Ph 2306 Experiment 2: A Look at Sound

Transcription

1 Name ID number Date Lab CRN Lab partner Lab instructor Ph 2306 Experiment 2: A Look at Sound Objective Because sound is something that we can only hear, it is difficult to analyze. You have probably seen drawings on the chalkboard that mimic what sound waves look like. In this investigation, we will try to force ordinary sound waves to become visible to us so that we can make measurements and try to describe these waves more precisely than what our ears normally allow us to do. Required background reading Young and Freedman, sections 16.1, 16.2, 16.4, 16.7 Introduction Sound is a longitudinal wave in a medium. The most familiar sound waves to us are those that propagate in air. The sound wave propagates as a pressure wave in the air. The pressure fluctuations cause a variation of the density of the air molecules along the path of the sound wave. The most extreme points are the compressions (points of greatest pressure and density) and rarefactions (points of lowest pressure and density). In this lab you will study sound waves using a microphone which converts the pressure differences into an electrical voltage that you can plot versus time. So you will get a good visual picture of how the pressure variations behave in sounds waves of various frequencies. You can also use the microphone to study the velocity of sound by generating a short duration sound burst and measuring the time it takes to travel a known distance. Finally, you can use the microphone to observe what happens to the amplitude of the total sound wave for two sounds close in frequency, a phenomenon called beats. 1

2 Name ID number Lab CRN Lab TA name Ph 2306 Experiment 2 Prelab assignment (complete and turn in at the beginning of your lab session) 1. You snap your fingers at the open end of a 1 meter long tube that is closed at the other end. With a microphone at the open end, you determine that it takes 5.8 msec between the time you snap your fingers and the echo from the closed end is detected. Based on this information, calculate the speed of sound in air. 2. You are studying standing sound waves in an organ pipe of length L with both ends open. a) What wavelengths of sound can exist as standing waves in this pipe? Express your answer in terms of the length L. b) Assume that the length of the organ pipe is L = 24 cm. You have excited a standing sound wave in the tube, and you observe that it has displacement nodes at 4 cm, 12 cm and 20 cm measured from one end of the pipe. In which harmonic, n, is the air in the pipe oscillating? c) What is the frequency of the musical tone produced by the organ pipe in the situation described in part b)? 2

3 3. You are studying standing sound waves in an organ pipe of length L with one end open and one end closed. a) What wavelengths of sound can exist as standing waves in this pipe? Express your answer in terms of the length L. b) Assume that the length of the organ pipe is L = 20 cm. You have excited a standing sound wave in the tube, and you observe that it has displacement nodes at 0 cm, 8 cm and 16 cm measured from the closed end of the pipe. In which harmonic, n, is the air in the pipe oscillating? c) What is the frequency of the musical tone produced by the organ pipe in the situation described in part b)? 3

4 Equipment o Pasco 750 Interface and DataStudio Software a. Pasco sound sensor (microphone) b. Pasco temperature sensor o Set of Tuning forks and mallet a. 256 Hz (middle C on piano) b. 288 Hz (D) c. 320 Hz (E) d Hz (F) e. 384 Hz (G) f Hz (A) g. 480 Hz (B) h. 512 Hz (C one octave higher than middle C) o Telescoping sound tubes with end caps a. Short tube cm long. b. Long tube cm long o Stand with clamps o 2-Meter stick Activity 1: The Nature of Sound In this activity, you will use equipment that will allow you to observe visually the time dependence of a sound wave. Locate the Pasco sound sensor on your lab tabletop. This sensor has a microphone that senses the pressure variations in the sound wave and converts them to an electrical signal. This microphone is called an electret condenser microphone. It consists of a movable electret membrane next to a fixed metal electrode. The pressure variations in the sound wave cause the movable membrane to vibrate relative to the fixed membrane. This changing separation causes the electrical capacitance to change, so an electrical signal proportional to the pressure vibrations is generated. (Note: you ll learn more about capacitance later in the term). The pressure variations in a sound wave have a typical period that is in the millisecond time range. So it is necessary to be able to rapidly record the voltage values from the sound sensor as a function of time. The DataStudio program has an oscilloscope mode that can do this (note: you will use the real oscilloscope on the shelf on your lab table later in the term). On your computer click through the following Class Notes 2306 Setup Files lab 2 Sound and open the sound1.ds DataStudio file. What you see is the oscilloscope mode of DataStudio. This is similar to graphs you ve seen before, except that the oscilloscope is looking at a much finer time scale than what we ve done before. On the bottom of the screen is the time scale, showing you that each horizontal division of the screen is equal to 5.0 ms (0.005s). This can be changed by clicking on the triangular buttons immediately next to the ms/div label. Because this time scale is so small, DataStudio must sample very quickly. You can change the vertical scale using the buttons in the upper right hand corner; in the start-up mode it is set to 1 volt per vertical 4

5 division. You will want to adjust both the horizontal time scale and vertical voltage scale as needed during data-taking to have the waveform fill as much of the screen as possible. The other primary difference between the oscilloscope ( scope ) and a traditional plotter graph is that the scope continuously samples data and redisplays it on the screen. Because of this, the scope is most useful when the signal being detected is repetitive. If it weren t, we would just see a blur of noise on the screen. However, with a regular pattern, we witness a very smooth set of shapes being traced across the screen. The sound sensor should be connected to port B of the 750 interface. When you click on the Start button, the scope will look for a signal from this microphone and display it for you on the screen, so long as it is regular and intense enough. In a sense, the scope will show you a snapshot of what sounds look like. When you click on STOP, the screen will freeze the waveform that is being displayed. The Smart Tool allows you to analyze your data by determining coordinate locations on the graph. At this point, you can click on the Smart Tool (upper left button in the row of buttons) to analyze the data. You will see in the middle of the graph the smart tool marker which looks like cross hairs with a box around them. As you drag the box around the graph the coordinates are displayed. An additional feature of the Smart Tool is the delta feature. It allows you to look at differences between coordinates. Drag the cross hair on top of the first data point. Click and drag the corner of the box to display the change in the coordinate values. With this tool you can calculate the time for one cycle of the wave. This, as you probably know, is the period (T) of this wave. And, the frequency (f) of a wave is simply equal to the inverse of the period: 1 f = T Locate the set of tuning forks. When you strike a tuning fork gently with a rubber mallet, it will produce almost a perfect pure tone at the frequency marked on the base. To hear it you need to hold it close to your ear. Select a tuning fork, strike it gently with the rubber mallet, and hold it next to the sound sensor. (Note: if you strike the tuning fork with a sharp rap, or with the wooden handle of the mallet, you will observe you will observe many higher frequency waveforms in the sound wave. So make sure you tap it gently enough so you only see a sinusoidal waveform with a single frequency). Observe the waveform on the DataStudio oscilloscope. Make adjustments to the horizontal time scale and vertical voltage scale to generate a snapshot of the waveform that will make it convenient to measure the period. The scale should be set so that about five cycles are displayed on the screen. When you are happy with your waveform, click stop data-taking and the final waveform will be preserved on the screen. You can use the Smart Tool to determine the period of the waveform. Print out your oscilloscope screen and include it after this page. (To print out do the following: Under the File menu click on Save Activity As. Save it to a filename on the Desktop that includes your name. Close DataStudio and reopen it using the file you saved. Then click on Print in the File menu. The reason for saving it to a file with your name is so that your plot has a name on it to distinguish it from the other 5

6 print-outs. You can pick up your printout on one of the four printers at the back of the lab room). Include the printout right after this page. Question 1-1: Determine the frequency of the tuning fork from your oscilloscope image. Show your calculations. Also, be sure to indicate what frequency and musical note is stamped on the base of the tuning fork you used. Compare your calculated value for the frequency of the tuning fork with the value stamped on it using a percent difference calculation. If you see a difference that is larger than about 15%, consult with your TA. faccepted fmeasured % difference = 100 faccepted The waves you observed last week were transverse waves, meaning the displacement of the medium (the string in that case) was perpendicular to the direction of travel of the wave. In contrast, sound is a longitudinal wave, meaning the displacement of the medium (the air in this case) is parallel to the direction of travel of the wave. The next question will demonstrate this for you. Question 1-2: Click on the Physlets link on the computer desktop and run Illustration Run both animations. What happens to an individual air molecule as a sound wave is passing by? Activity 2: Measuring the Speed of Sound with an Echo In this activity, you will use the microphone and a long telescoping sound tube to measure the speed of sound. Loosen the nylon set screws on the long telescoping sound tube and extend it to its longest length. Gently tighten the screws again (please tighten the screws on any of the sound tubes in this lab gently; there is no need to tighten them excessively). The end cap should be inserted into the tube with its set screw tightened gently. The sound tube with the end cap in place becomes an excellent echo chamber. Sound can travel to the end of the tube and reflect back out again. If the total distance that 6

7 the sound travels is known, and the time it takes this sound to travel is known, the speed can be easily measured. Open the experiment file sound2.ds and set up the microphone with the stand and clamp assembly on the edge of the table so it is very near the opening in the sound tube. There should be enough room between the sound tube and the microphone so that you can fit a hand snapping its fingers or two hands clapping. The photo below shows an example of a good setup for doing this. When you click the Start button, DataStudio will begin collecting data as soon as the microphone senses an adequate signal. A nice clean snap will trigger the data taking as the sound passes the microphone and good echo is usually recorded. (It can take several tries to get this to work well; if you are having trouble getting good echoes, make sure the microphone is very near to the exit of the tube so that it can pick up the faint echo.) Watch for a second signal that looks similar to the first, but trails behind by a few thousandths of a second. This is the echo. You must determine how far this echoed sound wave had to travel in that amount of time. (Use the Smart Tool to measure time differences.) Print out your graph to the printers in the back and include it after this page. Be sure to scale your graph so that the details can be fully seen in your printout. This can be done by the controls in the upper right hand corner of the scope window. Question 2-1: Using the information obtained above (along with any other measurements you need to make), calculate the speed of sound. Show your work below: 7

8 Question 2-2: This speed of sound is temperature dependent. In air an approximate calculation of the speed of sound can be made with the following equation: ν s = Τ where Τ is measured in degrees Celsius and the resulting velocity is in meters per second. To measure the temperature, use the Pasco temperature probe. You can read it out by opening the DataStudio file sound3.ds. Use this value of the temperature to compute the theoretical speed of sound in the air in the lab. Compute the percent difference between your measurement and this theoretical value. Question 2-3: You measured the speed of sound in air at a given temperature and pressure. What difficulties (besides not being able to breathe) would you encounter if you tried to measure the speed of sound in a vacuum? Why? Activity 3: Standing Waves in a tube As you already discovered in last week s laboratory activity, a standing wave is produced when a wave reflects at some boundary so that the reflected portion of the wave continually interferes with the incoming portion of the wave. In music, we rely on these standing waves to produce selected pitches from piano strings, organ pipes and even drumheads. In this activity, you will make a simulation of an organ pipe to study how standing waves are produced in air. You have available to you two telescoping sound tubes. You already used the longer one to measure the speed of sound using an echo earlier. These tubes will be used to simulate how an organ pipe makes sounds. 8

9 Question 3-1: Before you make sound waves in a tube, recall from last week s lab the conditions that had to exist for a standing wave to exist on a string with both ends fixed. For a given length string L, what is the condition so a wave of wavelength λ would produce a standing wave on the string? Prediction 3-2: From your earlier calculation of the speed of sound based on the temperature, predict the wavelength of a 512 Hz (C) tuning fork. Question 3-3: Take the short tube and loosen the set screws so that the two inner tubes can slide freely. Remove the end cap from the tube so that both ends are open to the air. Strike the tuning fork with the rubber mallet and place it near the end of the tube. Slide the tubes in and out until you hear a sharp increase in the amplitude of the sound. This is called the resonance condition for the tube and corresponds to when a standing wave is set up in the air of the tube. Record the length of the sound tube below. How does the ratio of the length of the sound tube compare to the wavelength of the 512 Hz tuning fork in air? Question 3-4: This standing wave is similar to the standing waves that you made last week on a string with both ends fixed. In last week s lab you had a fixed length string and for a given tension in the string you found the frequency that would produce a standing wave (resonance) on the string. With the sound tube you have a fixed frequency of sound produced by the tuning fork and a fixed wave speed. You can adjust the length of the tube to produce a standing wave (resonance) in the air in the tube. How are the resonance conditions in the fundamental mode similar for a string and a tube that is open at both ends? 9

10 Prediction 3-5: Predict the length of tube (open on both ends) that would be required to resonate with a 256 Hz tuning fork. Question 3-6: Test your prediction by taking a sound tube (of the appropriate length) and adjusting its length to the predicted length. Strike the tuning fork with the mallet and place it near the end of the tube. Adjust the tube in and out until resonance is achieved. Measure the length of the tube and compare it to your prediction. Question 3-7: Replace the end cap in the short tube and with the 512 Hz tuning fork find the resonance condition that a tube that is closed on one end will resonate. Record this length below. How is the length of the tube related to the wavelength of the 512 Hz sound wave? (Hint: you may need to remove the inner most tube to get a short enough tube.) Question 3-8: How do the resonance conditions (in the fundamental mode) for a tube open at both ends compare to those for a tube with one open and one closed end? In an organ pipe, standing waves can be set up that show a pattern of displacement nodes and antinodes. Displacement nodes and antinodes refer to points where air particles have zero displacement and maximum displacement, respectively. As you learned in class, standing waves in a tube, exhibit a series of normal modes, labeled by an index n. These normal modes represent the various frequencies that will resonate on a given length sound tube. This series of frequencies is known as a harmonic series. For example if a 100 Hz sound will resonate in a given tube then a 200 Hz sound will also resonate in that same tube. This is identical mathematically to the normal modes on a string fixed at both ends. 10

11 Question 3-9: Where must the displacement nodes and antinodes exist for resonance to occur in a tube closed at one end? Where must the displacement nodes and antinodes exist for resonance to occur in a tube that is open on both ends? On the diagram below indicate the location of the nodes and antinodes, for the first harmonic mode in a tube. Closed tube Open tube Prediction 3-10: Set up a sound tube with both ends open that is the length that you observed in Question 3-6. Verify again that you get resonance for a 256 Hz tuning fork in this configuration. Will other tuning forks of other frequencies resonate in the tube at (approximately) this length? Among the tuning forks in your set, which other one should resonate at this length? Question 3-11: Test your prediction from Adjust the length of the tube until you hear resonance; what length tube resonates? Did you have to change the length very much to get resonance? (You will probably find that you had to change the length a little bit; this is because the actual anti-node is not quite at the end of the tube the actual location varies a little bit with wavelength). Question 3-12: Based on your experiments, write a general formula that relates the allowed standing wavelengths to the length of the tube L for a) a tube with both ends open b) a tube with one open and one closed end 11

12 Activity 4: Beats The phenomenon of beats occurs when two different waves of equal amplitude but slightly different frequency interfere. Musicians are very familiar with this. When their instrument is slightly out of tune they notice a rising and falling of the intensity of the sound when their instrument is slightly out of tune with some reference standard (like a tuning fork). In this activity you will both hear and see (with an oscilloscope) beats. On your computer click through the following Class Notes 2306 Setup Files lab 2 Sound and open the sound4.ds DataStudio file. You will see a two panel display. This utility is both a sound creator and sound analyzer. Here are some details about its use: The sound creator will generate two sounds of different (selectable) frequencies. You can see the frequency of each sound by clicking on the red or green dot in the upper left side. The frequency of each sound can be adjusted by appropriate clicking on the buttons at the top of the screen. The top panel displays the wave form of each of the two sounds separately. The bottom panel displays the sum of the two waveforms. To turn the sounds on, click on the loudspeaker icon in the lower left corner. You can turn on or off each of the two sounds by clicking on the dot next to the loudspeaker icon. Before generating sounds, set the volume control of the computer to about 1/3 of maximum. The sounds will then be loud enough for you to hear but not so loud that they disrupt other lab groups. Question 4-1: First try two frequencies that are very close (say and Hz). Describe how the intensity of the sound you hear varies with time. Question 4-2: Now try two frequencies that are separated a little further (say and Hz). Describe how the intensity of the sound you hear varies with time. What is the main difference between the two cases? 12

13 Question 4-3: Explain the variation in the intensity of the sound when two sounds that are similar in frequency are made together with the same amplitude. (Hint: Think of the phase relationship between two waves when there is constructive and destructive interference.) Question 4-4: Now you will do some quantitative analysis of a beat frequency. Set the sound creator to produce two sounds of frequencies 400 Hz and 410 Hz. Adjust the time scale on the lower plot so that the maximum time is about 0.40 seconds. You should see the amplitude of the combined sound waves rise and fall. These patterns are called beat envelopes. This display will allow you to determine the period of time it takes for the two waves to move into and out of phase with each other. The beat period is defined as the time elapsed between two points of maximum amplitude (or two points of minimum amplitude). Calculate the period of the beat envelopes. When you are happy with what you have, you can click on the loudspeaker icon to turn the sound off and the last waveform will remain frozen on the screen. Print out a copy of this and include it after this page. Show on the graph how you determine the beat period. Write your result for the beat period below and calculate the beat frequency (the reciprocal of the beat period) from it. Show your calculations below. How do your results compare with the prediction for the beat frequency from your textbook ( f = f f )? beat a b 13

14 When there are 10 minutes left in the lab, please stop what you are doing and skip to these questions. These are questions intended to emphasize some of the concepts you have dealt with in the lab session today. Post lab questions 1. What is the condition that must exist at the closed end of a resonant sound tube? What wavelengths would resonate in such a tube (closed at one end and open at the other), expressed in terms of the length of the tube L? 2. How would you need to adjust the length of a resonance tube if the air temperature increased in the room (so that it continues to resonate at the same frequency)? How does this relate to warming up a wind instrument before playing a concert? 14