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Instruction Manual

No. 012-08798A

Instructions
Demonstrations
Experiments
Sample Data

String Vibrator

WA-9857

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Summary of Contents for WA-9857

Page 1: ...Instruction Manual No 012 08798A Instructions Demonstrations Experiments Sample Data String Vibrator WA 9857 ...

Page 2: ...on 1 String Density and Wavelength 9 Demonstration 2 Closed Tube Analogy 11 Experiment 1 Wave Speed 13 Experiment 2 Standing Waves In Strings 17 Experiment 1 Teachers Notes Wave Speed 21 Experiment 2 Teachers Notes Standing Waves In Strings 23 Safety 25 Technical Support 25 Copyright and Warranty Information 25 ...

Page 3: ... as well as the factors that affect those properties It is well suited for classroom demonstrations and hands on experiments The String Vibrator uses a coil and magnet design to vibrate a stainless steel blade to which you attach a string or elastic cord The driving signal and power come from the included power supply or for a variable signal from an optional signal generator such as the WA 9867 S...

Page 4: ... following Sine Wave Generator WA 9867 Digital Function Generator PI 9587 750 or 700 Interface with Power Amplifier II CI 6552A Mounting Options The String Vibrator can be fastened to a table in a variety of ways C Clamp Two recessed Clamping Surfaces on the String Vibrator allow it to be secured to a table with a C clamp You must use a C clamp wide enough to accommodate the thickness of the table...

Page 5: ...ring Selection The included elastic wave cord works well for demonstrations and many lab activities The elastic cord is easy to see produces good amplitude and it does not require a hanging mass to provide tension but it does not have constant linear density under tension For experiments exploring the relationship between wave speed and string density it is better to use an inelastic string such a...

Page 6: ...standing waves produced sometimes vibrate in a plane it may be necessary to rotate the case for the wave to be visible In the orientation pictured on the left the wave is visible from above but not as easily seen by a student sitting out in the classroom As shown on the right the wave is visible from the side which is most useful for demonstrations Applying Tension to Inelastic String When you use...

Page 7: ... node is shown in the second picture The blade rattling against the plastic case indicates a bad node The method for correcting a bad node depends on the type of experimental setup With the elastic cord the adjustment is usually made to the length and tension simultaneously by moving one of the end points With an inelastic string set up with a pulley and a hanging mass you can adjust the length of...

Page 8: ... of segments to increase or decrease 6 Adjust the tension until the cord vibrates in 4 segments Then adjust the tension slightly so that there is a good node at the blade Maintain that tension for the rest of the activity 7 Measure the wavelength How is the wavelength related to the length of one segment 8 Touch the cord at one of the antinodes the points of maximum vibration What happens 9 Touch ...

Page 9: ...as possible 2 Clamp the pulley at the end of the table and clamp the String Vibrator about 1 meter away Attach a 100 g mass to the end of the inelastic cord and run the cord over the pulley 3 Connect the power source to the String Vibrator If you are using the Sine Wave Generator set the frequency at around 50 Hz and turn up the amplitude midway Equipment Required Part Number String Vibrator WA 98...

Page 10: ... String Vibrator again so that the knot connecting the elastic and inelastic cords is at a node Confirm that the connection to the blade is also at a node Optional Setup for Variable frequency Sine Wave Generator First follow steps 1 5 After you have positioned the String Vibrator so that a node occurs at the knot adjust the driving frequency so that another node occurs at the blade As you adjust ...

Page 11: ... the end of the table and clamp the String Vibrator to the table about 70 cm away Hang a 150 g mass on the thread over the pulley 3 Connect the power source to the String Vibrator If you are using the Sine Wave Generator set the frequency to around 50 Hz and turn up the amplitude midway Equipment Required Part Number String Vibrator WA 9857 Power Supply Part of WA 9857 Elastic Wave Cord 50 cm Part...

Page 12: ...stration This demonstration is analogous to sound produced by a pipe with one open end and one closed end Notice that the segment with the anti node on the end is a quarter wavelength where the other segments are half wavelengths A dark background placed behind the wave can hide how this is done the white elastic cord shows up very well but the black thread disappears when the String Vibrator is r...

Page 13: ... pulse to travel a known distance and calculate the speed of the pulse Procedure 1 Use rods and clamps to connect the Force Sensor and String Vibrator to the table as shown Equipment Required Part Number String Vibrator WA 9857 Power Supply Part of WA 9857 Elastic Wave Cord 50 cm Part of WA 9857 or SE 9409 Universal Table Clamps qty 2 ME 9472 or similar 45 cm Rods qty 2 ME 8736 or similar Force Se...

Page 14: ...ting blade there should be a node at the point where the cord attaches to the blade It is more important to have a good node at the blade than to have the largest possible amplitude 6 Record the number of segments Tension You will use the force sensor to measure the tension of the cord 1 Set the sample rate to 100 Hz 2 Unhook the cord from the force sensor and zero or tare the sensor Reattach the ...

Page 15: ...ve from your values of F and µ Speed of a Single Pulse Another way to find the wave speed is to measure the speed of a single pulse You will use the force sensor and the voltage sensor to time a pulse traveling down the cord 1 Unplug the power supply from the String Vibrator Connect the voltage sensor to the power input of the String Vibrator 2 Set the sampling rates of force sensor and the voltag...

Page 16: ...3 Conclusions You have calculated the wave speed using three methods 1 Compare your results Are the similar If they deviate from one another can you explain why 2 Which method do you think is the most accurate Explain why Further Investigation Repeat this experiment with a different length of cord you will find that the tension to achieve a standing wave will be different Before you measure v usin...

Page 17: ...etched string has many natural modes of vibration three examples are shown above If the string is fixed at both ends then there must be a node at each end It may vibrate as a single segment in which case the length L of the string is equal to 1 2 the wavelength λ of the wave It may also vibrate in two segments with a node at each end and one node in the middle then the wavelength is equal to the l...

Page 18: ... the string and n is the number of segments Note that n is not the number of nodes Since a segment is 1 2 wavelength then eq 3 Setup 1 Measure the exact length of a piece of string several meters long Measure the mass of the string and calculate the linear density µ mass length If your balance is not precise enough to measure that length of string use a much longer piece of string to calculate the...

Page 19: ...ertainty Analysis Method 1 1 Calculate the tension including the uncertainty in the string Tension F mg 2 Calculate the speed including uncertainty of the wave from your observed values of tension F and linear density µ Record your calculated value with the uncertainty and the correct number of significant figures 3 Calculate the speed from the wavelength λ and frequency f vλf λ f In the U S f 60 ...

Page 20: ... difference How does the difference to compare the uncertainty that you calculated in step 7 9 Calculate the percent deviation of the measured value of µ from the accepted value of µ Further Investigations 1 Hang a mass on the string with a value that is about halfway between the masses that produced standing waves of 3 and 4 segments The string should show no particular mode Place a bridge so tha...

Page 21: ...One convenient combination of equipment which was used for the sample data below is PASPORT Force Sensor PS 2104 PASPORT Voltage Current Sensor PS 2115 PowerLink interface PS 2001 DataStudio software Because of the variety of equipment that may be used the instructions here do not go into detail about collecting data Students should be prepared to use the sensors interface and software to Set up t...

Page 22: ... The unstretched length measured in this part of the experiment will be less than the unstretched length measured initially because of the knots tied in the ends Unstretched Length with knots 1 162 m µ 2 11 10 3 kg m Speed of a Single Pulse The sudden decrease in tension may appear on the graph as a sudden decrease or increase in force depending on whether the force sensor is set up to register te...

Page 23: ...y of the AC power is usually very close to its nominal value so you can ignore its uncertainty You can also use the voltage sensor plugged into the output of the power supply to measure the frequency Do not attempt to measure the voltage directly from the wall Experiment 2 Teachers Notes Standing Waves In Strings The density of the recommended string is about 0 266 g m so it s best to use a balanc...

Page 24: ...987 0 001 m This result differs from the direct measurement of linear density by 0 01 10 4 kg m It is within the estimated uncertainty F vs n F vs 1 n2 Slope 3 74 0 01 N 4µf 2 L 2 3 74 0 01 N µ 3 74 0 01 N 4f 2 L 2 2 67 0 01 10 4 kg m Deviation 2 67 10 4 kg m 2 66 10 4 kg m 2 66 10 4 kg m 100 0 4 ...

Page 25: ...tion 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 are not sold for profit Reproduction under any other circumstances without the written consent of PASCO scientific is prohibited Limited Warranty For a description of ...

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