Conceptual Physics Sound Waves Electricity and Magnetism

Transcription

1 Conceptual Physics Sound Waves Electricity and Magnetism Lana Sheridan De Anza College August 2, 2017

2 Last time heat engines waves oscillations interference standing waves

3 Overview Doppler effect bow waves sound electric charge electric field

4 The Doppler Effect Waves from approaching sources seem to have higher frequency than waves from stationary sources. Waves from receding sources seem to have lower frequency than waves from stationary sources.

5 The Doppler Effect How much does the frequency change? f D = v v v s f s where v is the speed of the wave, f s is the frequency emitted by the source, and f D is the frequency detected by a stationary detector. v s is the speed of the wave source: here we use the convention that v s is negative if the source is approaching us and positive if it is moving away from us.

6 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?

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

8 Bow Waves and Shock Waves Bow waves and shock waves can be detected by nearby observers when the speed of the wave source exceeds the speed of the waves. This effect happens when an aircraft transitions from subsonic flight to supersonic flight. 1 Figure from Hewitt, 11ed.

9 Bow waves

10 Supersonic transition

11 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.

12 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.

13 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.

14 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

15 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.

16 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

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

18 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.

19 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-

20 Decibels: Scale for Sound Level The ear can detect very quiet sounds, but also can hear very loud sounds without damage. (Very, very loud sounds do damage ears.) As sound wave that has twice the energy does not sound like it is twice as loud. Many human senses register to us on a logarithmic scale. Decibels (db) is the scale unit we use to measure loudness / sound level. Roughly, a noise sounds twice as loud if its sound level is increased by 10 db, or it has 10 times the energy.

21 Perception of Loudness and Frequency Human hearing also depends on frequency. Humans can only hear sound in the range 20-20,000 Hz. Sound level b(db) Infrasonic frequencies 220 Large rocket engine Jet engine (10 m away) Rifle Thunder overhead Sonic frequencies Rock concert Ultrasonic frequencies Underwater communication (Sonar) Threshold of pain Car horn School cafeteria Motorcycle 80 Urban traffic Shout 60 Birds Conversation 40 Bats 20 Threshold of hearing Whispered speech Low frequency sounds need to be louder to be heard. Frequency f (Hz) 1 old of pain. Here the boundary of the white area appears straight because the psychological Figure from response R. L. is Reese, relatively University independent Physics, of frequency via Serway at this & high Jewett. sound level The Doppler Ef Figure 1 ranges of level of va normal hu the white University Brooks/C

22 Sound Sound waves can cause resonant vibrations in objects that will oscillate with the same frequency. (Tuning forks!) Sound waves can also interfere just like other waves.

23 The trigonometric identity Beats cos a 1 cos b 5 2 cos a a 2 b 1 b b cos aa 2 2 b Two sound waves with slightly different frequencies interfere to allows us to write the expression for y as form beats. y 5 c2a cos 2pa f 1 2 f 2 btd cos 2pa f 1 1 f 2 bt (18.10) These are louder and quieter variations 2 in sound2 level. Graphs of the individual waves and the resultant wave are shown in Figure From Amplitude the factors vsin tequation a fixed 18.10, position: we see that the resultant wave has an effective y a t y b t

24 Beats Thus the frequency of the beats is f beat = f 1 f 2 If f 1 and f 2 are similar the beat frequency is much smaller than either f 1 or f 2.

25 Beats Thus the frequency of the beats is f beat = f 1 f 2 If f 1 and f 2 are similar the beat frequency is much smaller than either f 1 or f 2. Humans cannot hear beats if f beat 30 Hz. If the two frequencies are very different we hear a chord. If the two frequencies are very close, we hear periodic variations in the sound level. This is used to tune musical instruments. When instruments are coming into tune with each other the beats get less and less frequent, and vanish entirely when they are perfectly in tune.

26 Figure Sound wave pat- property of the sound. More complex sounds Different musical instruments make different waveform patterns. a t b Tuning fork t For example this is why a flute and a clarinet playing the same note still sound a bit different. Flute More than one frequency is sounded. c t Clarinet

27 ve a brassy that More sound); complex sounds at of the saxowever, 554 both have similar o distinguish a Chapter 18 Superposition t and Standing Wave Tuning fork truments are flute, and a h instrument ifferences in r analysis of first sight to represented of sinusoidal dic function ue based on b Relative intensity c Flute Tuning fork Clarinet Harmonics Figure Sound wave patterns a produced by (a) a tuning t t Relative intensity b 1 2

28 have similar o More distinguish complex sounds a Tuning fork t truments are flute, and a b h Superposition instrument and Standing Waves ifferences in r analysis of Flute t ning first sight to rk represented of sinusoidal dic function ue based on the periodic is periodic in hat 6 this 7 8 func- 9 nics c Relative intensity t Flute Clarinet Figure Sound wave patterns produced by (a) a tuning fork, (b) a flute, and (c) a clarinet, each at approximately the same frequency Harmonics Relative intensity 1 2 3

29 instrument ifferences More complex in sounds r analysis of Flute first sight to represented of sinusoidal dic function ue based on the periodic Flute s periodic in at this func- (18.13) c Clarinet Figure Sound wave patterns produced by (a) a tuning Clarinet fork, (b) a flute, and (c) a clarinet, each at approximately the same frequency. Relative intensity Fourier s theorem t ger multiples ics t the amplionic analysis c Harmonics

30 Example: Square Wave sible, we must add all odd multiples of the fundamental frequ frequency. Using modern technology, musical sounds can be generate mixing different amplitudes of any number of harmonics. The tronic music synthesizers are capable of producing an infinite tones. Two frequencies f and 3f. a f 3f Waves 3f are a blue cu f Three frequencies, f, 3f, and 5f. b 5f 3f One m of freq to give Figure Fourier synthesis of a square wave, represented by the sum of odd multiples of the first harmonic, which has frequency f. Frequencies up to 9f. c Square wave The syn (red-br closer t (black freque added.

31 Electric Charge Charge is an intrinsic (essential) property of subatomic particles. Examples of charged particles: protons (positively charged) electrons (negatively charged) Static electric charge can be experienced on a large scale through static electricity.

32 Electrostatic force Charged objects exert a force (the electrostatic force) on one another. Charges with the same electrical sign repel each other. Charges with opposite electrical signs attract each other. The unit for charge is the Coulomb, written with the symbol C.

33 realignment of charges in Induced Chargethe Polarization molecules of the wall. in th Charged balloon a Wall Induced charge separation b

34 Conductors and Insulators Some materials allow charges to flow through them easily, some do not.

35 Conductors and Insulators Some materials allow charges to flow through them easily, some do not. Conductors materials through which charge can move readily Insulators (also called nonconductors) are materials that charge cannot move through freely

36 nductor like copper come together to form the solid, (and Induced so most Charge loosely held) electrons become free to solid, leaving behind positively charged atoms ( positive electrons If a conductor conduction iselectrons. brought close There toare a charged few (if any) object, positive and ductor. negative charges in the conductor start to separate and we say a g charge demonstrates is induced the mobility on the conductor. of charge in a conducplastic rod will attract either end of an isolated neutral r rod is electrically isoy being suspended on a r end of the copper rod rod. Here, conduction re repelled to the far end arge on the plastic rod. tracts the remaining posif the copper rod, rotating near end closer to the Neutral copper F F Charged plastic Overall, the conductor is neutral, but it is still attracted to the charged object.

37 he molecules to emit ultraviolet light. You cannot see this type of er, Question the wintergreen molecules on the surfaces of the candy pieces ltraviolet light and then emit blue light, which you can see it is the ing from your friend s mouth. A, B, and D are charged pieces of plastic. C is an electrically neutral copper plate. OINT 1 shows five s: A, B, and ged plastic A C C D B is an electral copper electrostatic en the pairs shown for B A D A D pairs. For the remaining two pairs, do the plates repel or attract each other? Plates C and D (A) attract each other (B) repel each other 1 Page 564, Halliday, Resnick, Walker, 9th ed.

38 he molecules to emit ultraviolet light. You cannot see this type of er, Question the wintergreen molecules on the surfaces of the candy pieces ltraviolet light and then emit blue light, which you can see it is the ing from your friend s mouth. A, B, and D are charged pieces of plastic. C is an electrically neutral copper plate. OINT 1 shows five s: A, B, and ged plastic A C C D B is an electral copper electrostatic en the pairs shown for B A D A D pairs. For the remaining two pairs, do the plates repel or attract each other? Plates C and D (A) attract each other (B) repel each other 1 Page 564, Halliday, Resnick, Walker, 9th ed.

39 he molecules to emit ultraviolet light. You cannot see this type of er, Question the wintergreen molecules on the surfaces of the candy pieces ltraviolet light and then emit blue light, which you can see it is the ing from your friend s mouth. A, B, and D are charged pieces of plastic. C is an electrically neutral copper plate. OINT 1 shows five s: A, B, and ged plastic A C C D B is an electral copper electrostatic en the pairs shown for B A D A D pairs. For the remaining two pairs, do the plates repel or attract each other? Plates B and D (A) attract each other (B) repel each other 1 Page 564, Halliday, Resnick, Walker, 9th ed.

40 he molecules to emit ultraviolet light. You cannot see this type of er, Question the wintergreen molecules on the surfaces of the candy pieces ltraviolet light and then emit blue light, which you can see it is the ing from your friend s mouth. A, B, and D are charged pieces of plastic. C is an electrically neutral copper plate. OINT 1 shows five s: A, B, and ged plastic A C C D B is an electral copper electrostatic en the pairs shown for B A D A D pairs. For the remaining two pairs, do the plates repel or attract each other? Plates B and D (A) attract each other (B) repel each other 1 Page 564, Halliday, Resnick, Walker, 9th ed.

41 Electrostatic Forces For a pair of point-particles with charges q 1 and q 2, the magnitude of the force on each particle is given by Coulomb s Law: F 1,2 = k q 1q 2 r 2 k is the electrostatic constant and r is the distance between the two charged particles. k = 1 4πɛ 0 = N m 2 /C 2

42 Coulomb s Law ric Fields F 1 2 = k q 1q 2 r 2 ˆr 1 2 When the charges are of the same sign, the force is repulsive. When the charges are of opposite signs, the force is attractive. r rˆ 12 q 2 S F 12 S F 21 S F 12 q 2 S F 21 q 1 q 1 a b same sign 1 as Figure in Figure from Serway 23.6a, & the Jewett, product Physics q 1 q 2 for is positive Scientists and andthe Engineers, electric 9th force ed. on one

43 Electrostatic Constant The electrostatic constant is: k = 1 4πɛ 0 = N m 2 C 2 ɛ 0 is called the permittivity constant or the electrical permittivity of free space. ɛ 0 = C 2 N 1 m 2

44 Conservation of Charge Charge can move from one body to another but the net charge of an isolated system never changes. This is called charge conservation.

45 Conservation of Charge Charge can move from one body to another but the net charge of an isolated system never changes. This is called charge conservation. What other quantities are conserved?

46 Fields Just as with gravity in Chapter 9: field A field is any kind of physical quantity that has values specified at every point in space and time. In EM we have vector fields. The electrostatic force is mediated by a vector field. vector field A field is any kind of physical quantity that has values specified as vectors at every point in space and time.

47 Fields A force-field can be used to figure out the interaction that particular particle will have with other objects in its environment. Imagine a charge q 0. We want to know the force it would feel if we put it at a specific location.

48 Fields A force-field can be used to figure out the interaction that particular particle will have with other objects in its environment. Imagine a charge q 0. We want to know the force it would feel if we put it at a specific location. The electric field E at that point will tell us that! F = q 0 E

49 Fields The source of the field could be another charge. We do not need a description of the sources of the field to describe what their effect is on our particle. All we need to know if the field!

50 Fields The source of the field could be another charge. We do not need a description of the sources of the field to describe what their effect is on our particle. All we need to know if the field! This is also true for gravity. We do not need the mass of the Earth to know something s weight: F G = m 0 g F E = q 0 E

51 22 Force from a Field F (a) Test charge q 0 at point P but also: E Charged object F = q 0 E The rod sets up an electric field, which can create a force on the test charge. E = F q 0 1 Figure from P Halliday, Resnick, Walker. ) E 22-1 WHAT IS The force on a particle 1 of c P Electric field at point P can create a forc on the test charg physics charge q 2.A nagging q ence of particle 2? Tha 2push on particle 1 ho One purpose of phy magnitude and direction deeper explanation of w such a deeper explanati tance. We can answer th field in the space surroun space, the particle know

52 Field Lines Fields are drawn with lines showing the direction of force that a test particle will feel at that point. The density of the lines at that PART 3 point in the diagram indicates the approximate magnitude of the 581 force at that point ELECTRIC FIELD LINES e the electric field of a charged charge. The field at point P in t charge of Fig. 22-1a was put the presence of the test charge rged object, and thus does not interaction between charged tric field produced by a given e that a given field exerts on a ections 22-4 through 22-7 for nd task in Sections 22-8 and int charges in an electric field. c fields. tric fields in the 19th century, d with lines of force. Although ow usually called electric field rns in electric fields. Electric field lines F Positive test charge (a) E (b)

53 Field Lines Notice that the lines c point outward from a positive charge and inward toward a negative charge. are intersections of these surfaces with the page) and elec- 1 Figure from Serway & Jewett metric electric An electric field produced by an a point The charge electrostatic field electric caused dipole by an electric dipole system looks something like:

54 the sphere would be directed radially away from ic Field field lines would Lines also extend radially away from the llowing rule: way from positive charge (where they originate) and ere they terminate). Imagine an infinite sheet of charge. The lines point outward from the positively charged sheet. t of an infinitely large, nonconducting sheet (or plane) of positive charge on one side. If we were to place a tic force a very unirge on ector E : e, and ce tend d (a) F Positive test charge (b) E (c) 1 Figure from Halliday, Resnick, Walker.

55 ve g e. t. Field Lines tric field it represents are said to have rotational symmetry about that axis.the electric field vector at one point is shown;note that it is tangent to the field line through that point. Compare the electrostatic fields for two like charges and two FIELDS opposite charges: n positive test charge at any point near the n of Fig. 22-3a,the net electrostatic force acti s the test charge would be perpendicular t s sheet, because forces acting in all other fi tions would cancel one another as a res the symmetry. Moreover, the net force o E test charge would point away from the sh E 2 shown. Thus, the electric field vector at any in the space on either side of the sheet it perpendicular to the sheet and directed a from it (Figs. 22-3b and c). Because the cha F uniformly distributed along the sheet, a field vectors have the same magnitude. Fig. Such 22-5 an Field electric lines for field, a positive with point the same nitude and direction at every point, is charge a uniform and a nearby electric negative field. point charge that are equal in magnitude.the charges at- T Of course, no real nonconducting sheet (such as a flat expanse of plastic) fi n

56 Field Lines Compare the fields for gravity in an Earth-Sun system and electrostatic repulsion of two charges: LECTRIC FIELDS positive test charge of Fig. 22-3a,the net the test charge wou sheet, because force tions would cancel the symmetry. More test charge would po shown. Thus, the elec in the space on eith perpendicular to th from it (Figs. 22-3b a uniformly distribute qual positive ach other. gative -dimenlly rotate axis passing of the page. d the elecave rotahe electric note that it that point. 1 Gravity figure from ; Charge from Halliday, Resnick, Walker E field vectors have the same magnitude. Such an electr nitude and direction at every point, is a uniform electr

57 E-Field Question ar more work an and Which physi-ofields byde : Spherical the following could be the charge on the particle hidden theofquestion mark? Gaussian hypothetical surface ssian surface, alculations of ution. For exsphere with a we discuss in? ace to the E n a Gaussian (A) 0 C Fig A spherical Gaussian ited example, (B) 1 C surface. If the electric field vectors ard from (C) the are Cof uniform magnitude and point ly tells us that (D) 1 µc radially outward at all surface points, a particle or you can conclude that a net positive 1 Figure from Halliday, Resnick, Walker

58 E-Field Question ar more work an and Which physi-ofields byde : Spherical the following could be the charge on the particle hidden theofquestion mark? Gaussian hypothetical surface ssian surface, alculations of ution. For exsphere with a we discuss in? ace to the E n a Gaussian (A) 0 C Fig A spherical Gaussian ited example, (B) 1 C surface. If the electric field vectors ard from (C) the are Cof uniform magnitude and point ly tells us that (D) 1 µc radially outward at all surface points, a particle or you can conclude that a net positive 1 Figure from Halliday, Resnick, Walker

59 Field from a Point Charge Remember, if q 0 is a test charge, E = F q 0. We want an expression for the electric field from a point charge, q. Using Coulomb s Law the force on the test particle is F 0 = k qq 0ˆr. r 2 ( ) 1 k q q0 E = ˆr q 0 r 2 The field at a displacement r from a charge q is: E = k q r 2 ˆr

60 Field from a Point Charge Example What is the magnitude of the electric field 1 cm from a 2 µc charge? Does the field point towards or away from the charge?

61 vectors is neatly displayed by the field lines in Fig. 22-2b, e directions as the force and field vectors. Moreover, the nes with distance from the sphere tells us that the magnidecreases with distance from the sphere. g were of uniform positive charge, the electric field ear the Consider sphere would an be infinite directed sheet radially ofaway charge. from ectric field lines would also extend radially away from the e following rule: Electric field due to an Infinite Sheet of Charge The field from this sheet is uniform! It does not matter how far a point P is from the sheet, the field is the same. nd away from positive charge (where they originate) and (where they terminate). part of an infinitely large, nonconducting sheet (or plane) tion of positive charge on one side. If we were to place a ostatic force near a very with unicharge on eld vector E : harge, and e space es extend arged (a) F Positive test charge (b) E (c)

62 Millikan s Oil Drop Experiment: Measuring e Units of field: N/C Problem 10, page 403. (a) If a drop of mass kg remains stationary in an electric field of N/C, what is the charge on this drop? (b) How many extra electrons are on this particular oil drop?

63 Millikan s Oil Drop Experiment: Measuring e The e field E : opposi P 1 Fig Oil spray Oil drop P 2 S A C B Insulating chamber wall Microscope The Millikan oil-drop appa- Measu Equatio Americ tation o them be drop th Let us a If s chambe positive positive

64 Summary Doppler effect bow waves sound electric charge electric field Homework Prepare a 5-8 minute talk for next week. Tuesday, Aug 8. Essay question (Due tomorrow) Waves worksheet (Due Monday) 2 new worksheets: Coulomb s law & E-field (due Monday) Hewitt, Ch 19, onward from page 347. Exercises: 35 Ch 20, onward from page 365. Exercises: 1, 3; Problems: 1, 3, 7 Ch 22, onward from page 403. Exercises: 3, 41; Problems: 1, 3