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Sine Wave Generator

Resonance Tubes

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Содержание WA-9867

Страница 1: ...Instruction Manual No 012 08678A Sine Wave Generator WA 9867 Instructions Demonstrations Experiments Sample Data ...

Страница 2: ...ons 9 Operational Flow Chart 10 Applications 11 Experiment 1 Standing Waves In Strings 15 Experiment 2 Resonance Tubes 21 Experiment 1 Teachers Notes Standing Waves in Strings 27 Experiment 2 Teachers Notes Resonance Tubes 29 Safety 31 Technical Support 31 Copyright and Warranty Information 31 ...

Страница 3: ...d Playback enhance classroom demonstrations and permanent displays requiring automated signal variation The Sine Wave Generator outputs AC power at up to about 10 volts amplitude 20 V peak to peak and 1 amp The output frequency adjustable in increments of 0 1 Hz ranges from 1 Hz to 800 Hz Included Equipment Replacement Part Number Sine Wave Generator WA 9867 Power Supply 540 057 Suggested Accessor...

Страница 4: ...erator is connected to a short circuit the unit s short circuit protection will shut off the output Remove the short and cycle the input power to restore it Mounting and Storage You can use the built in clamp on the back of the unit to mount the Sine Wave Generator on a vertical rod as shown Rod mounting makes the display more visible for demonstrations and allows you to position the controls conv...

Страница 5: ...Hz To change the stored increment see the Increment Keys section below If you press and hold the Increment keys a different function will occur so only use quick presses to change the frequency This following sections describe how to change the stored frequency increment and program the Sine Wave Generator to play automatic sequences of notes If you would like to skip to some practical demonstrati...

Страница 6: ...key the stored increment will change to the value on the display which is the output frequency Try this 1 Use the Increment keys and the Frequency knobs to set the output to 120 Hz 2 Press and hold the Store key After 1 second the display will blink and you can release the key The stored increment is now 120 Hz 3 Press the Up Increment key a few times the frequency changes by 120 Hz with every pre...

Страница 7: ...y Advanced Mode Record and Playback In Advanced Mode you can set store and play back a sequence of up to 80 notes The Sine Wave Generator will record the frequency and amplitude of each note Advanced Mode is especially useful when demonstrating resonance in vibrating strings because it allows you to set the optimal amplitude and frequency for each harmonic This mode is a hidden sub layer so as to ...

Страница 8: ...ake a mistake There is no way to edit a note in the sequence after it has been stored When you enter Record Mode all previous notes are erased and you start over Once you have stored a note you can not change or erase it Playback of Stored Notes With the Sine Wave Generator in Playback Mode and playing the stored sequence you have several options Amplitude If you turn the Amplitude knob all the wa...

Страница 9: ...rn to normal mode The output frequency will be set to the stored increment The sequence remains in storage You can go back to Advanced Mode and play the sequence again even if you turned the unit off and unplug it in the interim Specifications Frequency 1 to 800 Hz Adjustable in 0 1 Hz increments Output DC coupled push pull Short circuit protected Amplitude 0 to 10 V peak approx Current 1 A into 8...

Страница 10: ...D NOTES 0 HOLD PLAY AND STORE EXIT HOLD PLAY AND STORE EXIT INITIAL PRESS FREEZES DISPLAY IF HELD MAX FREQUENCY IS SET FREQUENCY REVERTS TO POINT WHEN NORMAL MODE EXITED RETURN AFTER DELAY DISPLAY FLICKERS IN RECORD MODE HOLD STORE EXIT HOLD STORE EXIT INC DEC FREQ by 1 INC DEC FREQ by 0 1 FREQ 0 1 FREQ 1 0 SLOW INC DEC FREQ by 4 FREQ 1 0 FAST INC DEC FREQ by 1 INC DEC FREQ by 0 1 FREQ 0 1 FREQ 1 ...

Страница 11: ...emonstrate resonance With the first method the Sine Wave Generator steps through a series of resonance frequencies With the second method it scans slowly through a frequency range encompassing one resonance frequency Method 1 Step Through the Harmonics 1 Using the Frequency knobs set the output to the fundamental resonance frequency of the tube 120 Hz in this case Listen carefully while adjusting ...

Страница 12: ...y reaches 130 Hz press and hold the Play key again to make the frequency wrap around and repeat 5 Use the Frequency knobs to adjust the duration of each note to about 0 5 seconds The Sine Wave Generator will now repeatedly scan across the resonance at 120 Hz Remove the tube to show that the sound level from the speaker is constant then put the tube back in place to show how much louder it gets eac...

Страница 13: ...nd Playback Mode If you were to use the regular Auto Play mode there are two problems that would occur First the optimal driving signal amplitude for the lower harmonics would be insufficient to excite visible vibrations at the higher harmonics Second it would be difficult to perfectly tune a single increment value so that the driving frequencies for all 10 harmonics were exactly correct Both of t...

Страница 14: ...Sine Wave Generator Applications 14 ...

Страница 15: ...el in opposite directions through the same medium The necessary conditions for the production of standing waves can be met in the case of a stretched string by having waves set up by some vibrating body reflected at the end of the string and then interfering with the oncoming waves Equipment Part Number Sine Wave Generator WA 9867 String Vibrator WA 9857 Braided String inelastic low density SE 805...

Страница 16: ...etched string at an arbitrary frequency you will probably not see any particular mode many modes will be mixed together But if the driving frequency the tension and the length are adjusted correctly one vibrational mode will occur at a much greater amplitude than the other modes For any wave with wavelength λ and frequency f the speed v is eq 1 v λ f In this experiment standing waves are set up in...

Страница 17: ...rates in one segment Adjust the driving amplitude and frequency to obtain a large amplitude wave but also check the end of the vibrating blade the point where the string attaches should be a node It is more important to have a good node at the blade than it is to have the largest amplitude possible However it is desirable to have a large amplitude while keeping a good node 2 Record the frequency H...

Страница 18: ... may have to use small masses to get a good waveform Remember that it is more important to have a good node at the end of the blade than to have the biggest amplitude possible 2 Record the total hanging mass including the mass hanger Calculate the ratio of the new mass to the original mass Why is the ratio not 2 You will learn more about the relationship between wave velocity and string tension in...

Страница 19: ...s applied by the hanging a mass m and is equal to the weight mg of the hanging mass For this part of the experiment you will always adjust the frequency so that the wave vibrates in four segments thus the length of the string will always equal two wavelengths L 2λ In this case F mg and L 2λ these equations can be combined with equations 1 and 2 to show eq 3 where f driving frequency of the Sine Wa...

Страница 20: ...ne through this data 8 As you can determine from Equation 3 the slope of the f 2 vs m graph is From the slope of your graph calculate the density µ of the string What is the uncertainty 9 Determine the actual density of the string by measuring the mass of a known length If you do not have a balance readable to 0 01 g use several meters of string 10 Compare the density that you measured in step 8 t...

Страница 21: ... Generator and turn the amplitude knob all the way down counter clockwise 2 Connect the generator to the speaker using two banana patch cords Polarity does not matter 3 Place the Resonance Tube horizontally as shown with the speaker near the open end Place the speaker at a 45 angle to the end of the tube not pointed directly into it Equipment Part Number Sine Wave Generator WA 9867 Open Speaker WA...

Страница 22: ...ngth Thus for a tube with one open end and one closed end the length of the tube L and the wavelength λ are related by eq 1 For all types of waves the relationship between the frequency f and the velocity v of the wave is eq 2 For a resonating tube v is the speed at which sound travels through the air in the tube and f is the frequency of the sound In this experiment the sound frequency is the fre...

Страница 23: ...he slope and the y intercept of the best fit line through this data 7 From Equation 3 we see that the slope of the graph is Use the slope from your graph to calculate the speed of sound in air Estimate the uncertainty 8 The actual speed of sound depends on the temperature of the air where T is the temperature of the air in degrees Celsius Measure the air temperature and calculate the actual speed ...

Страница 24: ...of sound How does it compare with your earlier value 5 Draw a companion sketch of the waveform diagram on page 22 showing two nodes and the same frequency Remember that there must be a node at the closed end and an anti node at the open end Hint the tubes in the two drawings should not be the same length but the wavelengths are the same Part II Open and Closed Tubes of Fixed Length Theory A resona...

Страница 25: ... and then replace the open tube with the closed tube Is it still at resonance Using the coarse frequency knob decrease the frequency until you find the fundamental resonance of the closed tube 7 Calculate the ratio of the open tube frequency to the closed tube frequency What should this ratio be Why 8 Press and hold the Store Exit key to store the fundamental frequency of the closed tube Press the...

Страница 26: ...Sine Wave Generator Resonance Tubes 26 ...

Страница 27: ... kg f Hz f 2 Hz2 f Hz f 2 Hz2 0 055 74 1 5491 34 8 1211 0 105 102 1 10424 48 2 2323 0 155 124 1 15401 58 9 3469 0 205 142 2 20221 67 7 4583 0 255 158 3 25059 75 4 5685 Density µ 4 9 8 m s 2 97900 Hz 2 kg 1 23 m 2 2 65 10 4 kg m 0 265 g m Actual Density 1 58 g 6 09 m 0 259 g m Density µ 4 9 8 m s 2 22400 Hz 2 kg 1 23 m 2 1 16 10 3 kg m 1 16 g m Actual Density 2 36 g 2 00 m 1 18 g m ...

Страница 28: ...imum Slope 5890 Hz2 kg Deviation 2 String m kg f Hz f 2 Hz2 0 055 19 3 372 0 105 25 7 660 0 155 31 0 961 0 205 36 3 1318 0 255 42 7 1823 0 310 49 4 2440 0 360 55 4 3069 Density µ 4 9 8 m s 2 5890 Hz 2 kg 1 23 m 2 4 4 10 3 kg m 4 4 g m Actual Density unstretched 5 58 g 1 3 m 4 3 g m ...

Страница 29: ...ted for simplicity Deviation 1 Tube Diameter 14 5 cm End Effect 0 3 14 5 4 4 cm as compared to the y intercept which is 6 7 cm Still this shows the concept that the wave extends outside the end of the tube by several centimeters Ask students to consider the uncertainty of the best fit line s y intercept Further investigations f 230 Hz Position of first node 104 cm Position of second node 28 cm λ 2...

Страница 30: ...ce Tubes 30 Part II f1 122 Hz fundamental λ 346 m s 122 Hz 2 84 m L 1 2 λ 1 42 m effective length Actual Tube Length 1 31 m End effect per end 1 42 m 1 31 m 2 5 5 cm which is between the values from Part I 1st Harmonic 3rd Harmonic 3rd Harmonic ...

Страница 31: ...16 786 3292 Web www pasco com Email techsupp pasco com Copyright and Warranty Information Copyright Notice The PASCO scientific 012 08678A Sine Wave Generator Instruction Manual is copyrighted and all rights reserved However permission is granted to non profit educational institutions for reproduction of any part of this manual providing the reproductions are used only for their laboratories and a...

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