat step / using the '333 hert6 tuning for-.
. ;ecord the room temperature and measure the diameter of the tube.
Calculations:
'. <or the +33 hert6 data, calculate the distance from each resonance to the
next. !hese distances should be similar and eual to half the wavelength.
"verage these distances and double the result to find the experimental
wavelength.
/. =alculate the velocity of sound in air by using
0elocity 1 (freuency)(wavelength)
*. ;epeat calculation steps ' and / for the '333 hert6 data.
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. =onvert the room temperature to absolute temperature and calculate the
velocity of sound in air at that temperature. =ompare this with the experimental
results from calculations / and *.
+. =alculate the position of the antinode near the open end of the tube (exactly
' of a wavelength from the highest resonance position.) Is it outside the tube by about .* times the tube diameter>