1. Copyright © 2009 Pearson Education, Inc. Chapter 16 Sound

2. Copyright © 2009 Pearson Education, Inc. Sections – 2, 4, 6, 7 only Mathematical Representation of Longitudinal Waves Sources of Sound: Vibrating Strings Quality of Sound, and Noise; Superposition Interference of Sound Waves; Beats Doppler Effect Units of Chapter 16

3. Copyright © 2009 Pearson Education, Inc. 16-2 Mathematical Representation of Longitudinal Waves Longitudinal waves are often called pressure waves. The displacement is 90° out of phase with the pressure.

4. Copyright © 2009 Pearson Education, Inc. 16-2 Mathematical Representation of Longitudinal Waves By considering a small cylinder within the fluid, we see that the change in pressure is given by ( B is the bulk modulus):

5. Copyright © 2009 Pearson Education, Inc. 16-2 Mathematical Representation of Longitudinal Waves If the displacement is sinusoidal, we have where and

6. Copyright © 2009 Pearson Education, Inc. So why does a trumpet sound different from a flute? The answer lies in overtones—which ones are present, and how strong they are, makes a big difference. The sound wave is the superposition of the fundamental and all the harmonics. 16-5 Quality of Sound, and Noise; Superposition

7. Copyright © 2009 Pearson Education, Inc. This plot shows frequency spectra for a clarinet, a piano, and a violin. The differences in overtone strength are apparent. 16-5 Quality of Sound, and Noise; Superposition

8. Copyright © 2009 Pearson Education, Inc. Sound waves interfere in the same way that other waves do in space. 16-6 Interference of Sound Waves; Beats

9. Copyright © 2009 Pearson Education, Inc. 16-6 Interference of Sound Waves; Beats Example 16-12: Loudspeakers’ interference. Two loudspeakers are 1.00 m apart. A person stands 4.00 m from one speaker. How far must this person be from the second speaker to detect destructive interference when the speakers emit an 1150-Hz sound? Assume the temperature is 20°C.

10. Copyright © 2009 Pearson Education, Inc. Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow “envelope” around two waves that are relatively close in frequency. 16-6 Interference of Sound Waves; Beats

11. Copyright © 2009 Pearson Education, Inc. 16-6 Interference of Sound Waves; Beats If we consider two waves of the same amplitude and phase, with different frequencies, we can find the beat frequency when we add them: This represents a wave vibrating at the average frequency, with an “envelope” at the difference of the frequencies.

12. Copyright © 2009 Pearson Education, Inc. 16-6 Interference of Sound Waves; Beats Example 16-13: Beats. A tuning fork produces a steady 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible frequencies produced by the guitar string?

13. Copyright © 2009 Pearson Education, Inc. The Doppler effect occurs when a source of sound is moving with respect to an observer. 16-7 Doppler Effect A source moving toward an observer appears to have a higher frequency and shorter wavelength; a source moving away from an observer appears to have a lower frequency and longer wavelength.

14. Copyright © 2009 Pearson Education, Inc. If we can figure out what the change in the wavelength is, we also know the change in the frequency. 16-7 Doppler Effect

15. Copyright © 2009 Pearson Education, Inc. The change in the frequency is given by: If the source is moving away from the observer: 16-7 Doppler Effect

16. Copyright © 2009 Pearson Education, Inc. If the observer is moving with respect to the source, things are a bit different. The wavelength remains the same, but the wave speed is different for the observer. 16-7 Doppler Effect

17. Copyright © 2009 Pearson Education, Inc. We find, for an observer moving toward a stationary source: And if the observer is moving away: 16-7 Doppler Effect

18. Copyright © 2009 Pearson Education, Inc. 16-7 Doppler Effect Example 16-14: A moving siren. The siren of a police car at rest emits at a predominant frequency of 1600 Hz. What frequency will you hear if you are at rest and the police car moves at 25.0 m/s (a) toward you, and (b) away from you?

19. Copyright © 2009 Pearson Education, Inc. 16-7 Doppler Effect Example 16-15: Two Doppler shifts. A 5000-Hz sound wave is emitted by a stationary source. This sound wave reflects from an object moving toward the source. What is the frequency of the wave reflected by the moving object as detected by a detector at rest near the source?

20. Copyright © 2009 Pearson Education, Inc. 16-7 Doppler Effect All four equations for the Doppler effect can be combined into one; you just have to keep track of the signs!

21. Copyright © 2009 Pearson Education, Inc. Sound is a longitudinal wave in a medium. The strings on stringed instruments produce a fundamental tone whose wavelength is twice the length of the string; there are also various harmonics present. Sound waves exhibit interference; if two sounds are at slightly different frequencies they produce beats. The Doppler effect is the shift in frequency of a sound due to motion of the source or the observer. Summary of Chapter 16

22. Copyright © 2009 Pearson Education, Inc. Chapter 31 Maxwell’s Equations and Electromagnetic Waves

23. Copyright © 2009 Pearson Education, Inc. Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current Gauss’s Law for Magnetism Maxwell’s Equations Production of Electromagnetic Waves Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations Light as an Electromagnetic Wave and the Electromagnetic Spectrum Units of Chapter 31

24. Copyright © 2009 Pearson Education, Inc. Measuring the Speed of Light Energy in EM Waves; the Poynting Vector Radiation Pressure Radio and Television; Wireless Communication Units of Chapter 31

25. Copyright © 2009 Pearson Education, Inc. Ampère’s law relates the magnetic field around a current to the current through a surface. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current

26. Copyright © 2009 Pearson Education, Inc. In order for Ampère’s law to hold, it can’t matter which surface we choose. But look at a discharging capacitor; there is a current through surface 1 but none through surface 2: 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current

27. Copyright © 2009 Pearson Education, Inc. Therefore, Ampère’s law is modified to include the creation of a magnetic field by a changing electric field – the field between the plates of the capacitor in this example: 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current

28. Copyright © 2009 Pearson Education, Inc. Example 31-1: Charging capacitor. A 30-pF air-gap capacitor has circular plates of area A = 100 cm 2. It is charged by a 70-V battery through a 2.0-Ω resistor. At the instant the battery is connected, the electric field between the plates is changing most rapidly. At this instant, calculate (a) the current into the plates, and (b) the rate of change of electric field between the plates. (c) Determine the magnetic field induced between the plates. Assume E is uniform between the plates at any instant and is zero at all points beyond the edges of the plates. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current

29. Copyright © 2009 Pearson Education, Inc. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current The second term in Ampere’s law has the dimensions of a current (after factoring out the μ 0 ), and is sometimes called the displacement current: where

30. Copyright © 2009 Pearson Education, Inc. 31-2 Gauss’s Law for Magnetism Gauss’s law relates the electric field on a closed surface to the net charge enclosed by that surface. The analogous law for magnetic fields is different, as there are no single magnetic point charges (monopoles):

31. Copyright © 2009 Pearson Education, Inc. 31-3 Maxwell’s Equations We now have a complete set of equations that describe electric and magnetic fields, called Maxwell’s equations. In the absence of dielectric or magnetic materials, they are:

32. Copyright © 2009 Pearson Education, Inc. Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created they can propagate on their own. These propagating fields are called electromagnetic waves. 31-4 Production of Electromagnetic Waves

33. Copyright © 2009 Pearson Education, Inc. Oscillating charges will produce electromagnetic waves: 31-4 Production of Electromagnetic Waves

34. Copyright © 2009 Pearson Education, Inc. 31-4 Production of Electromagnetic Waves Close to the antenna, the fields are complicated, and are called the near field:

35. Copyright © 2009 Pearson Education, Inc. Far from the source, the waves are plane waves: 31-4 Production of Electromagnetic Waves

36. Copyright © 2009 Pearson Education, Inc. The electric and magnetic waves are perpendicular to each other, and to the direction of propagation. 31-4 Production of Electromagnetic Waves

37. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations In the absence of currents and charges, Maxwell’s equations become:

38. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations This figure shows an electromagnetic wave of wavelength λ and frequency f. The electric and magnetic fields are given by where.

39. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations Applying Faraday’s law to the rectangle of height Δy and width dx in the previous figure gives a relationship between E and B :.

40. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations Similarly, we apply Maxwell’s fourth equation to the rectangle of length Δz and width dx, which gives.

41. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations Using these two equations and the equations for B and E as a function of time gives Here, v is the velocity of the wave. Substituting,.

42. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations The magnitude of this speed is 3.0 x 10 8 m/s – precisely equal to the measured speed of light.

43. Copyright © 2009 Pearson Education, Inc. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations Example 31-2: Determining E and B in EM waves. Assume a 60-Hz EM wave is a sinusoidal wave propagating in the z direction with E pointing in the x direction, and E 0 = 2.0 V/m. Write vector expressions for E and B as functions of position and time.

44. Copyright © 2009 Pearson Education, Inc. The frequency of an electromagnetic wave is related to its wavelength and to the speed of light: 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

45. Copyright © 2009 Pearson Education, Inc. Electromagnetic waves can have any wavelength; we have given different names to different parts of the wavelength spectrum. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

46. Copyright © 2009 Pearson Education, Inc. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum Example 31-3: Wavelengths of EM waves. Calculate the wavelength (a) of a 60-Hz EM wave, (b) of a 93.3-MHz FM radio wave, and (c) of a beam of visible red light from a laser at frequency 4.74 x 10 14 Hz.

47. Copyright © 2009 Pearson Education, Inc. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum Example 31-4: Cell phone antenna. The antenna of a cell phone is often ¼ wavelength long. A particular cell phone has an 8.5-cm-long straight rod for its antenna. Estimate the operating frequency of this phone.

48. Copyright © 2009 Pearson Education, Inc. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum Example 31-5: Phone call time lag. You make a telephone call from New York to a friend in London. Estimate how long it will take the electrical signal generated by your voice to reach London, assuming the signal is (a) carried on a telephone cable under the Atlantic Ocean, and (b) sent via satellite 36,000 km above the ocean. Would this cause a noticeable delay in either case?

49. Copyright © 2009 Pearson Education, Inc. The speed of light was known to be very large, although careful studies of the orbits of Jupiter’s moons showed that it is finite. One important measurement, by Michelson, used a rotating mirror: 31-7 Measuring the Speed of Light

50. Copyright © 2009 Pearson Education, Inc. Over the years, measurements have become more and more precise; now the speed of light is defined to be c = 2.99792458 × 10 8 m/s. This is then used to define the meter. 31-7 Measuring the Speed of Light

51. Copyright © 2009 Pearson Education, Inc. Energy is stored in both electric and magnetic fields, giving the total energy density of an electromagnetic wave: Each field contributes half the total energy density: 31-8 Energy in EM Waves; the Poynting Vector

52. Copyright © 2009 Pearson Education, Inc. This energy is transported by the wave. 31-8 Energy in EM Waves; the Poynting Vector

53. Copyright © 2009 Pearson Education, Inc. The energy transported through a unit area per unit time is called the intensity: 31-8 Energy in EM Waves; the Poynting Vector Its vector form is the Poynting vector:

54. Copyright © 2009 Pearson Education, Inc. 31-8 Energy in EM Waves; the Poynting Vector Typically we are interested in the average value of S:.

55. Copyright © 2009 Pearson Education, Inc. 31-8 Energy in EM Waves; the Poynting Vector Example 31-6: E and B from the Sun. Radiation from the Sun reaches the Earth (above the atmosphere) at a rate of about 1350 J/s·m 2 (= 1350 W/m 2 ). Assume that this is a single EM wave, and calculate the maximum values of E and B.

56. Copyright © 2009 Pearson Education, Inc. In addition to carrying energy, electromagnetic waves also carry momentum. This means that a force will be exerted by the wave. The radiation pressure is related to the average intensity. It is a minimum if the wave is fully absorbed: and a maximum if it is fully reflected: 31-9 Radiation Pressure

57. Copyright © 2009 Pearson Education, Inc. 31-9 Radiation Pressure Example 31-7: Solar pressure. Radiation from the Sun that reaches the Earth’s surface (after passing through the atmosphere) transports energy at a rate of about 1000 W/m 2. Estimate the pressure and force exerted by the Sun on your outstretched hand.

58. Copyright © 2009 Pearson Education, Inc. 31-9 Radiation Pressure Example 31-8: A solar sail. Proposals have been made to use the radiation pressure from the Sun to help propel spacecraft around the solar system. (a) About how much force would be applied on a 1 km x 1 km highly reflective sail, and (b) by how much would this increase the speed of a 5000-kg spacecraft in one year? (c) If the spacecraft started from rest, about how far would it travel in a year?

59. Copyright © 2009 Pearson Education, Inc. This figure illustrates the process by which a radio station transmits information. The audio signal is combined with a carrier wave. 31-10 Radio and Television; Wireless Communication

60. Copyright © 2009 Pearson Education, Inc. The mixing of signal and carrier can be done two ways. First, by using the signal to modify the amplitude of the carrier (AM): 31-10 Radio and Television; Wireless Communication

61. Copyright © 2009 Pearson Education, Inc. Second, by using the signal to modify the frequency of the carrier (FM): 31-10 Radio and Television; Wireless Communication

62. Copyright © 2009 Pearson Education, Inc. At the receiving end, the wave is received, demodulated, amplified, and sent to a loudspeaker. 31-10 Radio and Television; Wireless Communication

63. Copyright © 2009 Pearson Education, Inc. The receiving antenna is bathed in waves of many frequencies; a tuner is used to select the desired one. 31-10 Radio and Television; Wireless Communication

64. Copyright © 2009 Pearson Education, Inc. 31-10 Radio and Television; Wireless Communication A straight antenna will have a current induced in it by the varying electric fields of a radio wave; a circular antenna will have a current induced by the changing magnetic flux.

65. Copyright © 2009 Pearson Education, Inc. 31-10 Radio and Television; Wireless Communication Example 31-9: Tuning a station. Calculate the transmitting wavelength of an FM radio station that transmits at 100 MHz.

66. Copyright © 2009 Pearson Education, Inc. Maxwell’s equations are the basic equations of electromagnetism: Summary of Chapter 31

67. Copyright © 2009 Pearson Education, Inc. Electromagnetic waves are produced by accelerating charges; the propagation speed is given by The fields are perpendicular to each other and to the direction of propagation. Summary of Chapter 31

68. Copyright © 2009 Pearson Education, Inc. The wavelength and frequency of EM waves are related: The electromagnetic spectrum includes all wavelengths, from radio waves through visible light to gamma rays. The Poynting vector describes the energy carried by EM waves: Summary of Chapter 31