Physics Traditional 1213 Williams. Waves & Sound. Chapters 11 & 12. Page 1

Transcription

1 Physics Traditional 1213 Williams Waves & Sound Chapters 11 & 12 Page 1

2 Concept Map Some (not all) Waves/Sound Connections Page 2

3 Name: No: Super Slinky Lab! Purpose: The purpose of this lab is to explore and investigate the properties of mechanical waves using a giantsized 25 foot slinky lots o phun! Materials: Super Slinky and holder, small piece of masking tape, stopwatch. CAUTION: PLEASE DON'T kinky your slinky! Do NOT let go of your slinky so it goes flying at your partner! If you overstretch, tangle, or damage your slinky you will have to pay a laboratory replacement fee for your slinky! Be nice to your slinky and your slinky will be nice to you!! Part 1: Transverse vs. Longitudinal Waves Energy in Motion! 1. Have two lab partners stretch out the slinky about 10 feet in the hallway so there is a medium-level of tension in the slinky so you can see good wave patterns as directed by your teacher. Line your slinky up with the tiles in the hallway as a way to reference the resting equilibrium point of your slinky. You may need to gather up more coils at the end or slide further or closer apart to adjust the tension. 2. Optional: Put a small piece of masking tape on a coil towards the middle of your slinky on top as a visual reference point. 3. Snap your wrist with a sharp flick sideways along the ground about 1-tile to generate a transverse pulse. Be sure your partner holds the other end fixed so you get a clean reflection of a pulse as the wave travels. Observe the motion of the pulse and the coil's vibrations. Remember: When something vibrates, it moves back and forth because of a restoring force of some kind, like a spring bounces up or down, or a guitar string moves back and forth after being struck. Repeat as necessary to generate a series of pulses in order to better observe the wave motion. When you are done, be sure to remove the tape and throw it away. For a Transverse Wave, the vibration of the coils is (perpendicular / parallel) compared to the motion of the wave. [Circle one]. 4. Now, gather a few bunches of coils and pluck your slinky to generate a Longitudinal pulse as shown in the diagram on the right. Observe the motion of the pulse and the motion of coils. Repeat as necessary to generate a series of pulses in order to better observe the wave motion as well as the vibration. For a Longitudinal Wave, the coils vibrate (perpendicular / parallel) compared to the motion of the wave. [Circle one]. Part 2: Reflection of a Wave from a Fixed End Bounce! 5. Have your partner hold one end of the slinky fixed. Send a Transverse pulse to the rigid end and observe the phase of reflected pulse does the pulse bounce back on the same or on the opposite side? Make a sketch of what happens on diagram on the right on the dotted line of the reflected pulse. the side the Page 3

4 Part 3: The Speed of All Waves of the Same Kind in a Given Medium 6. Generate a Transverse pulse in the coil by having one person stretch the Wave Amplitude Time (seconds) slinky with an amplitude of 1 tile. Your partner should keep their end fixed so that the transverse pulse reflects back. Have a 3 rd person time how 1 Tile long it takes for the pulse to travel one round trip. Repeat for timing a pulse 2 Tiles with an amplitude of 2 tiles and then 3 tiles and record your data. What do you notice about the size (amplitude) of the wave does it 3 Tiles significantly affect the speed of the wave? For your voice amplitude is loudness. How many tiles represents a whisper? A shout? (Yes / No) [Circle One ] Part 4: The Interference of Waves Unlike masses, waves are energy and two waves can occupy the same space at the same time - INTERFERENCE! 7. Constructive Interference: Have each partner generate a wave that has an amplitude of 1 tile in the same direction on the ground by stretching your slinky sideways from the center equilibrium line. Release the pulses at the same time and observe what happens when the waves collide. Sketch what happens on the diagram. (Hint: The waves either combine and get bigger or get smaller) 8. Destructive Interference: Have each partner generate a wave that has an amplitude of 1 tile in the opposite direction on the ground by stretching your slinky sideways from the center equilibrium line. Release the pulses at the same time and observe what happens when the waves collide. Sketch what happens on the diagram. (Hint: The waves either combine and get bigger or get smaller) Part 5: Resonance & Standing Waves Shake It Baby! 9. Generate a standing wave by having your partner hold their end fixed and you shaking your end along the ground until you reach the right rhythm (kind of like spinning a jump rope) so that you generate a standing wave with 1 antinode (a big hump in the middle like in the diagram below) this is called the 1 st Harmonic for your slinky wave. Time how long it takes for you to shake back and forth 10 complete cycles and record on your data table below. Then determine how long it takes for just 1 cycle. Then try generating the 2 nd and 3 rd harmonics by making more antinodes. If you have trouble generating the 1 st, 2 nd, or 3 rd harmonics, then just try generating any 3 harmonics and write down below on the table which ones you did st Harmonic 2 nd Harmonic 3 rd Harmonic Time for 10 cycles: Time for 10 cycles: Time for 10 cycles: Time for 1 cycle: Time for 1 cycle: Time for 1 cycle: What do you notice about the time for 1 cycle to generate standing waves how do the times compare for the 1 st, 2 nd, and 3 rd harmonics of your slinky change as you generate higher and higher harmonics? Guitar strings work exactly like our slinky does. Can YOU make a 2.5 harmonic with your slinky? WHY would it not be possible for a guitar to make a 2.5 harmonic? Page 4

5 Name: No: Music & Resonance 1. Any object can generate sound as long as it can vibrate & disturb a medium to set up oscillations in pressure. 2. Musical sounds arise when sounds are resonant in nature that is standing waves are generated because the driving source matches the natural vibrating frequency of the medium resulting in waves with large amplitudes at the antinodes and zero displacement at nodes. 3. The simplest standing wave set-up in an object is called the 1 st harmonic or the fundamental and is often the dominating wave present because of its simplicity. 4. Successive resonant frequencies are known as harmonics. The second simplest standing wave set-up in an object is called the 2 nd harmonic or 1 st overtone. 5. Overtones are the successive resonant frequencies that occur in an object and often accompany the fundamental in varying amounts resulting in the unique timbre, or character, of each unique instrument (such as a saxophone vs. a piano) or person s voice (such as distinguish your Aunt Harriet s voice vs. Mel Gibson s). 6. Note that successive harmonic frequencies are simply multiples of the fundamental frequency. Name of Standing Wave & Frequency (Harmonic / Overtone) Fixed End System Free End System Asymmetrical System (1 End Closed-Pipe) 1 st Harmonic (Fundamental f 1 ) 2 nd Harmonic (1 st Overtone f 2 ) 3 rd Harmonic (2 nd Overtone f 3 ) 4 th Harmonic (3 rd Overtone f 4 ) 5 th Harmonic (4 th Overtone f 5 ) Page 5

6 How a Guitar Makes Loud sounds (strings alone would be very quiet!) i. The interaction looks roughly like this: (Low Frequencies) (High Frequencies) Schematic of Frequency-dependent Component Oscillations. Arrows show main direction of vibratory interaction. Note that some of these influences act in both directions as mechanical feedback, eg. Bridge vibration affects the string's motion as a secondary influence Page 6

7 Physics of Musical Scales Western Just Diatonic Scale (secret = whole number ratios) C 4 # D 4 # F 4 # G 4 # A 4 # do re mi fa so la ti do C 4 D 4 E 4 F 4 G 4 A 4 B 4 C 5 D 5 E 5 F Hz 297 Hz 330 Hz 352 Hz 396 Hz 440 Hz 495 Hz 528 Hz 594 Hz 66o Hz 297/264 = 9/8 330/264 = 5/4 352/264 = 4/3 396/264 = 3/2 440/264 = 5/3 Frequency Ratios 495/264 = 15/8 528/264 Octave = 2 Equally Tempered Scale (secret = 12 steps of the semitone ratio= 2^(1/12)= ) C 4 # D 4 # F 4 # G 4 # A 4 # do re mi fa so la ti do C 4 D 4 E 4 F 4 G 4 A 4 B 4 C 5 D 5 E 5 F Hz Hz Hz Hz Hz Hz Hz Hz (Why it works = double your frequency in an octave of 12 steps = 2^(1/12)^12 = 2!) Page 7

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12 harmonics 1. Decide if each instrument is open-open, open-closed, or closed-closed. 2. Draw the smallest part of a wave which fits in the tube. 3. Write the equation for L and. 4. Find the fundamental frequency for each instrument. a) flute b) violin c) clarinet (a reed instrument) L = L = L = f = f = f = d) drums e) palm pipe /organ f) xylophone L = L = L = f = f = f = Page 12

13 Sound: Loudness, Intensity and Relative Intensity Consider an automatic toast-butterer. This soon-to-be-patented device ejects melted butter onto waiting pieces of toast. If a single piece is place before the machine, it gets a pretty thick layer of butter. If four slices are placed a bit farther away, the butter will spread a bit thinner but will cover all four. If sixteen slices are placed even farther away, the layer of butter will be quite thin. Thus the finite amount of butter gets spread thinner and thinner as it is required to cover a greater and greater surface area. Similarly, as sound waves expand from their source, their energy and power (energy per second) is spread out more and more. The measure of how much power the sound waves have at a particular location is called Intensity. I = P / A Because sound waves expand spherically, the area the energy is spread over is 4 r 2. So: I = P / (4 r 2 ) where P = power of sound wave in watts r = radius (how far the detector is from the source) The human ear can detect noises with as low an intensity as W/m 2, and the threshold of pain is about 1 W/m 2. Because of the enormous range of values of Intensity, we use a logarithmic scale called Relative Intensity, with all measurements being compared to the threshold of hearing, zero decibels. As a noise goes up the scale by ten decibels, its Intensity increases by a power of ten. A noise which increases by 30dB has 1000 times more intensity, which means there is 1000 times more energy than before. There is a chart to convert between Intensity (W/m 2 ) and Relative Intensity (db). But a noise which increases its intensity by 30dB doesn't sound 30 times louder. Each rise of 10dB makes a noise sound twice as loud as before. So, a 30dB increase in noise level means it sounds 2x2x2 or 8 times louder to a human listener. See if you can answer these questions using the charts on the next page. 1. How much louder is a mosquito buzzing than rustling leaves? 2. How much more intense are the sound waves of a mosquito s buzz than those of rustling leaves? 3. How much louder is a vacuum cleaner than conversation? 4. How much more intense are the waves of a vacuum than conversation? 5. How far must a dolphin which emits sound at a power of.050w be from an underwater microphone if the resulting noise is recorded at 10dB? Hint: convert 10dB to intensity first. Answers: 8 times; 1000 times; 4 times; 100 times; 19,900 meters Page 13

14 Relative Intensity (Decibels) Intensity (W/m 2 ) Intensity vs. db values with real-world examples Sound source Intensity level (d ) Threshold of hearing x Rustling leaves x Quiet whisper x Whisper Mosquito buzzing x Normal conversation A/C at 6 meters x Vacuum cleaner Busy traffic x 10-9 Lawn Mower Subway; ipod at max x 10-8 Front row rock concert Threshold of pain x 10-7 Thunderbolt/machinegun Military jet takeoff x 10-6 Eardrum perforation , , , , x 10 6 Page 14

15 Audacity Tip Sheet Begin the lab by turning on the computer and plugging in the microphone. Double check the microphone and make sure that if it has an on/off switch it is turned on (not all microphones have an on/off switch). Throughout this lab we will be using the program Audacity, which is a freeware sound recording and editing program ( and so to do this lab well you need to be familiar with how Audacity works. To begin, click on the start menu and find Audacity, start the program and the following screen should appear. Editing Tools Playba ck Copy & Paste Volum e Input Device Zoom Control Sample Rate Selection Info The first thing we have to do is make sure that the settings are correct for recording. To do this, start with making sure that the input device is set to Microphone and that the volume control for the microphone is set about halfway (if the recording comes back distorted too loud or too soft be sure to adjust this setting accordingly). Next look at the sample rate in the lower left corner and check that it is set to Hz, this audio setting will give us good quality sound without causing the audio file to be too big. Page 15

16 Finally we re ready to record, so go ahead and hit the record button (the red circle in the playback controls) and say something into the microphone (something like I love physics! or Physics rules! would definitely be appropriate). Once your done speaking click the stop button and you should be able to see your voice like below. Go ahead and play it back, you probably sound pretty funny! Next we are going to see what kinds of things Audacity can do to a sound. Click and drag on your voice sample to highlight it. Then click on the Effect heading to see a bunch of transformations that Audacity can do. For each of the following transformations click on it, play the transformed sound, and then click on Edit Undo to get your original sound back. Page 16

17 Audacity Sample Calculations 1. The wave above appears square because it was a loud whistle which overwhelmed the microphone. a. What is the frequency of the wave above? b. This was taken at room temperature of about 25 C. What was the wavelength of this wave? Page 17

18 2. I made this voice print of me going meeeeeeeeeeeeeeeeeeeeeeeee. A low voice for me is about 85 to 90 Hz and a high pitched voice for me is about 250 Hz. Show whether I was making a high or low pitched voice (do the math). Page 18

19 Names: Find the speed of sound in a metal rod Your instructor will demo how many waves or what portion of a wave resonates on a metal rod. Takes notes on how it s known where the nodes and antinodes are and therefore how many waves are on the metal rod. Figure for yourself how to find the speed of sound (hint: what do you need to find wavespeed?). Rod material (steel, alumunim?) Equation you used Your calculations (draw a sketch too) Final answer (with units) for the speed of sound in your metal! Page 19

20 Audacity lab Class demo/lab due at end of class (one per group), take additional notes in journal to study for lab quiz 1. Do tuning fork together (share file, show how to adjust mic sensitivity and clear old file, use your headphones if you want to hear) waves Stamped frequency Hz Measured frequency = f = = = Hz sec. 2. Determine speed of sound in steel as a class (need bar and meter stick, share same file) a. Prove where node is b. Prove bar length is what fraction of a wavelength in bar (draw a pic) c. Do calculation on Audacity (below) 3. Flute plays G: Determine frequency of 1 st and 2 nd harmonics. Draw a picture of waveform showing both. In pairs 4. Using your tuning fork, write down the stamped frequency and use Audacity to measure the actual frequency. Make sure you don t create square waves and use proper technique (strike against sole of shoe, partner helps determine how close to microphone to get good waveform) waves Stamped frequency Hz Measured frequency = f = = = Hz sec. 5. Determine the speed of sound in an aluminum bar (need bar & meter stick) a. Length of bar meters, b. Number of waves in fundamental (1 st harmonic) for bar = c. Calculate speed of sound (show work below) Speed of sound in aluminum = m/s Page 20

21 Mystery Tone Plain sheet of paper you turn in. You will get an example of a Mystery Tone. You will hear it twice. Record it and find its frequency. Points will be awarded according to how close you are to the real frequency and the sense of your calculations. Turn in one paper with you and your partner s name. Show all work! Page 21

22 Waves Practice Problems Label the parts of the following wave. Include crest, trough, amplitude, and wavelength. Is this a transverse wave or a longitudinal wave? Label the parts of the following wave. Include crest, trough, and wavelength. Is this a transverse wave or a longitudinal wave? For these following problems, presume the speed of sound in air is 340 m/s and the speed of waves in a guitar string is 5000 m/s. 1. A pipe is.24 m long and open at both ends. a. What is the picture of the first harmonic? b. What is the fundamental frequency for this instrument? c. What is the picture of the second harmonic? d. What is the frequency which is heard at the second harmonic? 2. A second pipe is.38m long and is closed at one end. a. What is the picture of the first harmonic? Page 22

23 b. What is the fundamental frequency for this instrument? c. What is the picture of the second harmonic? d. What is the frequency which is heard at the second harmonic? 3. A guitar s strings can produce frequencies ranging from 330 hz to 1320 hz. If the velocity of waves through the string is 5000 m/s, what are the wavelengths of the waves produced in the strings? 4. You yodel across a mountain range and hear your echo 12 seconds later. How far is the next mountain? 5. A whisper is typically about 30dB. Regular conversation happens at about 50dB. a. How much louder is conversation than a whisper? b. How much more energy is produced by conversation than by a whisper? c. If 50 decibels translates to 10-7 W/m 2 and the listener is 1.5m away, what was the power of the speaker? Answers: 1b) 708hz 1d) 1417hz 2b) 224hz 2d) 671hz 3) 15m, 3.8m 4) 2040m 5a) 4 times 5b) 100 times 5c) 2.8 x 10-6 W Page 23

24 Sound and waves review questions (from A. Breig) 1. Draw a transverse and longitudinal wave, label their parts, and give an example of each. Which characteristic is hard to draw on a longitudinal wave? 2. What is a typical speed of sound? Of light? 3. Which type of wave requires a medium? Why? 4. Explain the following terms: period, frequency, natural frequency, forced vibration, sympathetic vibration, constructive interference, destructive interference, resonance, beats 5. When do you hear the Doppler effect? 6. What are the harmonics of an instrument? 7. What are the three types of instrument categories? 8. When you turn up the volume, what variable have you changed? 9. What determines the speed of a wave: its wavelength, its frequency, or what it s in? 10. In what types of material will sound travel fastest? Slowest? 11. How can you determine the speed of a boat from its wake? 12. What do the first three harmonics of a guitar string look like? Of a pop bottle? 13. What are some examples of destructive interference? Of constructive interference? 14. As you go up a step of 10dB on the scale, what happens to the intensity of sound being produced? To the volume you hear? 15. What is the connection between the power of sound being produced and the intensity which reaches you at a particular location? 16. If you stand twice as far from the source, what happens to the intensity? 17. Does sound accelerate? Why or why not? 18. How can you use reflection to determine how deep the ocean is? 19. What is the connection between air temperature and the speed of sound? Why isn t it a constant? 20. Why should a runner in a race watch the starting gun instead of listening for its bang? 21. If one swing in a swingset is set into motion, others will often begin to move as well. Why? 22. How does a sounding board work? 23. What determines the wavelength of a wave? 24. Our radio station transmits at 88.5Mhz. Does it produce sound or light waves? 25. When a wave enters a new medium, what changes: frequency? wavelength? velocity? Page 24

25 Vocabulary: previous vocabulary simple harmonic motion wave, wavelength, wave speed medium, mechanical wave frequency, period, equilibrium line, amplitude crest, trough, hertz (Hz) transverse wave, longitudinal wave standing wave, pulse wave node, anti-node reflection, free end, fixed end harmonics, fundamental frequency natural frequency, resonance sound, timbre, pitch interference, superposition principle constructive interference, destructive interference rarefaction, compression, condensation Doppler effect, Mach number shockwave, bow wave sound intensity, decibel, bel, watt ultrasonic, infrasonic beat, beat frequency Unit 11 Traditional Vocabulary and Equations Waves & Sound Symbols: f, T, v, λ, I, M, T( C) Equations & constants: You get these on test: f = 1/T, v = f λ wave speed = v, Period = T, Frequency = f, Wave length = λ d = v t V light = c = 3 x 10 8 m/s, v sound ~ 340 m/s v sound = T( C); +10 db = 2x volume (human perception of loudness) = 10x intensity (W/m 2 ) Beats = f 1 f 2 P I = M = V 0 /v sound P = W/t 4πr 2 closed-closed open-open open-closed Unit Objectives - Williams 1. I understand all the vocabulary & math of this unit and all demos, videos, equations, and class assignments. 2. I remember objectives & vocabulary from previous units. 3. I know wave anatomy, waves carry energy not mass, wave speed depends on properties of the medium (not frequency or wavelength), and sound waves required a medium 4. I can explain the difference between a longitudinal and transverse waves and relate them to sound waves 5. I can use the wave speed equation, relate frequency and period, and use the definition of frequency 6. I know the basic relationship between pendulum length, string tension and period 7. I understand interference, and can cite real-world examples of constructive and destructive interference 8. I am able to apply the principle of superposition to interfering waves to find resulting amplitude 9. I know what happens when waves reach fixed boundaries and for free boundaries too 10. I can explain how standing waves are made including how nodes and antinodes form 11. I predict/recognize frequencies, wavelengths nodes, anti-nodes, for harmonics knowing the boundary types 12. I know how sound is made including compressions and rarefactions 13. I know the range of human hearing, and the basics of how hearing works 14. I can predict and explain the Doppler effect in various situations 15. I know how and why shock waves and bow waves form 16. I can relate loudness, sound intensity & decibel scale to each other and to distance from sound source 17. I understand how humans & musical instruments have distinct sounds & why that differs from a tuning fork 18. I can explain what beats are and how they can be used to tune a piano 19. I know the basics of the Western Musical Scale 20. I know the approx. speed of sound vs. light to gage lightning distance; I can compute Mach speed 21. I can predict the harmonics and wave appearance for all closed/open resonator combinations DuPage ROE Objectives 801. I can distinguish between transverse or longitudinal waves I can identify waves as either mechanical or electromagnetic I can identify: wavelength, amplitude, crest, trough, and period, given a visual representation I can solve problems using the relationships between velocity, wavelength, frequency, and period I can recognize that the speed of a wave is dependent upon the material/medium through which the wave travels I can recognize that waves transfer energy and not matter I can analyze wave superposition in terms of the effects of constructive and destructive interference. Page 25

26 Physics Calendar - Waves & Sound: (Williams) - Chapters (11 days) Bold and underlined means put in journal notes (for any problems: Show your work!); Mod Date Plans Homework (11-01) Notes: Wave definitions, anatomy, interference (superposition) & slinky demo, standing waves (simulation):3,4,7,8,9,10 Suggestion: There are a lot of challenging concepts! Confused about anything? The book is well written and covers about everything, try reading their explanation! Start Physics of music (34:00) (11-02) p 388: 1,2a,2d; p 397+: 23-27, 36 1 Tu:04/02/13 sheet? (11-04) p 394: 1-5; (11-03) Notes: Pre-slinky lab (short): p 397: We:04/03/13 Slinky lab sheet? (11-06) p 387: 1-3 p 397+: 35, Th:04/04/13 HW Quiz sheet? Happy non-attendance day! Online standing wave, doppler, etc. (11-07) p. 398: 40-43, 4 Fr:04/05/13 Mr. Jiggly demo Demo: Mr. Jiggly, paired tuning forks & Orange Dilly Boppers teach us about resonance & harmonics (11-08) Notes: Resonance, harmonics (even & odd), closed & opened resonators, Western music scale:6,11,17,19,21 If requested, go over problems SIMILAR to p. 427 HW (11-09) p. 427: 1-4; 5 Mo:04/08/13 Continue Physics of Music p 431: 1,2 Beats demo: tone generator + tuning fork (11-10) Notes: Beats, three sound scales:12,13,16,18 HW Quiz (11-11) p. 415: 1-5; 6 Tu:04/09/13 Physics of Music? p 431: 3 Preview Audacity with speed of sound demo (11-12) p. 434+: 4,6- We:04/10/13 Go over HW Quiz 8, H3 Homeroom 3 Do mystery tone practice with tone generator Audacity Laptop day 1 Run program, choose mono, zoom for enough digits (11-13) p. 434+: Become familiar with program (#22 use table in packet Measure frequency of tuning fork together if you want) 8C Th:04/11/13 Mystery tone practice Audacity Laptop day 2 Holding the sounding bar properly Mystery Tone Challenge One node means how many waves? Music wave form (flute) vs tone (11-14) p. 434+: 28-30, Fr:04/12/13 Finish lab sheet including mystery tone 34-37, 43a 9C ACT Saturday Short lab quiz, and/or collect/check 10 Mo:04/15/13 Review for test/finish Physics of Music Study for test! 11 Tu:04/16/13 College nt Waves and Sound exam Resources: Chapters 11,12; Notes, Website Page 26