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)



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.



. =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>

Longitudinal Standing Waves in an Air Column

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