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Pasco Scientific WA-9612, Инструкция по эксплуатации и руководство по экспериментам, Страница: 24 / 28

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20

Resonance Tube

012-03541F

Experiment 2: Standing Waves in a Tube

Notes on Procedure

➀➁

 If you have already done experiment 1, use the

known open-tube resonant frequencies from that

experiment.

➂

The node points near the open ends of the tube may

actually be located beyond the ends, outside of the

tube.

Notes on Analysis

➀➁

 The wave activity pattern will be similar to the

diagrams in the “theory” section of the manual, ex-

cept that the microphone detects pressure variation

rather than displacement variation. Because of this,

the standing wave pattern will be shifted 90° from

the pattern shown.

Displacement representation

Pressure representation

Displacement representation

Pressure representation

The Theory section of the manual shows the

displacement representation for the open and closed

tubes; but the microphone will see the pressure

representation.

➂

The velocity of the sound wave inside the tube is

theoretically higher than outside the tube; but

within the limits of this experiment they will be the

same.

➃

The pressure wave reflects without inversion at the

face of the piston. It reflects with an inversion at

the open end of the tube.

Содержание WA-9612

Страница 1: ... 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 WA 9612 RESONANCE TUBE 13 13 SPEAKER INPUT 1 W MAX 100 5 Hz ON OFF ON OFF Instruction Manual and Experiment Guide for the PASCO scientific Model WA 9612 Includes Teacher s Notes and Typical Experiment Results ...

Страница 2: ...Note On several pages the impedance of the small speaker is listed as 32 ohms This is incorrect The impedance of the small speaker is 8 ohms at 1500 hertz Hz ...

Страница 3: ...er Interface 3 with the Power Amplifier 3 with the Data Monitor Program 3 Waves in a Tube Theory 4 Experiments Experiment 1 Resonant Frequencies of a Tube 7 Experiment 2 Standing Waves in a Tube 9 Experiment 3 Tube Length and Resonant Modes 13 Experiment 4 The Speed of Sound in a Tube 15 Suggested Demonstration 17 Suggested Research Topics 18 Teacher s Guide 19 Technical Support Inside Back Cover ...

Страница 4: ...revent damage and shipped postage or freight prepaid Damage caused by improper packing of the equipment for return shipment will not be covered by the warranty Shipping costs for returning the equipment after repair will be paid by PASCO scientific Copyright Warranty and Equipment Return Please Feel free to duplicate this manual subject to the copyright restric tions below Equipment Return Should ...

Страница 5: ...a rod and moved through the tube to examine wave characteristics inside the tube NOTE To use the Resonance Tube you will need an oscilloscope to examine the signal detected by the microphone and a signal genera tor capable of driving the 5 Ω 0 1 W speaker Equipment and Setup 1 2 3 4 5 6 7 8 9 10 11 12 13 14 WA 9612 RESONANCE TUBE SPEAKER INPUT 1 W MAX Speaker Tube mounting stands Moveable piston T...

Страница 6: ...so you may need to reduce the amplitude as you raise the frequency Turn on the oscilloscope and switch on the battery powered amplifier Set the sweep speed to approxi mately match the frequency of the signal generator and set the gain until you can clearly see the signal from the microphone If you can t see the micro phone signal even at maximum gain adjust the fre quency of the signal generator u...

Страница 7: ...er end of the tube is open If a resonance mode is excited in the tube a pressure antinode a displacement node will always exist at a closed end of the tube An open end of the tube corresponds more or less to a pressure node a displacement antinode However the pressure node will in general not be located exactly at the end of the tube You can investigate the behavior of the sound waves near the ope...

Страница 8: ... with a maxi mum amplitude Analogously a standing sound wave has displacement nodes points where the air does not vibrate and displacement antinodes points where the amplitude of the air vibration is a maximum Pressure nodes and antinodes also exist within the waveform In fact pressure nodes occur at displace ment antinodes and pressure antinodes occur at displacement nodes This can be understood ...

Страница 9: ...ement node occurs naturally at the closed end of the tube As for the open tube each successive value of n describes a state in which one more half wavelength fits between the ends of the tube NOTE The first four resonance states for open and closed tubes are diagramed below The first resonance state n 1 is called the fundamental Successive resonance states are called overtones The representation i...

Страница 10: ... the length of the tube and d is the diameter NOTE When using the microphone to investigate the waveform within the tube be aware that the microphone is a pressure trans ducer A maximum signal therefore indicates a pressure antinode a displacement node and a minimum signal indicates a pressure node displacement antinode NOTE The following four experiments require the WA 9612 Resonance Tube and a f...

Страница 11: ...d to reduce the amplitude as you increase the frequency Increase the frequency slowly and listen carefully In general the sound will become louder as you increase the frequency because the function generator and speaker are more efficient at higher frequencies However listen for a relative maximum in the sound level a frequency where there is a slight decrease in the sound level as you increase th...

Страница 12: ...ur resonant frequencies n by the lowest resonant frequency n0 that you were able to find Your results should give you a series of whole numbers Record this series for each tube configuration If you do not get a series of whole numbers you may not have found the lowest resonant frequency for the tube If this is the case try to use your results to determine what the lowest resonant frequency would h...

Страница 13: ...mV div Figure 2 1 Equipment Setup T T L H I Ω G N D L O Ω M I N R A N G E A D J U S T M A X OUTPUT FREQUENCY AMPLITUDE PI 9587B DIGIT AL FUNCTION GENERA TOR AMPLIFIER H E R T Z WAVEFORM I N P U T G N D E X T E R N A L BK PRECISION 200 Mhz OSCILLISCOPE MODEL 2120 INTENSITY FOCUS TRACE NOTATION TRIG LEVEL COUPLE SOURCE SLOPE λ Y TIME DIV X POS VAR VAR VAR SWEEP CAL CAL m V V CH 1 VOLTZ DIV CH 2 VOLT...

Страница 14: ...y occurs at those frequencies Mount the microphone on the end of the probe arm and insert it into the tube through the hole in the speaker microphone stand As you move the microphone down the length of the tube note the positions where the oscilloscope signal is a maximum and where it is a minimum Record these positions in table 2 1 You will not be able to move the probe completely down the tube b...

Страница 15: ...termine the wavelength for the waves in at least two of your trials Given the frequency of the sound wave you used in each configuration calculate the speed of sound in your tube How does this agree with the accepted value of 331 5 m sec 607 T where T is the temperature in Celsius degrees Describe the nature of the wave behavior at the end of an open tube based on your measure ments Also describe ...

Страница 16: ...Resonance Tube 012 03541F 12 Notes ...

Страница 17: ...sary Introduction For any given tube length there are a variety of resonant frequencies frequencies at which standing waves will be formed in the tube Likewise for a given frequency there are a variety of tube lengths at which a standing wave will be formed In this experiment you will examine the series of tube lengths which will resonate with a set frequency Procedure Set up the Resonance Tube os...

Страница 18: ...eaker How do the successive piston posi tions that produced a standing wave relate to this sketch Is the apparent spacings of nodes and antinodes consistent with the wavelength of your sound waves as calculated from λ V ν where V speed of sound Table 3 1 Closed Tube Resonances Frequency Piston Positions Frequency Piston Positions Frequency Piston Positions Frequency Piston Positions ...

Страница 19: ... MODEL 2120 INTENSITY FOCUS TRACE NOTATION TRIG LEVEL COUPLE SOURCE SLOPE λ Y TIME DIV X POS VAR VAR VAR SWEEP CAL CAL m V V CH 1 VOLTZ DIV CH 2 VOLTZ DIV CAL m V V VERTICAL MODE PULL XS PULL XS CH2 CH1 AC DC AC DC AC CH1 CH2 ALT EXT POS POS NORM EXT CH1 CH2 NORM EXT CH1 CH2 MANUAL AUTO T X Y T X Y LINE CAL EXT CH4 POWER 200VMAX 400VMAX 400VMAX T T L H I Ω G N D L O Ω M I N R A N G E A D J U S T M...

Страница 20: ... move the microphone around to the open end of the tube Determine how long it takes the sound wave to travel from the speaker to the microphone Analysis Use the data that you have recorded to calculate the speed of sound in the closed tube Assuming that the speed of sound in the open tube is equal to the speed of sound in the closed tube a good assumption how long does the tube appear to be for th...

Страница 21: ... of the tube as shown in the diagram Adjust the amplitude and frequency until you obtain a standing wave in the tube Accompanied by a marked increase of amplitude of the sound At this point displacement antinodal areas will show rapid movement of the cork dust while nodal areas will show no movement You can now adjust the frequency to other standing wave frequencies or you can put the plunger in o...

Страница 22: ...eed outside the tube compare with the speed inside the tube Seal the tube and fill it with a gas such as C02 N2 or O2 Determine the speed of sound in various gases With one end of the tube open calculate the speed of sound in the tube with air flowing through the tube This can be done with the flow of air going toward or away from the speaker The speed of sound as it moves with and against the str...

Страница 23: ...osed tube Closed tube v v vo v v vo 185 1 00 94 1 00 369 1 99 282 3 00 555 3 00 473 5 03 740 4 00 663 7 05 918 4 96 852 9 06 1102 5 96 1042 11 09 1271 6 87 1230 13 09 1369 7 40 1434 15 26 1676 9 06 1626 17 30 1870 10 11 1812 19 28 2056 11 11 2006 21 34 There will be some data points which seem to be resonant but aren t at the theoretical resonant frequencies Italicized points on the open tube data...

Страница 24: ... rather than displacement variation Because of this the standing wave pattern will be shifted 90 from the pattern shown Displacement representation Pressure representation Displacement representation Pressure representation The Theory section of the manual shows the displacement representation for the open and closed tubes but the microphone will see the pressure representation The velocity of the...

Страница 25: ...f this method Plot the length of the tube as a function of n where n is the number of antinodes in the standing wave pattern The graph shown is for the tube with both ends closed The slope of this line will be equal to λ 2 and from this you can find the velocity 5 5 5 5 5 5 5 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 Length cm n f x 1 142500E 1 x 2 857143E 2 R 2 9 999954E 1 1 5 kHz v 342 75 m s Co...

Страница 26: ...ays steady and easy to read Analysis v 340 m s For better precision use the method described in the teacher s guide to experiment 3 We were able to measure this by building a corner cube reflector out of some scrap lexan sheets and tape The signal was very weak though and practi cally useless beyond 1m The reflected sound pulse will be inverted when the end of the tube is open and non inverted whe...

Страница 27: ...d be helpful to prepare the following information If your problem is computer software related note Title and Revision Date of software Type of Computer Make Model Speed Type of external Cables Peripherals If your problem is with the PASCO apparatus note Title and Model number usually listed on the label Approximate age of apparatus A detailed description of the problem sequence of events In case ...

Страница 28: ......

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