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Design Project #2 – Musical Instrument: Mechanical and Electrical Oscillations ENGR-111 Main Goal of the Project To build a musical instrument and to play a simple tune of your choice. Summary Sounds we hear are due to acoustic waves propagating in air, where the frequency of the acoustic wave determines the sound’s pitch. Humans can hear sounds in the frequency range from about 20 Hz to about 20,000 Hz. Thus, any object (such as a loudspeaker membrane or a beam) vibrating within this frequency range will create an audible sound, and the dominating frequency of vibration will determine the sound’s pitch. Low frequencies correspond to low pitch (e.g., bass guitar) and high frequencies correspond to high pitch (e.g., flute). In this project, mechanical vibration and electrical oscillation will be used in tandem to build an instrument capable of playing a tune with at least six musical notes (the frequencies will be chosen based on the selected tune). Each team will create two notes using electronic circuits and the remaining notes using selected mechanical components (one cantilevered beam, three tubular chimes and three palm pipes). Note that not all components need to be used. In the end, all the teams will perform their tune in front of other students in their section. Schedule Week 1 Specific Goals Project Introduction Learn the project goals, equipment, and underlying physics. Build a simple circuit and demonstrate Ohm’s Law using electronic breadboard. Electrical components Select tunes and identify the required frequencies to be generated. 2 Electronic Oscillation Generate electronic note(s): Build and test electronic oscillators to generate two notes. Observe the output signal on the oscilloscope and measure its frequency. Start working on Week 3. 3&4 Mechanical Vibration Explore mechanical vibration: Set up vibrating components (beams, chimes, palm pipes) and measure the frequency of selected components using piezofilm sensors. Determine the frequency dependence on length. Select the lengths of all components to get the right frequencies. Build the instrument: Combine the electronic and mechanical notes into one instrument. Music Machine 4 Finishing up and Performance Finishing up: Finish building the instrument. Practice playing the tune. Perform in front of other students. 1 Note: This document has two parts: “Schedule and Instructions” below and “Reference” at the end. Read entire document before working on detailed tasks. SCHEDULE AND INSTRUCTIONS Week 1: Project Introduction The aims of this week are to:         Form teams Understand the project goals thoroughly Understand the fundamentals of mechanical vibration, oscillating electrical circuits, natural frequency, and the relation between sound frequency and notes in a musical scale Introduce the available electronic and mechanical devices that can make musical notes Become familiar with all electronics and instrumentation used in the project such as power supply, multi-meter, and oscilloscope. This also includes brief demonstration of electronic components: resistors (including variable resistors, or potentiometers), capacitors, integrated circuits, etc. Introduce breadboard. Build a simple circuit on a breadboard to demonstrate Ohm’s Law. Identify all electrical components available to the teams in their project bins. Select a tune and identify the required frequencies of oscillation Introductory Activity: Building a simple circuit and demonstrate the Ohm’s Law. 1. Become familiar with the power supply (Figure 15 in the Reference), multi-meter, resistors, variable resistors (potentiometers) and electronic breadboard (Figure 18 in the Reference). 2. Using a breadboard, assemble one resistor and one potentiometer in series, as shown in Figure 1. Do not connect the power supply or the meters yet. 3. Using a multi-meter, measure the actual resistance R1 (it should be close to the nominal 1 k value). 4. Adjust the resistance R2 to the lowest possible (practically zero). Also measure resistance between nodes 1 and 3, which should be R1-3 = R1 + R2 ≈ R1 5. Connect the power supply and set it to 5V DC. 6. Measure current I, voltage V1-2 across resistor R1 and voltage V2-3 across resistor R2 7. Repeat steps 4, 5 and 6 for four more values of resistance R2. The second value should be R2 = R1 (measured in step 3). The last value should be the maximum resistance (about 10 k). 8. For each measurement, calculate and record the product R1-3 * I Figure 1 Circuit to investigate Ohm’s Law: Measuring current (top) and voltage (bottom) 2 Constant Values R1 = V1-3 = 5 (V) (k) Table 1: Ohms Law Variable Meas. 1 Meas. 2 Meas. 3 Meas. 4 Meas. 5 Values 0 R2 (k) R1-3 (k) I (mA) V1-2 (V) V2-3 (V) Core Activity: Selecting tunes and note frequencies Your instrument must generate between 6 and 8 notes. Play a tune at the end of the project. 1. Determine all frequencies needed to play the tune. 2. Decide which frequency will be generated using what method and record the frequencies in Table 2. Assign lower frequencies to mechanical components and higher frequencies to electronics. Table 2 Selected frequencies and methods Note # Note Frequency Method Name (Hz) (electronic or mechanical) 1 2 3 4 5 6 7 8 Table 3 lists the frequencies of musical notes from middle C to C’. The frequencies are based on the so called A 440 scale (440 Hz corresponding to the A note), which is the most widely used1 in music. Table 3 Frequencies of musical notes Note: If your tune contains notes outside the one octave shown, you Musical Frequency will need to research your frequencies. Note (Hz) C 261.6 C# 277.2 HW Assignment 1 – Graph Ohm’s Law results. Calculate theoretical D 293.7 value of resistance R2 for Week 2. – See Project 2 HW 1 in My D# 311.1 Assignments for details. E 329.6 F 349.2 F# 370.0 G 392.0 G# 415.3 A 440.0 A# 466.2 B 493.9 C 523.3 1 For physics experiments a “scientific” scale is often used, in which all C tones have power of 2 frequencies (for example 256 Hz or 512 Hz) 3 Week 2: Electronic Oscillation The goal of this week is for each team to build and test two electronic oscillators to generate the two assigned notes. The instruction below is for a single note. Core Activity: Generation one musical note with square wave oscillations Each note will require building an oscillator module based on the 555 timer (Integrated Circuit, IC) from individual components and using an electronics ‘breadboard’. The diagram of the oscillator module is shown in Figure 2. Theoretical value of resistance R2 was calculated in Week 1 HW Assignment. Building the Oscillator: 1. Collect all the components needed based on Figure 2. Note that R2 is a 50 kpotentiometer (different from the 10 k potentiometer used in the previous activity). 2. Set multimeter to resistance mode and adjust the variable resistor R2 to the value calculated in the Week 1 HW Assignment. Make sure to document whether the required Figure 2 Oscillator based on the 555 resistance is set from Pin 1 to Pin 2 or Pin 2 to Pin 3 on the timer (produces a square wave) variable resistor. It may be easier to place the variable resistor in the breadboard to complete this task. 3. Build the oscillator circuit (Figure 2) by placing all components on the left half of a breadboard. 4. Set up the DC power supply. Follow the dc power supply guide in the Reference section. 5. Connect the Ground (GND) and +5V leads from power supply to the breadboard. 6. Turn on the power supply and set the voltage on both voltage dials to +5V Confirming the output signal 7. Connect the oscilloscope ground clip to ground and the test clip to Pin 3 of the 555 timer. 8. Verify that a square wave similar to Figure 12 can be seen on the oscilloscope. Debug the connections, if needed. 9. Set the oscilloscope to frequency measurement and measure the signal frequency 10. If needed, adjust the potentiometer R2 until the frequency matches your target frequency Core Activity: Generating two notes from the tune and connecting to a speaker 1. Add second (virtually identical) oscillator to the breadboard 2. Add one headphone jack 3. Add two switches 4. Connect the speaker 5. Turn power supply on 6. Play two notes 7. Tune each of the notes using oscilloscope 8. Verify each frequency using electronic tuning device. Figure 3 Electronic module for generating two notes 4 HW Assignment 2 – Create theoretical curves f1(L) for Week 3. Calculate target lengths of the vibrating components based on theoretical calculations.—See Project 2 HW 2 in My Assignments. Optional Extension Activity: Cleaner sounds – converting square waves into sine waves While the square wave can deliver a sound with a dominating pitch corresponding to the square wave frequency, the signal also contains higher frequency harmonics, resulting in undesired ‘noise.’ In order to obtain cleaner sounds, these higher frequency harmonics need to be filtered out. Figure 4 shows one relatively simple system which can be used to accomplish this goal. It is a combination of a buffer amplifier (right side of Figure 4) and low pass filter module (left side). Note that a single Integrated Circuit (IC), a TL 082, provides two Op Amps needed for the two modules. The resistance and capacitance values were calculated in Week 2 HW Assignment. Figure 4 Combined LPF and Buffer Amplifier. Converts square wave to sine wave. Building the Oscillator with Filtering: 1. Collect all the components needed based on the values determined in the Week 2 HW Assignment. a. Standard resistors closest to the calculated values of R1 and R2 should be used b. C1 = 2C2 can be formed by using two capacitors C2 in parallel 2. Build the circuit. Place all components on right half of a breadboard 3. Connect with the output signal from the Oscillator 4. Connect the Ground (GND), +5V and -5 V leads from power supply 5. Turn on the power supply and set the voltage to +5V and -5V Confirming the output signal 6. 7. 8. 9. Connect the oscilloscope ground clip to GND and the test lead to Out 1 pin of the TL082 IC (Pin 1) Verify that the square wave has now become a sine wave. Debug the connections, if needed Set the oscilloscope to frequency measurement and confirm the frequency of the output signal. If needed, adjust the potentiometer R2 of the Oscillator (Figure 2) until the frequency matches your target frequency 5 Weeks 3 and 4: Mechanical Vibration Mechanical tones will be generated using any combination of the three methods: 1. Striking a steel cantilever beam and making it vibrate 2. Striking a tubular chime (made of either steel or copper) and making it vibrate 3. Striking a PVC palm pipe against the palm of your hand and making the air inside vibrate The vibrations of cantilevered beams or tubular chimes will be studied by using piezoelectric sensors. By placing double-stick tape on the underside of a sensor, the sensor can be attached (and easily removed) anywhere on the surface of the vibrating element. The main goals for this week are to observe free vibration of cantilevered beam and/or tubular chimes and to determine the dependence of the fundamental frequency of vibration on the lengths of vibrating element. Core Activity: Measurement of the fundamental frequency for various lengths of vibrating elements Select either a cantilevered beam or tubular chimes for this investigation Instructions for cantilevered beam: 1. Clamp the beam with the cross plates to the table edge using a large C-clamp such that the long axis extends past the edge of the table at a 90○ angle out from the table (see Figure 5). Start with a length of about 4.0 inches. Make sure that the clamp is tightened well. 2. Attach the sensor to the beam using double sided tape. Orient the sensor so that is mid-width of the beam and close to the point where the beam is clamped to the table. The long direction of the sensor should follow the length of the beam (see Figure 5). a. Be sure that the leads to the sensor are not clamped or are in the way of the vibrating beam. Also make sure any exposed metal on the sensor leads does not short out by touching the beam or clamp. 3. Turn on the oscilloscope, being sure that the scale factor used by the oscilloscope channels and the scale factor Figure 5 Clamped beam with sensor imprinted on the probes are the same, i.e. “X1” or “X10” or “X100” for the channel you wish to use. If this step is skipped the oscilloscope scale (as shown on the screen) will be off from the actual value by a factor of 10 or 100. 4. Pluck the free end of the beam and view the response on the oscilloscope. You may need to adjust the horizontal (time/div) and vertical (volts/div) to ensure a full signal is on the screen. Approximate settings for these are voltage: 100mV/div and time: 10ms/div. Determine the fundamental frequency f1 by “freezing” the oscilloscope trace and measuring the distance between signal peaks using vertical cursors on the oscilloscope. a. “Freezing” is done by pressing the Stop button shortly after plucking the beam. i. Cursors are turned on by pressing the Cursors button and choosing vertical bars. You can move the cursors using the knob to the left of the cursor button. You can choose which cursor to move by using the select button to the left of this knob. Horizontal distance between the two cursors is displayed automatically, and is defined as the period T of oscillation. b. Calculate the fundamental frequency as: 1 i. 𝑓1 = 𝑇 6 c. Sketch the “frozen” trace and neatly record, t1, t2, and T (see Figure 7 in the Reference section). 5. Determine the fundamental frequencies f1 three times for each length investigated. Select at least four lengths between 2.5 and 4 inches. Record all results in Table 4 and calculate the averages. Table 4 Vibration of cantilevered beam – quantities to be measured. Beam Length L ____inch ____inch ____inch ____inch ____inch Fundamental Freq. f1 (Hz) Measurement 1 Fundamental Freq. f1 (Hz) Measurement 2 Fundamental Freq. f1 (Hz) Measurement 3 Average Freq. f1 (Hz) 6. Using averaged results in Table 4 determine the beam length which will result in vibration at your target frequency (as listed in Table ). You can determine L by either linear interpolation or careful graphing of the data in Table 4. 7. Set the target beam length L and confirm the vibrating frequency with an oscilloscope. Instructions for tubular chimes: One set of tubular chimes of various lengths will be provided per section (you will need to share them with other teams). Perform the following steps for at least four chimes: 1. Measure its length 2. Attach the piezo sensor using double sided tape. Position the sensor near the half-length point with the long direction of the sensor following the length of the chime 3. Hang the chime using a zip tie positioned about 20% of the length from the top 4. Perform a similar procedure as described above for cantilever beams (steps 3 through 5). 5. Record all results in Table 5 below. Table 5 Vibration of tubular chime – quantities to be measured. Chime Length L ____inch ____inch ____inch ____inch ____inch Fundamental Freq. f1 (Hz) Measurement 1 Fundamental Freq. f1 (Hz) Measurement 2 Fundamental Freq. f1 (Hz) Measurement 3 Average Freq. f1 (Hz) 6. Using averaged results in Table 5 determine the chime length which will result in vibration at your target frequency (as listed in Table 2). You can determine L by either linear interpolation or careful graphing of the data in Table 5. 7 Core Activity: Building the instrument 1. 2. 3. 4. Make all mechanical tones listed in Table 2 using selected mechanical elements. Combine the electronic oscillators (from Week 2) and the mechanical tones into one ‘instrument’. Fine tune the frequencies, if needed. Electronic tuner will be available. Practice playing tunes for the performance. Week 3 HW Assignment -- Graph f(L) for both theoretical and experimental values for either cantilevered beams or tubular chimes. Add a trendline to experimental data. Compare with theoretical values. Determine the target value of L. See Project 1 HW 3 in My Assignments. Week 4: Performance – playing the tune Each team will perform their tune in front of other students in their section. You are allowed to bring additional instruments as long at least 6 notes are from the instrument built in this project. Competition Rules:   The tune must have at least 25 notes, total You can bring additional instruments, but the built instrument must dominate Optional (decided by your instructor)   Instant scoring by all people in the audience Prizes for the winning band HW Assignment 3 – Each student will write an Executive Summary of the project. See Project 2 Executive Report assignment in My Assignments. 8 REFERENCE Vibration of Cantilevered Beams A cantilevered beam is a beam fixed (cemented, clamped) at one end with the other end remaining free to move. This type of beam is very common in structures and machines, e.g. airplane wings, helicopter blades, beams supporting traffic lights. Even sky scrapers can be viewed as cantilevered beams. When a free end of a cantilevered beam is displaced and then released, the beam will start to oscillate back and forth. From the energy perspective, this oscillation manifests cyclic conversion from elastic (spring) energy to kinetic energy and back. Because of various energy losses in the system, the amplitude of the oscillation becomes smaller with time, and eventually stops. Cantilevered beam can vibrate in many modes, each with the associated so called natural frequency of vibration. The modes of vibration are commonly ordered Figure 6 First mode (top) and second mode of vibration of from the lowest frequency to the cantilevered beam. Right end free to move. highest, and the frequency associated with the first mode is called the fundamental frequency. Figure 6 present the first two modal shapes. The fundamental frequency of the cantilevered beam can be calculated by using (Eq. 1) below. (Eq. 1) 𝑓1 = 𝐾1 2𝜋 𝐿 2 𝐸𝐼 √ 𝜌𝐴 Where f1 represents the fundamental frequency; E and  are Young’s Modulus and density for the beam material, respectively; A and I are cross-sectional area and its moment of inertia, respectively; K1 is a constant associated with the fundamental frequency; and L is the length of the beam. (One can think of Young’s modulus as a ‘spring constant’ of the beam material F = kx where F is the spring force, k is the spring constant and x is the distance stretched.) The cantilevered beam used in this project is made of steel known as ANSI 1095 blue tempered spring steel (carbon steel with about 1% of Carbon and about 0.5% of Manganese). The beam dimensions are 6.6” x 1.0” x 0.062” (L x b x d). Table 6 lists the values for the constants needed in (Eq. 1) for the vibrating beams used in this project (1095 spring steel). Table 6 Physical Constants Used for Vibrating Beam Quantity Symbol Value Units 1 f1 Natural Frequency (Eq. 1) Hz K1 Constant 3.5156 unitless E Young’s Modulus 2.0 × 105 MPa d Beam Thickness 0.062 in b Beam Width 1.00 in I Moment of Inertia I= bd3/12 m4 A Cross-sectional area A= bd m2 Density of 1095 Steel 7,900 kg/m3  2 L Beam Length Adjust in 1. f1 represents the fundamental frequency 2. Beam length is measured from the free end to where the clamp is placed. 9 Figure 7 shows a typical oscilloscope trace generated by a vibrating beam. As one can see, the amplitude of the voltage signal decreases as time elapses after the cantilevered beam has been set in motion. Figure 7 Decaying amplitude of vibrations This is because the energy introduced into the system is absorbed by the surrounding hardware, table surface, table supports, and like structures. The waveform decreases in a logarithmic manner. The parameter that governs how fast this occurs is the time constant τ. This time constant can be found using (Eq. 2) given below using the values measured from the oscilloscope trace. (Eq. 2)   T / ln(V ' / V ) Where T is the period taken from one peak to the next, V is the amplitude of the first peak, and V’ is the amplitude of the succeeding peak. The “ln” stands for the natural logarithm. The negative sign appears since the ratio V’/V is less than unity which means that ln(V’/V) < 0. The time constant, τ is an important parameter in that in practice approximately 4 time constants (4τ) are required for the system to come to rest, i.e. settle down. Vibration of Tubular Chimes Vibration of a tubular chime is more complex than the one of a simple cantilevered beam. However, the dominating mode can be studied with vibrating beam theory. In this case, none of the beam ends is supported, (free-free configuration) resulting in different modes of vibration than for cantilevered beam. The first two modes are presented in Figure 8. Figure 8 First two modes of vibration of tubular chimes 10 Interestingly, the fundamental frequency of this free-free oscillation can be determined by the same equation as before (Eq. 1): 𝑓1 = (Eq. 1) 𝐾1 2𝜋 𝐿 2 𝐸𝐼 √ 𝜌𝐴 The only differences are that the constant K1 has a different value for this configuration, and that the material properties (E, ) and the properties of the cross sectional area (I, A) are different (see Table 7). There are two kinds of tubing available for tubular chimes in this project: steel and copper. The steel tube is referred to as ½ inch nominal size electrical metallic tubing, or EMT. It has the inside diameter (ID) of 0.622” and the outside diameter (OD) of 0.706". The copper tube is referred to as ½ inch nominal size Type M copper tubing , with 0.569" ID and 0.625" OD. Table 7 lists the values for the constants needed in (Eq. 1) for the tubular chimes used in this project. Table 7 Physical Constants Used for Tubular Chimes Quantity Symbol Quantity f1 Natural Frequency1 (Eq. 1) K1 Constant 22.373 E Young’s Modulus, Steel 2.0 × 105 E Young’s Modulus, Copper 1.1 × 105 ID Tube ID See text above OD Tube OD See text above I Moment of Inertia I= (OD4- ID4)/64 A Cross-sectional area A= (OD2- ID2)/4 Density, Steel 7,900  Density, Copper 8,960  L Beam Length Variable Units Hz unitless MPa MPa in in m4 m2 kg/m3 kg/m3 in 1. f1 represents the fundamental frequency in bending mode Vibration of Air in Palm Pipes A palm pipe is simply a short rigid tube. When one of the ends is stroke against the palm of your hand, the air in the tube gets excited and oscillates longitudinally. An excellent applet showing the longitudinal waves in a pipe (written by Walter Fendt) can be find here: http://www.walterfendt.de/html5/phen/standinglongitudinalwaves_en.htm Study the applet and try different lengths and modes of vibration. You can observe that when one of the sides is Figure 9 Longitudinal waves applet closed, the wavelength of the fundamental mode equals four times the tube length:  = 4 L. The period of this oscillation is T =  /c , where c is the speed at which the disturbance travels, also known as the speed of sound, which at room temperature is about 344 m/s. Recalling that f = 1/T, the oscillation frequency can be found as: f = c / = c /(4L) = 0.25 c /L (Eq. 3) You can observe that (Eq. 3) does not depend on the tube diameter. A more precise empirical equation (based on experiments with ½” Schedule 40 PVC tubes and accounting for pipe end effects) is: (Eq. 4) f = 0.23 c /L + 24 (Hz) 11 Complete Musical Instrument (electronic tones) Figure 10 presents block diagram of the electronic part of the musical instrument generating two tones. Examining the block diagram, one can see that there will be two oscillators, one for each electronic note selected by your team. Figure 10 Block Diagram of the electronic circuit generating two tones. Each component is described in more detail below. Note that an optional low pass filter (not shown) can be added between the output pin 3 and the switches to remove unwanted harmonics and convert square wave signal into a sine wave. Oscillator Figure 11 shows the connections needed for the NE 555 Timer to produce a series of output pulses as was shown in Figure 12. The NE 555 integrated circuit (abbreviated as an “IC”) produces a sequence of pulses with an output frequency set by a capacitor and two resistors. The frequency of pulses produced by the NE 555 Timer is given as: (Eq. 5) f= 1.46 (R1 +2R2 )C The 10nF capacitor shown in Figure 11 is optional, i.e. may be left open (no connection). The pin out of the NE555 Timer is shown in Figure 17. The timer, as the name suggests, is used as a low frequency clock, for instance in orchestrating the processing of a synchronous logic circuit. 12 Figure 11 Oscillator Using a 555 Timer. The 10nF capacitor is optional. To obtain 50% duty cycle (same time low signal as high) R1 should be much less than R2. It is recommended that R1 = 1kΩ and C = 0.1 F. Then R2 can be calculated and accurately set by using a potentiometer. The pulse train generated by the oscillator is shown in Figure 12 where the x-axis represents time and the y-axis represents voltage. Figure 12 A Pulse Train (In our case τ = T/2.) One can see that the ‘square wave’ signal differs from a single-frequency sinusoidal signal, and therefore the generated sound would not be clear. Some additional signal processing is needed to remove the unwanted frequencies Low Pass Filter (optional): The filter we can use to remove much of the unwanted frequencies (but not all) is a Sallen-Key Low Pass Filter (LPF). The LPF filter allows low frequencies to pass through and higher frequencies to be attenuated. Figure 13 illustrates the basic Sallen-Key LPF. We note that this form of a LPF is a very simple design requiring only two resistors and two capacitors along with an operational amplifier (or op amp, represented by the triangle in Figure 13). To design a Sallen-Key LPF, one must first determine what maximum frequency will be allowed to pass through. This is called the break frequency. Although the DC supplies are not shown, they must be included. Refer to Figure 4 for more detail. The resistors R1 and R2 are the same and equal to R. The break frequency, fb (for this project the fundamental frequency for the musical note) of the low pass filter can be calculated using the relationship below. 13 fb  (Eq. 6) 1 2R C1C2 Where C1 = 2C2 and R1 = R2 =R. As an example, by using C2 = 0.1μF (a standard size), then C1 = 0.2μF (which can be formed by placing two 0.1μF in parallel). With fb = 256 Hz, a musical C note, we calculate that R = 4398 Ω. Since this is not a standard size, choose the closest available value. Figure 13 Sallen-Key Low Pass Filter Buffer Amplifier: The function of a buffer amplifier (in this case referred to as a unity gain amplifier) is to minimize the problem of loading. Loading degrades the operation of the circuit due to the electrical characteristics of subsequent stages. The buffer acts to isolate one stage from its downstream neighbors. Figure 14 illustrates the circuit connections of the buffer amplifier. The pin out for the Op Amp used in this circuit is found in Figure 16. Remember that the DC voltages (+VCC and –VCC) are not shown in Figure 14 for simplicity, but must be included in practice. Refer to Figure 4 for more detail. Figure 14 Buffer Amplifier Using an Op Amp 14 Major Components and Equipment Piezofilm: The piezoelectric sensor that we will use is made of a special polymer, named polyvinylidene fluoride or PVDF for short. The material is heated and then rolled to form thin sheets. The material is allowed to cool in the presence of a strong electric field. The cooling “freezes” the alignment of the molecules in the crystalline structure in such a way that the net charge of the polymer is zero. The upper and lower surfaces are then metalized by a deposition process using silver ink. Cutting the metalized sheets into appropriate sizes, attaching electrical terminals with twisted-pair leads and covering the surfaces with a clear plastic coating completes the fabrication process of the sensor. Although the resulting piezofilm can be employed in various ways, for instance to measure temperature (pyro-electronic property) or to drive a speaker (electro-mechanical property), the mechano-electric property will be used in this experiment. A mechano-electric transducer transforms the energy of mechanical deformation into electrical energy. In its natural state, the symmetry of the charge distribution within the crystal leads to a cancellation of the net charge. However, when the piezofilm is mechanically deformed, the molecular arrangement is no longer symmetric in that local redistribution of alignments has occurred. A net charge is the result of the deformation. This gives rise to an electric field. This in turn is detected by an oscilloscope as a voltage. Multimeter: A multimeter is used to measure different electrical values of parts. For our purposes, it will be used to measure resistors (ohms) and capacitors (farads). To measure a component you must first have the probes in the correct holes. The black probe is always used in the COM. The red probe however is moved depending on whether you are measuring resistance or capacitance. For resistance use Ω and for capacitance use Cx. You then must set the dial to the correct position and value for resistance or capacitance. DC Power Supply: The DC Power Supply provides us with a constant -5volt +5volt and ground connections for our circuit. To set up the supply in this manner, place a wire from the + of the first set of probes to the – of the second set of probes (see Figure 15). Then make sure the tracking buttons are both in the out position to be set to independent. Lastly set the current knobs to 12 o’clock and the voltage knobs so both displays read 5v. The connections can be seen in Figure 15 below. Oscilloscope: This electrical measurement instrument can be thought of as a dynamic voltmeter, which can measure voltages as they evolve in time. The input to the oscilloscope is obtained by attaching probes that extend from the oscilloscope to the circuit. When the oscilloscope is turned on, one or two traces (depending on what option is selected) appear on the screen. By using the switches and control features of the oscilloscope, one can determine the frequency and amplitude of a waveform displayed on the screen. The “Run/Stop” buttons on the oscilloscope can be used to save the waveform on the screen at any given instant of time. One can determine the frequency and amplitude of an electrical system by using the cursors located on the oscilloscope. In the Electrical Engineering laboratories there are examples of both analog and digital oscilloscopes. The manner in which an oscilloscope is used is described in Wikipedia under the name “Oscilloscope”. It provides an overview of the console controls and the manner in which the oscilloscope probes are used. Additionally, videos are available through YouTube which demonstrates how the oscilloscope is set up to take measurements. Specifically, the video entitled, “The Oscilloscope: A Beginners Guide to the Oscilloscope” which was produced by Berkeley Engineering is especially helpful since it uses a similar scope to that available for this project 15 Figure 15 DC Power Supply Setup Op Amp: The major component in the buffer amplifier and LPF is an operational amplifier (op amp for short). It is an example of an integrated circuit (IC). The plastic package (in this case a “mini” DIP 8 pin, dual-in-line package) has eight pins. The “chip” is encased inside the black plastic package and connected to the surrounding circuit via metal pins. Looking down on the pins from above, the pins are numbered sequentially counterclockwise around the periphery of the IC from 1 to 8. A notch or imprint is provided on the top of the IC which indicates the location of pin 1. Each pin has a specific purpose. For example, pins 4 and 8 are reserved for the DC (constant voltage) inputs that serve to power the IC. The remaining pins are used according to the application. We will be using the Texas Instruments TL082 Op Amp. Refer to the Figure 16 below. Notice that there are two identical but separate op amps. The DIP 8 package is also shown. The result of connecting the proper pins together is an amplifier. An amplifier simply takes a voltage input and produces a larger version of this waveform at the output. A helpful YouTube short entitled 741 Op Amp Demo (the uA741 is similar to the TL082 but contains only one Op Amp.) by All American Five Radio provides additional technical details. Figure 16 TL082 Op Amp Pin Out and DIP-8 Plastic Package 16 Timer: The numbering scheme as described for the op amp is the same (but not the labels for each pin) that is used for the Timer. Although the packaging is identical, the timer does not amplify, but rather provide a series of pulses at the output that are 5.0 V in amplitude with a frequency that has been selected by including an appropriate capacitor and several resistors. We will be using the NE 555 Timer. Refer to Figure 17 below for the pin out and a view of the plastic package. The names for the terminals are ground (GND), trigger (TRIG), output (OUT), reset (RESET), discharge (DIS), threshold (THR), and a positive 5.0 V DC voltage source goes to pin (VCC). Figure 17 NE 555 Timer Op Amp Pin Out and DIP-8 Plastic Package Breadboard: Figure 18 shows a photo and a schematic of electrical connections in an electronics breadboard. The breadboard allows building electrical circuits without soldering. Figure 18 Photo and schematic of a breadboard. Lines in the schematic indicate electrical connections inside the breadboard. Note the placement of NE555 integrated circuit. Speakers: The speaker is an electro-mechanical device (a transducer) that converts electrical signals into mechanical vibrations that are in the audible range. A coil of wire is wrapped around the pointed end of a flexible, fabric cone. As the coil of wire receives current, a magnetic field is produced in proportion to the direction and the magnitude of the current. This field interacts with the magnetic field of a permanent magnet that is housed with the coil. This interaction creates forces on the cone which generate vibrations that are eventually perceived as sounds by the human ear. The speakers that we will be using are the XBOOM Mini, 3 W output portable speakers. 17

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