PHYSICS LAB. Sound. Date: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY

Transcription

1 PHYSICS LAB Sound Printed Names: Signatures: Date: Lab Section: Instructor: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY Revision August 2003

2 Sound Investigations Sound Investigations 78

3 Part I - Speed of Sound Sound Investigations Compared to most objects, sound waves travel very fast. It is fast enough that measuring the speed of sound is a technical challenge. One method you could use would be to time an echo. For example, if you were in an open field with a large building a quarter of a kilometer away, you could start a stop watch when a loud noise was made and stop it when you heard the echo. You could then calculate the speed of sound. To use the same technique over short distances, you need a faster timing system, such as a computer. In this experiment you will use this technique with a Microphone connected to a computer to determine the speed of sound at room temperature. The Microphone will be placed next to the opening of a hollow tube. When you make a sound by snapping your fingers next to the opening, the computer will begin collecting data. After the sound reflects off the opposite end of the tube, a graph will be displayed showing the initial sound and the echo. You will then be able to determine the round trip time and calculate the speed of sound. ULI Closed end Microphone 1-m tube OBJECTIVES Measure how long it takes sound to travel down and back in a long tube. Determine the speed of sound. Compare the speed of sound in air to the accepted value. where: T is in degrees Celsius v is in m/sec v = 331 (1 + T/273) 0.5 MATERIALS Dell computer LabPro Logger Pro Vernier ULI Microphone tube, 1-2 meters long your physics text meter stick Part II - Sound Waves and Beats Sound Investigations 79

4 Sound Investigations A Simple Waveforms Sound waves consist of a series of air pressure variations. A Microphone diaphragm records these variations by moving in response to the pressure changes. The diaphragm motion is then converted to an electrical signal. Using a Microphone and a computer interface, you can explore the properties of common sounds. The first property you will measure is the period, or the time for one complete cycle of repetition. Since period is a time measurement, it is usually written as T. The reciprocal of the period (1/T) is called the frequency, f, the number of complete cycles per second. Frequency is measured in hertz (Hz). 1 Hz = 1 s 1. A second property of sound is the amplitude. As the pressure varies, it goes above and below the average pressure in the room. The maximum variation above or below the pressure mid-point is called the amplitude. The amplitude of a sound is closely related to its loudness. B Beats When two sound waves overlap, air pressure variations will combine to form a single sound wave. For sound waves, this combination is additive. We say that sound follows the principle of linear superposition. Beats are an example of superposition. Two sounds of nearly the same frequency will create a distinctive variation of sound amplitude, which we call beats. You can study this phenomenon with a Microphone, lab interface, and computer. OBJECTIVES Measure the frequency and period of sound waves from tuning forks. Measure the amplitude of sound waves from tuning forks. Observe beats between the sound of two tuning forks. MATERIALS Dell computer LabPro Vernier Microphone Logger Pro 2 tuning forks very close in pitch Sound Investigations 80

5 Part III Tones and Vowels Sound Investigations In this experiment, you will analyze various common sounds. You will use a Microphone connected to a computer. Logger Pro will display the waveform of each sound, and will perform a Fast Fourier Transform (or FFT) of the waveform. The FFT tells you the amplitudes and frequencies of a collection of sine waves that, when added together, would sound the same as the original waveform. In the first part of the experiment, you will study the sound of a tuning fork which produces a tone composed mainly of a single frequency. Next, you will observe the production of overtones on a tuning fork. Overtones are frequencies that are multiples of the fundamental. You will also analyze the sound produced when you say two vowels. An FFT graph will reveal that your voice is composed of a large number of individual frequencies. OBJECTIVES Use a Microphone to analyze the frequency components of a tuning fork and your voice. Record overtones produced with a tuning fork. MATERIALS Dell computer LabPro Logger Pro Vernier Microphone 2 tuning forks Part I SPEED OF SOUND PROCEDURE 1. Connect the Vernier Microphone to LabPro. 2. Prepare the computer for data collection by opening Exp 24 from the Intro Physics folder. A graph of sound level vs. time will be displayed. The time of data collection will be s. 3. You may need to adjust the trigger level for the michrophone. This adjustment can be found on the data collection dialog box. Data Collection button is next to the LabPro button on top right. 4. Close the end of the tube. This can be done by standing your text book against the end so it is sealed. Measure and record the length of the tube. 5. Use the thermometer at the front of the classroom and record the value in the data table. 6. Place the Microphone as close to the end of the long tube as possible, as shown in Figure 1. Position it so that it can detect the initial sound and the echo coming back down the tube. Sound Investigations 81

6 Sound Investigations Open end of tube Microphone Figure 1 7. Click to begin data collection. Snap your fingers near the opening of the tube. This sharp sound will trigger the interface to begin collecting data. 8. If you are successful, the graph will resemble the one below. Repeat your run as necessary. The second set of vibrations with appreciable amplitude marks the echo. Click the Examine button,. Move the mouse and determine the time interval between the start of the first vibration and the start of the echo vibration. If the start is difficult to define, you can use any unique spike in the original and reflected sound. Record this time interval in the data table. 9. Repeat the measurement for a total of five trials and determine the average time interval. Use an acceptable method to determine the uncertainty in your final value. Be prepared to show your work and defend it. ANALYSIS 1. Use the data you have collected to calculate the speed of sound. Include a correctly determined uncertainty. PROCEDURE PART II SOUND WAVES AND BEATS 1. Connect the Vernier Microphone to LabPro. 2. Prepare the computer for data collection by opening Exp 21 from the Intro physics folder. The computer will take data for just 0.1s to display the rapid pressure variations of sound waves. The vertical axis corresponds to the variation in air pressure and the units are arbitrary. Sound Investigations 82

7 Part II A Simple Waveforms Sound Investigations 3. Produce a sound with a tuning fork, hold it close to the Microphone and click. The data should be sinusoidal in form, similar to the sample on the front page of this lab. Strike the tuning fork with the rubber mallet. Striking it against a hard object can damage it. If you strike it too hard or too softly, the waveform may be too rough; try again. 4. Note the appearance of the graph. Count and record the number of complete cycles shown after the first peak in your data. 5. Click the Examine button,. Drag the mouse across the graph and record the times for the first and last peaks of the waveform. Divide the difference, t, by the number of cycles to determine the period of the tuning fork. 6. Calculate the frequency of the tuning fork in Hz and record it in your data table. 7. Drag the mouse across the graph and record the maximum and minimum y values for an adjacent peak and trough. 8. Calculate the amplitude of the wave by taking half of the difference between the maximum and minimum y values. Record the values in your data table. 9. Copy the data to Excel. Plot the data.using the speed of sound determined earlier, calculate the wavelength of this sound. Record on the graph (or under the graph) the sounds wavelength, amplitude, period, and frequency. 10. Save your data by choosing Store Latest Run from the Experiment menu. All data sets appear in the table unless you hide them. 11. Repeat Steps 3 9 for the second frequency. Remember to store data if you want to keep the most recently recorded data. Part II B Beats 12. Two pure tones with different frequencies sounded at once will create the phenomenon known as beats. Sometimes the waves will reinforce one another (constructive interference) and other times they will combine to a reduced intensity (destructive interference). This happens on a regular basis because of the fixed frequency of each tone. To observe beats, strike your tuning forks at the same time and listen for the combined sound. If the beats are slow enough, you should be able to hear a variation in intensity. If the beats are rapid, you may hear a third pitch emerge. 13. Collect data while the two tones are sounding. First, change the time duration for collection to about 0.3 s. You should see a time variation of the sound amplitude. Strike the tuning forks equally hard and hold them the same distance from the Microphone. When you get a clear waveform, choose Store Latest Run in the Experiment menu. 14. The pattern will be complex, with a slower variation of amplitude on top of a more rapid variation. Ignoring the more rapid variation and concentrating in the overall pattern, count the number of amplitude maxima after the first maximum and record it in a data table. 15. Click the Examine button,. Drag the mouse across the graph and record the times for the first and last amplitude maxima. Divide the difference, t, by the number of cycles to determine the period of beats (in s). Calculate the beat frequency in Hz from the beat period. Record these values in your data table. Sound Investigations 83

8 ANALYSIS Part II A Simple Waveforms Sound Investigations 1. In the following analysis, you will see how well a sine function model fits the data. The displacement of the particles in the medium carrying a periodic wave can be modeled with a sinusoidal function. Your textbook may have an expression resembling this one: y = Asin( 2π f t) In the case of sound, a longitudinal wave, the y refers to the change in air pressure that makes up the wave. A is the amplitude of the wave (related to loudness), and f is the frequency. Time is represented with t and the sine function requires a factor of 2π when evaluated in radians. Logger Pro will fit the function y = A * sin(b*x + C) + D to experimental data. A, B, C, and D are parameters (numbers) that Logger Pro reports after a fit. This function is more complicated than the textbook model, but the basic sinusoidal form is the same. Comparing terms, listing the textbook model s terms first, the amplitude A corresponds to the fit term A, and 2π f corresponds to the parameter B. The time t is represented by the x, Logger Pro s x-axis. The new parameters C and D shift the fitted function left-right and up-down, respectively and are necessary to obtain a good fit. Only the parameters A and B are important to this experiment. In particular, the numeric value of B allows you to find the frequency f using B = 2π f. Show the waveform from the first tone on plot. Select a region to fit with the mouse. Click the Curve Fit button,, select A*sin(B*x +C) + D from the list of model. Click to perform the curve fit. 2. Click to return to the graph. The model and its parameters appear in a floating box in the upper left corner of the graph. Record the parameters A and B of the model in this a data table. 3. Since B corresponds to 2πf in the curve fit, use the curve fit information to determine the frequency. Enter the value in your data table. Compare this frequency to the frequency calculated earlier. Which would you expect to be more accurate? Why? 4. Compare the parameter A to the amplitude of the waveform. 5. Fit the waveform of the second tone. Part II B Beats 6. Is there any way the two individual frequencies can be combined to give the beat frequency you measured earlier? Compare your conclusion with information given in your textbook. 7. The beats you observed in Run 3 resulted from the overlap of sound waves from the two tuning forks. How would the data you recorded compare to a simple addition of the waveforms from the forks individually? If the sound waves combined in air by linear addition, then the algebraic sum of the data of the individual waveforms should be similar to data of the beats. The following steps will help you perform the addition: Show Runs 1 and 2 and hide the other runs. These are the waveforms of the first two tones taken individually. Move the data to Excel. Place in adjacent columns. Add the two amplitude columns together. Plot. Compare this to the real data of the beats by moving Run3 into Excel and plotting. How is the sum similar to the real data? How are they different? Do the graphs support the model of additive sound wave superposition? What if the superposition rule were multiplicative? Would that change the graph? Sound Investigations 84

9 Sound Investigations 8. Most of the attention in beats is paid to the overall intensity pattern that we hear. Use the analysis tools to determine the frequency of the variation that lies inside the pattern (the one inside the envelope). How is this frequency related to the individual frequencies that generated the beats? PROCEDURE PART III TONES AND VOWELLS In this final section we will dispense with the focus on experimental technique and measurement. No errors are required. Qualitative observations are sufficient. Start a new worksheet. Answer the questions focusing on the physics of sound. Data from the measurements need to tabulated but only to aid in the understanding not to demonstrate good experimental technique. Part III A A Pure Tone 1. Prepare the computer for data collection by opening Exp 22 from the intro PhysicsLab folder. The display will include both a graph and an FFT window. The horizontal axis of the graph has time scaled from 0 to 0.05 s and the vertical axis corresponds to the variation in air pressure; the units are arbitrary. The FFT display has frequency on the horizontal axis scaled from 0 to 2000 Hz. 2. Using the same two tuning forks from part II, gently strike a tuning fork with a rubber mallet and hold it near the Microphone. Click to begin data collection. If you strike the fork too hard, it will create overtones, or a blend of higher frequencies in addition to the main frequency. 3. As you move the mouse across the FFT graph, record the predominant frequency as displayed. 4. Repeat Steps 3 & 4 with the second tuning fork. How does the FFT analysis of the two tuning forks compare with your earlier work with the two forks? Part III B Overtones on a Tuning Fork 5 In this step, you will make the tuning fork produce an overtone. This time, strike the tuning fork sharply with the wooden side of the mallet and listen to the sound. Describe the difference. 6 Strike the tuning fork sharply with the wooden side of the mallet and hold it near the Microphone. Click to begin data collection. The overtones damp away quickly so you must be sure to capture the sound immediately. 7 Compare the waveform and the FFT to the ones produced in Part I. Click the Examine button,. Move the mouse cursor across the FFT graph and determine the fundamental frequency and the strongest overtone. Record these values in the data table. Part III C FFT of Two Vowels 8 Hold the Microphone near your mouth, say the vowel e and hold it while you click the button. Print or sketch copies of the Graph Window and FFT Graph. 9 Repeat Step 12 and this time say o. 10 Have two students with very different pitches of voice say the vowels e and o. You may need to borrow a voice from a different lab group. Sound Investigations 85

10 ANALYSIS Sound Investigations 1. For each tuning fork, compare the frequency calculated from the waveform and the FFT to the value stamped on the tuning fork and that determined by part II of sound investigations. 2. Which overtone is produced on the tunig fork when it is struck sharply? 3. Describe the difference in the frequency structure between the two vowels examined in Part III C. 4. Compare and contrast the vowels spoken by the two different students. What characterizes the vowel sounds even when spoken by very different voices. Item Evaluation Speed of sound: several trials, uncertainty, comparison with known speed Simple waveform: amplitude, freq, period, ampl. tabulated with uncertainties. Simple waveform: amplitude, freq, amplitude tabulated with uncertainties using logger pro fitting. Comparison of above. Beat freq. and measured by location of peaks. Sum data from two frequencies in spreadsheet and compare to beat data. The faster frequency (beats data) measured. Question on this frequency's origin. Data and questions from Tones an Vowels. Emphasis on the physics of sound no evaluation of experimental technique. Sound Investigations 86