Instructions Demonstrations Experiments Sample Data Instruction Manual No.
String Vibrator Model No. WA-9857 Contents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Equipment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Introductory Activity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Demonstration 1: String Density and Wavelength. .
Model No. WA-9857 String Vibrator String Vibrator Model No. WA-9857 String Vibrator Power Supply Included Equipment Replacement Part Number String Vibrator WA-9857 Power Supply 540-050 Wave Cord (3 meters, not pictured) SE-9409 (90 m roll) The demonstrations and experiments described in this manual call for additional equipment. For details, see the equipment list for each activity.
String Vibrator Equipment Setup Equipment Setup Power Input Clamping Surfaces Stacking Pin (one per corner) Built-in Rod Clamp Vibrating Power The AC Power supply plugs into the Power Input of the String Vibrator. It drives the String Vibrator with a constant-frequency, constant-amplitude sine wave. The driving frequency equals the frequency of the mains power supply (50 or 60 Hz in most countries).
Model No. WA-9857 Equipment Setup Rod Clamp The case of the String Vibrator has a built-in rod clamp for mounting it either horizontally or vertically on a rod with a diameter up to 12.7 mm (1/2 inch). Slide the rod through the case in the preferred orientation and tighten the thumb screw. The Universal Table Clamp (ME-9472) and 45 cm Rod (ME-8736) work well in this application because you can clamp the rod vertically to the edge of a table.
String Vibrator Equipment Setup Vertical String The vertical arrangement with the elastic cord makes a good classroom or lecture demonstration. It requires a vertical rod and a horizontal component at the top of the rod, such as a Pendulum Clamp (SE-9443), to attach the elastic cord. To adjust the length and tension, move the top mount vertically on the rod. Horizontal String The pictures below show the horizontal arrangement in two ways.
Model No. WA-9857 Equipment Setup Good Nodes Versus Bad Nodes Most demonstrations and experiments involve adjusting the length, tension or frequency to produce a standing wave pattern. It is tempting to look only at the amplitude of the wave and concentrate on making it as large as possible; but it is also important to check that the nodes are “clean” and well defined, especially the node at the vibrating blade. Good Node Check the end of the vibrating blade.
String Vibrator Introductory Activity Introductory Activity Equipment Required Part Number String Vibrator WA-9857 Power Supply Part of WA-9857 Elastic Wave Cord (1 meter) Part of WA-9857 (or SE-9409) Clamp or other device for securing the String Vibrator SE-7286 or similar This activity works best with two or more people. 1. Attach the String Vibrator to the table. You’ll be stretching the cord to about 2 m, so leave enough space. 2.
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String Vibrator String Density and Wavelength 4. Loosen the clamp on the String Vibrator and slide it along the table to adjust the length of the vibrating part of the inelastic cord. Adjust it so that knot connecting the elastic and inelastic cords is at a node. (The amplitude may be low, but it will increase after the next steps.) 5. Observe the elastic cord. You want a node to occur at the point where the cord is attached to the vibrating blade, but that will probably not be the case initially.
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String Vibrator Closed Tube Analogy 4. Adjust the hanging mass (or the driving frequency) so that there is a node at the blade and an anti-node at the knot connecting the thread and the elastic cord. Demonstration 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.
Model No. WA-9857 String Vibrator Experiment 1: Wave Speed 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.
String Vibrator Wave Speed 2. Cut about 1 m of elastic cord. Measure its exact unstretched length. Measure the mass using a balance. Calculate the Unstretched Linear Density (mass/length). (If your balance is not precise enough to measure 1 meter of cord, measure the mass and length of a much longer piece of cord, and use those measurements to calculate the linear density.) 3. Attach the cord to the blade of the String Vibrator.
Model No. WA-9857 Experiment 1: Wave Speed Wave Speed Calculated from Tension and String Density You can also calculate the wave speed from the tension (F) and the linear density (µ) of the cord with: (eq. 2) v = F --µ The linear density is the mass per unit length of the cord when it is stretched. This will be less than the value that you calculated for the unstretched cord. You will now calculate the stretched linear density. 1.
String Vibrator Wave Speed 4. Start recording data just before you pluck the string, then immediately stop recording. 5. View the force and voltage data on a graph, and find the elapsed time, ∆t, between the sudden decrease in tension and the change in voltage. 6. Calculate the pulse speed: (eq. 3) Lv = ---∆t Conclusions You have calculated the wave speed using three methods. 1) Compare your results.
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String Vibrator Standing Waves In Strings adjusted to the frequency of the driving vibrator, 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 v=λf (eq. 1) The speed of a wave on a string is also given by (eq. 2) F --µ v = where F is the tension in the string and µ is the linear density (mass/length) of the string.
Model No. WA-9857 Experiment 2: Standing Waves In Strings Procedure 1. Adjust the tension by adding to or subtracting from the hanging mass so that the string vibrates in 2 segments. Adjust the tension further to achieve a “clean” node at the center. 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.
String Vibrator Standing Waves In Strings 2. For every value of mass, calculate the tension (including uncertainty) in the string. Tension = F = mg 3. Make a graph of F versus n. Describe in words the shape of the graph. 4. For every value of n, calculate 1/n 2. Make a graph of F versus 1/n 2. Does the graph look linear? 5. Find the slope (including uncertainty) of the best fit line through this data. 6.
Model No. WA-9857 String Vibrator Experiment 1: Teachers’ Notes–Wave Speed Equipment Notes Clamps Instead of table clamps and rods, you can use two C-clamps to fasten the String Vibrator and force sensor to the table. Use a block or book to elevate the force sensor a few centimeters above the surface of the table. Be careful when applying clamping pressure to the force sensor. Balance The density of the elastic wave cord is about 1.5 g/m, so it’s best to use a balance readable to 0.01 g.
String Vibrator Teachers’ Notes–Wave Speed Tension F = 10.4 N Wave Speed Calculated from Wavelength and Frequency Stretched Length = L = 2.343 m Number of segments = 4 λ = 1.172 m f = 60.0 Hz v = λ f = 70.2 m/s Wave Speed Calculated from Tension and String Density 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 v = F --- = 70.
Model No. WA-9857 Experiment 2: Teachers’ Notes–Standing Waves In Strings Be sure to measure from the sudden force change, not the relatively slow variation that may occur before the actual pluck. It may be helpful to repeat the measurement a few times and take the average value. ∆t = 3.4 × 10-2 s v = L/∆t = 68.8 m/s Conclusions 1) In the sample data above, all three calculations of v were within 5% of each other. (The first two calculations were exactly equal, but that is not typical.
String Vibrator Teachers’ Notes–Standing Waves In Strings Analysis Method 2 F vs. n F vs. 1/n 2 Slope = 3.74 ± 0.01 N 2 2 4µf L = 3.74 ± 0.01 N f = (60.0 ± 0.1) Hz L = (0.987 ± 0.001 m) ( 3.74 ± 0.01 N ) –4 µ = -------------------------------------- = ( 2.67 ± 0.01 ) × 10 kg/m 2 2 4f L This result differs from the direct measurement of linear density by 0.01 × 10 -4 kg/m. It is within the estimated uncertainty. –4 –4 2.67 × 10 kg/m – 2.66 × 10 kg/m - × 100% = 0.
Model No. WA-9857 Safety Read the instructions before using this product. Students should be supervised by their instructors. When using this product, follow the instructions in this manual and all local safety guidelines that apply to you. Technical Support For assistance with any PASCO product, contact PASCO at: Address: Phone: Fax: Web: Email: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95747-7100 (916) 786-3800 (800) 772-8700 (916) 786-3292 www.pasco.com techsupp@pasco.
