Waves Wave Behaviors Sound

Transcription

1 Waves Wave Behaviors Sound Lana Sheridan De Anza College Dec 5, 2018

2 Last time pendula and SHM waves kinds of waves sine waves

3 Overview refraction diffraction standing waves sound and musical instruments the Doppler effect

4 Refraction zon due to the curvature of the Earth. Explain this phenomenon. 13. When Figure wavescq35.13 pass fromshows one medium a pencil into partially another, immersed they can change in a direction. cup of water. Why does the pencil appear to be bent? s s e o Figure CQ35.13 Cengage Learning/Charles D. Winters

5 Refraction If a wave enters a medium where it moves more slowly, what happens? 1 the frequency cannot change the source still updates the medium about a new wave front every T seconds.

6 Refraction If a wave enters a medium where it moves more slowly, what happens? 1 the frequency cannot change the source still updates the medium about a new wave front every T seconds. 2 the wavelength changes (v = f λ) When the wavefronts slow, they bend.

7 Refraction 1 McGraw-Hill Concise Encyclopedia of Physics. c 2002 by The McGraw-Hill Companies, Inc.

8 Refraction electrons, and the vertical arrows represent their oscillations. Concrete Grass This end slows first; as a result, the barrel turns. v 2 v 1 1 Serway & Jewett, Figure 9th ed, page Overhead view v 1 v 2 may encounter a light is absorbed sented by the do an antenna and again absorbed. in terms of quan light passing fro from one atom t place cause the m/s. On and the light tra A mechanica of the rolling ba on the concrete the barrel to piv Index of Refr In general, the

9 Refraction The same thing happens when waves move into shallower water on a beach. 1

10 Diffraction 35.4 Analysis Model: Wave Under Reflection Light and other waves that travel through a small gap (< λ) diverge, and that the smaller the gap, the more divergence. We introduced the concept of reflection of waves in a discussion of waves on strings in Section As with waves on strings, when a light ray traveling in one medium encounters a boundary with another medium, part of the incident light When l,, d, the rays continue in a straight-line path and the ray approximation remains valid. When l d, the rays spread out after passing through the opening. When l.. d, the opening behaves as a point source emitting spherical waves. d l,, d l d a b c This is called diffraction. l.. d Figure wavelen rier in of diam The effect is particularly pronounced when the gap is about the size of the wavelength or smaller.

11 Diffraction Visible light have wavelengths of 500 nm = m. Sound waves have wavelengths 1 m. (centimeters meters).

12 Diffraction Visible light have wavelengths of 500 nm = m. Sound waves have wavelengths 1 m. (centimeters meters). Why can you hear someone yelling from around a corner, but you can t see them?

13 Interference of Waves When two wave disturbances interact with one another they can amplify or cancel out. Waves of the same frequency that are in phase will reinforce, amplitude will increase; waves that are out of phase will cancel out.

14 Interference of Waves

15 Wave Reflection

16 Standing Waves It is possible to create waves that do not seem to propagate. They are produced by a wave moving to the left interfering with the wave reflected back the right.

17 Standing Waves Notice that there are a whole number of half wavelengths between the child and the tree.

18 Nodes and Antinodes The amplitude of the vertical oscillation of any element of the string depends on the horizontal position of the element. Each element vibrates within the confines of the envelope function 2A sin kx. Antinode Node Antinode Node 2A sin kx Richard Megna/Fundamental Photographs otice that Equation 18.1 does not contain a function of kx 2 vt. Therefore, ot an expression for a single traveling wave. When you observe a standing wav re is no sense of motion in the direction of propagation of either original wav

19 Standing Waves and Resonance Standing wave motions are called normal modes. normal mode A pattern of motion in a physical system where all parts of the system move sinusoidally with the same frequency and with a fixed phase relation.

20 Standing Waves and Resonance on a String 542 Chapter 18 Superposition and Standing Waves Fundamental, or first harmonic Second harmonic Third harmonic N A N N A N A N N A N A N A N f 1 f 2 f 3 a n 1 Wavelengths of normal modes L 1 2 l 1 b n 2 L l 2 mode is the longest-wavelength mode that is consistent with our boundary conditions. The first normal mode occurs when the wavelength l 1 is equal to twice the length of the string, or l 1 5 2L. 2L The section of a standing wave from one node to the next node is called a loop. In the first normal mode, the string is vibrating in one loop. In the second normal mode (see Fig b), the string vibrates in two loops. When the left half of the string is moving upward, the right half is moving downward. In this case, the wavelength l 2 is equal to the length of the string, as expressed by l 2 5 L. The third normal mode (see Fig c) corresponds to the case in which l 3 5 2L/3, and the string vibrates in three loops. In general, the wavelengths of the various normal modes for a string of length L fixed at both ends are l n 5 2L n n 3 L 3 2 l 3 Figure The normal modes of vibration of the string in Figure 18.9 form a harmonic series. The string vibrates between the extremes shown. The natural frequencies of a string are given by: f n = nv where n is a positive natural number, L is the length of the string, and v is the speed of the wave on the string. A long string has a low fundamental frequency. A short string has a high fundamental frequency. n 5 1, 2, 3, c (18.4) where the index n refers to the nth normal mode of oscillation. These modes are possible. The actual modes that are excited on a string are discussed shortly. c

21 Standing Waves and Resonance on a String When a string is plucked, resonant (natural) frequencies tend to persist, while other waves at other frequencies are quickly dissipated. Stringed instruments like guitars can be tuned by adjusting the tension in the strings. Changing the tension changes the speed of the wave on the string. That changes the natural frequencies. While playing, pressing a string against a particular fret will change the string length, which also changes the natural frequencies.

22 Sound Sound is a longitudinal wave, formed of pressure fluctuations in air. At sea level at 20 C, sound travels at 343 m/s. All sound waves will travel at this speed relative to the rest frame of the air. v = f λ A low frequency means a longer wavelength. 1 In higher layers, the speed of sound varies with the temperature.

23 Sound Sound is a longitudinal wave, formed of pressure fluctuations in air. At sea level at 20 C, sound travels at 343 m/s. All sound waves will travel at this speed relative to the rest frame of the air. v = f λ A low frequency means a longer wavelength. Sound can travel at different speeds in other materials. It travels faster in water, and slower at higher altitudes in the atmosphere (troposphere layer). 1 1 In higher layers, the speed of sound varies with the temperature.

24 and the harmonic series contains all integer multiples of the Standing Sound fundamental. Waves in air columns a node. The harmonic series contains only odd integer multiples of the fundamental. L L First harmonic A N l1 2L f 1 v v l1 2L A A First harmonic N Standing sound waves can be set up in hollow tubes. l1 4L f 1 v v l1 4L Second harmonic A A N N l2 L f 2 v 2f L 1 A A A N This is the idea behind how pipe organs, clarinets, didgeridoos, etc. work. 4 l3 L 3 f 3 3v 3f 4L 1 N Third harmonic A A A A Third harmonic N N N 3 2 l 3 L f 3 3v 3f 2L 1 1 Figure from Serway a & Jewett, page 547. A b A A N N 5 4 l 5 L f 5 5v 5f 4L 1 N Fifth harmonic

25 Musical Instruments Didgeridoo: Longer didgeridoos have lower pitch, but tubes that flare outward have higher pitches and this can also change the spacing of the resonant frequencies. 1 Matt Roberts via Getty Images.

26 Musical Instruments, Pipe Organ The longest pipes made for organs are open-ended 64-foot stops (tube is effectively 64 feet+ long). There are two of them in the world. The fundamental frequency associated with such a pipe is 8 Hz. 32 stops give 16 Hz sound, 16 stops give 32 Hz, 8 stops give 64 Hz, etc. 1 Picture of Sydney Town Hall Grand Organ from Wikipedia, user Jason7825.

27 Musical Instruments 458 CHAPTER 17 WAVES II Bass saxophone Baritone saxophone Tenor saxophone Alto saxophone Soprano saxophone More gen open ends co where n is ca write the reso f v Figure 17 Violin standing sou Viola open end. As Cello the closed en Bass having a wav pattern requ In general, larger instruments can create lower tones, whether A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C so on. string instruments or tube instruments. More ge Fig The saxophone and violin 1 Halliday, Resnick, only one open end families, Walker, showing 9th ed, the page relations 458. between in-

28 The Doppler Effect observe the op stern) of the than 3.0 s has The frequency of a sound counts how many wavefronts (pressure peaks) arrive per second. you observe a These effec depends on th When you are than that of t quency. When the observed f Let s now e waves become becomes an o and a sound s ary and the o moves with a means at rest If you are moving towards a source of sound, you encounter more wavefronts per second the frequency you detect is higher! O S vo Figure 17.9 An observer O S

29 you observe a lower fr These effects occu depends on the direct When you are moving than that of the wave quency. When you tur the observed frequenc O S Let s now examine waves become sound becomes an observer S and a sound source S vo ary and the observer moves with a speed v Figure 17.9 An observer O means at rest with res The speed you see (the waves cyclist) traveling moves with relative a speed to you is v O toward a stationary point If a point source em v = v + v O, while relative to the source the speed is v. source S, the horn of a parked at the same speed in truck. The observer hears a frequency f = f v ( ) spherical wave as men 9 that is greater v + than the fronts equals the wav source frequency. λ = vo f v these three-dimension (v and v O are positive numbers.) We take the freque and the speed of soun The Doppler Effect

30 The Doppler Effect The speed you see the waves traveling relative to you is v = v + v O, while relative to the source the speed is v. f = v ( ) v + λ = vo f v (v and v 0 are positive numbers.) Moving away from the source, the relative velocity of the detector to the source decreases v = v v O. ( ) v f vo = f v

31 The Doppler Effect A similar thing happens if the source of the waves is moving. A point source is moving to the right with speed v B S l Observer B S v S Observer A A C a In the diagram, the source is moving toward the wavefronts it has created on the right and away from the wavefronts it has created on the left. toward the source, and a negative value is substituted when the away from the source. This changes Now thesuppose wavelength the source of the is waves in motion aroundand the the source. observer Theyis at re are shorter moves on the directly right, toward and longer observer on A the in left. Figure 17.10a, each new wave is position to the right of the origin of the previous wave. As a result, heard by the observer are closer together than they would be if the b

32 lr 5l2Dl5l2 v S f The Doppler Effect A point source is moving to the right with speed v S. B S l Observer B S v S Observer A A C a b Courtesy of the Educational Development Center, Newton, MA Observer A detects the wavelength as λ = λ v S T = λ v S For A: toward the source, and a negative value is substituted when f. the observer m away from the source. Now suppose the source is in ) motion ( and the ) observer is at rest. If the sou moves directly toward vobserver A in Figure 17.10a, v each new wave is emitted fro = f position to the v/f right of the v origin of the previous wave. As a result, the wave fr S /f v v S heard by the observer are closer together than they would be if the source were moving. (Fig b shows this effect for waves moving on the surface of wa As a result, the wavelength l9 measured by observer A is shorter than the w length l of the source. During each vibration, which lasts for a time interval T period), the source moves a distance v S T 5 v S /f and the wavelength is shortene this amount. Therefore, the observed wavelength l9 is f = v λ = (

33 lr 5l2Dl5l2 v S f The Doppler Effect A point source is moving to the right with speed v S. B S l Observer B S v S Observer A A C a b Courtesy of the Educational Development Center, Newton, MA Observer A detects the wavelength as λ = λ v S T = λ v S For A: For Observer B: toward the source, and a negative value is substituted when f. the observer m away from the source. Now suppose the source is in ) motion ( and the ) observer is at rest. If the sou moves directly toward vobserver A in Figure 17.10a, v each new wave is emitted fro = f position to the v/f right of the v origin of the previous wave. As a result, the wave fr S /f v v S heard by the observer are closer together than they would be if the source were moving. (Fig b shows this effect for waves moving on the surface of wa As a result, the wavelength ( l9 measured ) by observer A is shorter than the w length l of the source. During v each vibration, which lasts for a time interval T period), the source f = moves a distance f v S T 5 v S /f and the wavelength is shortene this amount. Therefore, the observed wavelength l9 is f = v λ = ( v + v S

34 The Doppler Effect In general: ( v ± f vo = v v S ) f The top sign in the numerator corresponds to the observer/detector moving towards the source. The top sign in the denominator corresponds to the source moving towards the observer/detector. The bottom sign in the numerator corresponds to the detector moving away from the source. The bottom sign in the denominator corresponds to the source moving away from the detector.

35 The Doppler Effect In general: ( v ± f vo = v v S ) f Summary: top sign if towards, bottom sign if away.

36 The Doppler Effect Quick Quiz Consider detectors of water waves at three locations A, B, and C in the picture. Which of the following statements is true? A point source is moving to the right with speed v S. S l rver B S v S Observer A A C source, and a negative value is substituted when the observer moves e source. (C) The detected frequency is highest at location C. ose the source is in motion and the observer is at rest. If the source tly toward (D) observer The detected A in Figure frequency 17.10a, each isnew highest wave is at emitted location from A. a he right of the origin of the previous wave. As a result, the wave fronts observer are 2 Serway closer & together Jewett, than pagethey 520. would be if the source were not b B Courtesy of the Educational Development Center, Newton, MA (A) The wave speed is highest at location C. (B) The detected wavelength is largest at location C The Doppler Effect Figure (a) A sourc ing with a speed v S toward tionary observer A and awa a stationary observer B. Ob A hears an increased frequ and observer B hears a dec frequency. (b) The Dopple in water, observed in a ripp Letters shown in the photo to Quick Quiz Pitfall Prevention 17.1 Doppler Effect Does Not D on Distance Some people that the Doppler effect de on the distance between th source and the observer. A

37 The Doppler Effect Quick Quiz Consider detectors of water waves at three locations A, B, and C in the picture. Which of the following statements is true? A point source is moving to the right with speed v S. S l rver B S v S Observer A A C source, and a negative value is substituted when the observer moves e source. (C) The detected frequency is highest at location C. ose the source is in motion and the observer is at rest. If the source tly toward (D) observer The detected A in Figure frequency 17.10a, each isnew highest wave is at emitted location from A. a he right of the origin of the previous wave. As a result, the wave fronts observer are 2 Serway closer & together Jewett, than pagethey 520. would be if the source were not b B Courtesy of the Educational Development Center, Newton, MA (A) The wave speed is highest at location C. (B) The detected wavelength is largest at location C The Doppler Effect Figure (a) A sourc ing with a speed v S toward tionary observer A and awa a stationary observer B. Ob A hears an increased frequ and observer B hears a dec frequency. (b) The Dopple in water, observed in a ripp Letters shown in the photo to Quick Quiz Pitfall Prevention 17.1 Doppler Effect Does Not D on Distance Some people that the Doppler effect de on the distance between th source and the observer. A

38 The Doppler Effect Question A police car has a siren tone with a frequency at 2.0 khz. It is approaching you at 28 m/s. What frequency do you hear the siren tone as? Now it has passed by and is moving away from you. What frequency do you hear the siren tone as now?

39 The Doppler Effect Question A police car has a siren tone with a frequency at 2.0 khz. It is approaching you at 28 m/s. What frequency do you hear the siren tone as? Now it has passed by and is moving away from you. What frequency do you hear the siren tone as now? ( ) v f = f v v S

40 The Doppler Effect and Astronomy 1 Image from Wikipedia by Georg Wiora.

41 Summary refraction diffraction standing waves sound and musical instruments the Doppler effect Final Exam Tuesday Dec 11, 9:15 11:15am, S16. Extra Office Hour Monday, 1:30-3pm. Homework Ch 17 Prob: 5, 39a,c,d(not b), 41, 43, 55, 57, 59 extra credit multiple choice on website (optional)