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• When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. These questions are designed to elicit ideas about sound. They will help you assess whether students really understand sound waves, how they travel, why they sound different, and so on. Continue discussion until all students have committed to ideas about these questions.
• Ask students the difference between transverse and longitudinal waves as a review.
• The video clip on the next slide shows the production of sounds waves, compressions and rarefactions, and the graph of pressure-position. Point out to students that the graph is simply a mathematical representation. It makes the wave appear to be transverse, so they must remember that each “crest” is really a compression or high pressure point.
• Students may think of ultrasound as a medical procedure instead of as high-frequency sound waves. Ask them if they have ever had been around someone during an ultrasound examination or treatment. Did they hear any sound?
• BEFORE SHOWING THIS SLIDE, ask your students if they have ever learned a method of determining the distance to the point where lightning strikes by watching and listening for the thunder. Some may know the rule (“Every 5 seconds is about a mile”) and some may have a wrong notion (“Every second is a mile”) or may not have any idea at all. After putting up this slide, ask them to calculate the time required for sound to travel a mile (1609 m). They should find the time required is 4.65 s (at 25°C). Since light arrives almost instantaneously, the time between lightning and thunder should be almost 5 seconds if the lightning is 1 mile away.
• Point out to students that this diagram shows circles, not spheres, since it is only a 2-D view. In reality, sound waves propagate out from the source in three-dimensional spheres. Ask students to imagine the spheres getting farther and farther from the source. Hopefully they will be able to see that the spheres become nearly flat and parallel. You might ask them why Earth appears to be flat. It is a sphere, but we are a great distance from the center.
• Before showing this slide, go to the website listed below: http://www.hazelwood.k12.mo.us/~grichert/sciweb/applets.html Choose “Sound” then choose “Doppler Effect 4”. This simulation allows you to place a sound source in the center and observe the waves while it is at rest. You can then ask the students: How would the sound compare for a person to the right and to the left of the source? How would the wave pattern change if the source is given a velocity to the right? How would the sound compare for the two observers now? At this time, you can drag out a small velocity arrow so the source begins to move. The ratio at the top is the speed of the source compared to the speed of the waves, so start with a value of about 0.3 and gradually increase it. it is interesting to see the effect of a speed greater than sound (ratio &gt;1). A “shock wave” can be seen, similar to the wake behind a speed boat. There are other interesting Doppler Effect simulations that are worth exploring at this web site.
• Students might say the sound is “louder” as the vehicle approaches and “quieter” as it moves away. This is true. But, it is not the Doppler effect. The Doppler effect refers to the observed change in pitch or frequency as the vehicle passes.
• Students might say the sound is “louder” as the vehicle approaches and “quieter” as it moves away. This is true. But, it is not the Doppler effect. The Doppler effect refers to the observed change in pitch or frequency as the vehicle passes.
• Sound is a longitudinal wave. All sounds occur as a result of vibrating objects. They may differ in frequency (pitch), loudness, or in other ways. Sounds can travel through any material (including solids, liquids, and gases), but not through a vacuum. The speed is greater in materials in which the molecules are tightly packed. The Doppler effect makes the pitch of the sound change when the source is moving. This is because the waves are more closely spaced (higher frequency) in front of the source of the sound as it moves.
• When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. Students may know of decibels as a measure of sound level. If so, explore their understanding of it. Try to fully explore their understanding of the concept of loudness before starting the lesson.
• Students should be able to deduce the equation for intensity from the definition. The equation is given on the next slide.
• Point out to students the bel levels are zero through 15, and each time the intensity goes up by a factor of 10, the bel level increases by 1. For example, between rustling leaves (1 bel) and a vacuum cleaner (7 bels) there is a difference of 6 bels, so the intensity is 106 greater or 1 million times greater. You can see this factor in the intensity column ( 1 x 10-11 to 1 x 10-5 or 1 000 000 times louder).
• Show the next slide to discuss the different combinations of frequency and intensity necessary to make sounds audible. Sounds with frequencies near 20 Hz or 20 000 Hz must be very intense in order to be heard.
• Point out the dB levels that would be assigned to the intensities on the left.
• Show students the video of the Tacoma narrows bridge collapse. A colorized and commented video is available at http://physics.kenyon.edu/coolphys/FranklinMiller/protected/tacoma.html The video is also available at wikipedia with slightly more footage.
• Show students the video of the Tacoma narrows bridge collapse. A colorized and commented video is available at http://physics.kenyon.edu/coolphys/FranklinMiller/protected/tacoma.html The video is also available at wikipedia with slightly more footage.
• Loudness measures the power (or energy per second) absorbed per square meter. It is called intensity. The units are watts/square meter, and these can be converted into decibels. To reduce the loudness, you can increase your distance from the source (r), decrease the power (P), or wear ear plugs to absorb some of the energy.
• When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. This is a difficult concept. Comments may center on the string instrument vs. the wind instrument. If so, ask them to clarify why the instruments would sound different even if they play the same note. You could also ask why a violin and a viola (both string instruments) sound differently when playing the same note. This elicitation may raise more questions than provide answers. That is a very worthwhile process. You may want to make a note of the questions raised and be sure they are answered before the end of this section.
• If possible, use the web site below prior to this slide. http://www.phy.ntnu.edu.tw/ntnujava/ Choose “Wave” and then choose “Superposition Principle of Wave.” Change the frequency of each wave to 5 (this will be easier to see). Observe the two waves as they overlap. Point out to students that the standing wave pattern is the only thing an observer would see because it is the resultant of the two component waves. The red wave appears to be standing still (not moving right or left). Pause the simulation and show them the nodes (points that never move because the two components always cancel) and the antinodes (points that have the maximum displacement in each direction).
• In order to see the wavelengths, trace a single path on the loop so students are not trying to analyze all five lines. Explain that these diagrams are like strobe photos showing five different positions for the wave as it moves.
• To show how standing waves are produced, go to the following web site: http://www.walter-fendt.de/ph14e/ Choose “Standing Waves (Explanation by superposition).” When showing this, pause and point out that the nodes are produced by waves that always cancel. This demonstration shows a six loop standing wave.
• Now that students understand why f1 = v/(2L), help them see why the wavelengths for the next three harmonics are as shown. It is helpful to look at just one segment of the wave instead of the four that are shown for each mode. Point out the “harmonic” terminology for each mode. These are sometimes called overtones instead of harmonics. The second harmonic is called the 1st overtone, and so on. Ask students to come up with a general equation for f in terms of v and L, using n where n represent the number of loops. Show them f1 = v/(2L), f2 = v/L, f3 = (3v)/(2L), and so on, and see if they see the pattern to write fn = ???? The answer is on next slide.
• Shorter strings (decreased L) have higher pitches. Higher-tension strings (increased v) have higher pitchers. More dense strings (decreased v) have lower pitches. Point out to students that v in the equation is the speed of the waves as they move back and forth on the string. It is not the speed of the sound. The speed of waves on the string ranges from 100’s to 1000’s of m/s depending on the string tension and density. The vibrating string then produces sound waves that travel at 346 m/s (at 25°C) through the air.
• Sound

1. 1. ++SoundChapter 12Pg.
2. 2. ++12.1Sound Waves
3. 3. ++ What do you think? • What is sound? • What do all of the sounds that you hear have in common? • How do they differ? • Can sounds travel through solids? Liquids? Gases? • Is one type of material better for transmitting sound waves? • When race cars or emergency vehicles pass you, the sound changes. In what way, and why?
4. 4. ++ What is Sound? Sound is a longitudinal wave. Allsound waves are produced by vibrating objects. Tuningforks, guitar strings, vocal cords, speakers The vibrating object pushes the air molecules together, forming a compression. Itthen spreads them apart, forming a rarefaction.
5. 5. ++ Graphing Sound Waves The diagram shows compressions (dark) and rarefactions (white). If you measured the pressure or density of the air and plotted these against position, how would the graph appear?
6. 6. ++ Characteristics of Sound Frequency is the number of waves per second. You have heard of ultrasound. What is it? Frequencies audible to humans are between 20 Hz and 20 000 Hz. MiddleC on a piano is 262 Hz. The emergency broadcast signal is 1,000 Hz. Infrasound frequencies are lower than 20 Hz. Ultrasound frequencies are greater than 20,000 Hz.
7. 7. ++ Pitch Pitch is the human perception of how high or low a sound appears to be. Pitch is primarily determined by frequency. Pitch also depends slightly on other factors. Higher frequencies appear to have a higher pitch when played loudly, even though the frequency does not change.
8. 8. ++ Speed of Sound Sound waves travel through solids, liquids and gases. In which would the speed generally be greatest? Why? Solids. Because the molecules are more closely packed, the particles respond more rapidly to compressions. How might the temperature of air affect the speed of sound waves? Why? Higher temperature increases the speed of the waves because the particles are moving faster and colliding more often.
9. 9. ++ Speed of Sound
10. 10. ++ Spherical Waves Sound propagates in three dimensions. The diagram shows: Crests or wave fronts (blue circles) Wavelength (λ) Rays (red arrows) Rays indicate the direction of propagation. How would these wave fronts appear different if they were much farther from the source?
11. 11. ++ Spherical Waves Wave fronts and rays become more nearly parallel at great distances. Plane waves are simply very small segments of a spherical wave a long distance from the source.
12. 12. + Doppler Effect An observed change in frequency when there is relative motion between the source waves and the observer. In our example, when the ambulance is moving there is relative motion between the ambulance and the two stationary observers.
13. 13. ++ Doppler Effect Why are the waves closer together on the left? Waves are closer because the vehicle moves to the left along with the previous wave. • For observer A the wavelength is less, so the frequency heard by observer A is greater than the source frequency. • Continued on the next slide….
14. 14. ++ Doppler Effect • Now for observer B the wave fronts reach observer B less often. So the wavelength is greater and the frequency heard by B is less than the source frequency.
15. 15. ++ Doppler Effect • How would the wave pattern change if the vehicle moved at a faster speed? How would it sound different? – At a higher speed, waves would be even closer together and the pitch difference would be even greater.
16. 16. ++ Now what do you think? What is sound? What do all of the sounds that you hear have in common? How do they differ? Cansounds travel through solids? Liquids? Gases? Isone type of material better for transmitting sound waves? When race cars or emergency vehicles pass you, the sound changes. In what way, and why?
17. 17. ++12.2 Sound Intensity and Resonance
18. 18. ++ What do you think? • Members of rock bands generally protect their ears from the loud sounds to prevent damage to their hearing. • How do we determine the loudness of a sound? • What quantity is loudness measuring? • What units are used? • Name three ways you can reduce the loudness of the music heard by a person in the audience.
19. 19. ++ Sound Intensity Vibrating objects do work on the air as they push against the molecules. Intensity is the rate of energy flow through an area. Power (P) is “rate of energy flow” - ΔE/t Since the waves spread out spherically, you must calculate the area of a sphere. A = 4π2r So, what is the equation for intensity?
20. 20. ++ Sound Intensity SI unit: W/m2 This is an inverse square relationship. Doubling r reduces intensity by ¼. What happens if r is halved? Intensity increases by a factor of 4.
21. 21. ++ Example Problem What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when the power output of the trumpet is 0.20W? P= 0.20W r = 3.2m 00 .2 W I t ni y= ne st π3 m 4 ( .2 )2 Intensity= 1.55 X 10-3 W/m2
22. 22. ++ Intensity and Decibels An intensity scale based on human perception of loudness is often used. The base unit of this scale is the bel. More commonly, the decibel (dB) is used. 0.1 bel = 1 dB,1 bel = 10 dB, 5 bels = 50 dB, etc. The lowest intensity humans hear is assigned a value of zero. The scale is logarithmic, so each increase of 1 bel is 10 times louder. An increase in intensity of 3 bels is 1 000 times louder.
23. 23. ++
24. 24. ++ Audible Sounds The softest sound humans can hear is called the threshold of hearing. Intensity = 1 × 10-12 W/m2 or zero dB The loudest sound humans can tolerate is called the threshold of pain. Intensity = 1.0 W/m2 or 120 dB Human hearing depends on both the frequency and the intensity.
25. 25. ++
26. 26. ++ Forced Vibrations Sympathetic vibrations occur when a vibrating object forces another to vibrate as well. A piano string vibrates the sound board. A guitar string vibrates the bridge. This makes the sound louder and the vibrations die out faster. Energy is transferred from the string to the sound board or bridge.
27. 27. ++ Resonance A phenomenon that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration.
28. 28. ++ Resonance Thered rubber band links the 4 pendulums. Ifa blue pendulum is set in motion, only the other blue pendulum will have large-amplitude vibrations. Theothers will just move a small amount. Since the vibrating frequencies of the blue pendulums match, they are resonant.
29. 29. ++ Resonance Bridges have collapsed as a result of structural resonance. Tacoma Narrows in the wind A freeway overpass during an earthquake http://www.youtube.com/watch?v=3mclp9QmCGs
30. 30. ++ Now what do you think? Members of rock bands generally protect their ears from the loud sounds to prevent damage to their hearing. How do we determine the loudness of a sound? What quantity is loudness measuring? What units are used? Name three ways you can reduce the loudness of the music heard by a person in the audience.
31. 31. ++11.4 Standing Waves & 12.3 Harmonics
32. 32. ++ What do you think? • A violin, a trumpet, and a clarinet all play the same note, a concert A. However, they all sound different. • What is the same about the sound? • Are the frequencies produced the same? • Are the wave patterns the same? • Why do the instruments sound different?
33. 33. ++ Standing Waves Standing waves are produced when two identical waves travel in opposite directions and interfere. Interference alternates between constructive and destructive. Nodes are points where interference is always destructive.  No motion happens here Antinodes are points between the nodes with maximum displacement.
34. 34. ++ Standing WavesA string with both ends fixed produces standing waves. Only certain frequencies are possible.A single loop = 12wavelengthThe one-loop wave (b) has a wavelength of 2L.The two-loop wave (c) has a wavelength of L.What is the wavelength of the three-loop wave (d)? 2/3L
35. 35. ++ Standing Waves on a String There is a node at each end because the string is fixed at the ends. The diagram shows three possible standing wave patterns. Standing waves are produced by interference as waves travel in opposite directions after plucking or bowing the string. The lowest frequency (one loop) is called the fundamental frequency (f1).
36. 36. ++ Standing Waves on a String Tothe left is a snapshot of a single loop standing wave on a string of length, L. What is the wavelength for this wave? Answer: λ = 2L What is the frequency? Answer: f1
37. 37. ++
38. 38. ++ Harmonics n is the number of loops or harmonic number. v is the speed of the wave on the string. Depends on tension and density of the string L is the length of the vibrating portion of the string. How could you change the frequency (pitch) of a string?