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Chapter 16 Sound

Chapter 16 Sound. ConcepTest 16.6c Pied Piper III. If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change?. 1) frequency will increase

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Chapter 16 Sound

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  1. Chapter 16Sound

  2. ConcepTest 16.6cPied Piper III If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change? 1) frequency will increase 2) frequency will not change 3) frequency will decrease

  3. ConcepTest 16.6cPied Piper III If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change? 1) frequency will increase 2) frequency will not change 3) frequency will decrease By drinking some of the soda, you have effectively increased the length of the air column in the bottle. Alonger pipemeans that the standing wave in the bottle would have alonger wavelength. Because the wave speed remains the same, and we know thatv = fl,then we see that thefrequency has to be lower. Follow-up: Why doesn’t the wave speed change?

  4. A L B ConcepTest 16.9Interference 1)intensity increases 2) intensity stays the same 3) intensity goes to zero 4) impossible to tell Speakers A and B emit sound waves of l = 1 m, which interfere constructively at a donkey located far away (say, 200 m). What happens to the sound intensity if speaker A is moved back 2.5 m?

  5. A L B ConcepTest 16.9Interference 1)intensity increases 2) intensity stays the same 3) intensity goes to zero 4) impossible to tell Speakers A and B emit sound waves of l = 1 m, which interfere constructively at a donkey located far away (say, 200 m). What happens to the sound intensity if speaker A steps back 2.5 m? If l = 1 m, then a shift of 2.5 m corresponds to 2.5l, which puts the two waves out of phase, leading to destructive interference. The sound intensity will therefore go to zero. Follow-up: What if you move back by 4 m?

  6. 16-7 Doppler Effect The Doppler effect occurs when a source of sound is moving with respect to an observer. 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.

  7. 16-7 Doppler Effect If we can figure out what the change in the wavelength is, we also know the change in the frequency.

  8. 16-7 Doppler Effect The change in the frequency is given by: If the source is moving away from the observer:

  9. 16-7 Doppler Effect 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.

  10. 16-7 Doppler Effect We find, for an observer moving toward a stationary source: And if the observer is moving away:

  11. 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?

  12. 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?

  13. 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! Basic point: if source and receiver moving closer – f’ > f if source and receiver moving apart – f’ < f

  14. ConcepTest 16.11aDoppler Effect I 1) frequency is highest at A 2) frequency is highest at B 3) frequency is highest at C 4)frequency is the same at all three points Observers A, B, and C listen to a moving source of sound. The location of the wave fronts of the moving source with respect to the observers is shown below. Which of the following is true?

  15. ConcepTest 16.11aDoppler Effect I 1) frequency is highest at A 2) frequency is highest at B 3) frequency is highest at C 4)frequency is the same at all three points Observers A, B, and C listen to a moving source of sound. The location of the wave fronts of the moving source with respect to the observers is shown below. Which of the following is true? The number of wave fronts hitting observer C per unit time is greatest—thus the observed frequency is highest there. Follow-up: Where is the frequency lowest?

  16. 16-8 Shock Waves and the Sonic Boom If a source is moving faster than the wavespeed in a medium, waves cannot keep up and a shock wave is formed. The angle of the cone is:

  17. Chapter 31Maxwell’s Equations and Electromagnetic Waves

  18. Units of Chapter 31 • 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

  19. Units of Chapter 31 • Measuring the Speed of Light • Energy in EM Waves; the Poynting Vector • Radiation Pressure • Radio and Television; Wireless Communication

  20. E&M Equations to date Two for the electric field; only one for the magnetic field – not very symmetric!

  21. Plastic Copper ConcepTest 31.1a EM Waves I 1) theplasticloop 2) thecopperloop 3) voltage issamein both A loop with an AC current produces a changing magnetic field. Two loops have the same area, but one is made of plastic and the other copper. In which of the loops is the induced voltage greater?

  22. Plastic Copper ConcepTest 31.1a EM Waves I 1) theplasticloop 2) thecopperloop 3) voltage issamein both A loop with an AC current produces a changing magnetic field. Two loops have the same area, but one is made of plastic and the other copper. In which of the loops is the induced voltage greater? Faraday’s law says nothing about the material: The change in flux is the same (and N is the same), so the induced emf is the same.

  23. 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):

  24. E&M Equations to date - updated

  25. E&M Equations to date - updated No effect since RHS identically zero These two not pretty, i.e., not symmetric

  26. E&M Equations to date – more updated Wouldn’t it be nice if we could replace ??? with something?

  27. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current Ampère’s law relates the magnetic field around a current to the current through a surface.

  28. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current 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:

  29. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current 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:

  30. 31-1 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current Example 31-1: Charging capacitor. A 30-pF air-gap capacitor has circular plates of area A = 100 cm2. It is charged by a 70-V battery through a 2.0-Ωresistor. 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. 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 μ0), and is sometimes called the displacement current: where

  32. 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:

  33. 31-4 Production of Electromagnetic Waves 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.

  34. 31-4 Production of Electromagnetic Waves Oscillating charges will produce electromagnetic waves:

  35. 31-4 Production of Electromagnetic Waves Close to the antenna, the fields are complicated, and are called the near field:

  36. 31-4 Production of Electromagnetic Waves Far from the source, the waves are plane waves:

  37. 31-4 Production of Electromagnetic Waves The electric and magnetic waves are perpendicular to each other, and to the direction of propagation.

  38. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations In the absence of currents and charges, Maxwell’s equations become:

  39. 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

  40. 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:

  41. 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

  42. 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,

  43. 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations The magnitude of this speed is 3.0 x 108 m/s – precisely equal to the measured speed of light.

  44. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum The frequency of an electromagnetic wave is related to its wavelength and to the speed of light:

  45. 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 E0 = 2.0 V/m. Write vector expressions for E and B as functions of position and time.

  46. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum Electromagnetic waves can have any wavelength; we have given different names to different parts of the wavelength spectrum.

  47. 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 1014 Hz.

  48. 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.

  49. ConcepTest 31.2 Oscillations 1) in the north-south plane 2) in the up-down plane 3) in the NE-SW plane 4) in the NW-SE plane 5) in the east-west plane The electric field in an EM wave traveling northeast oscillates up and down. In what plane does the magnetic field oscillate?

  50. ConcepTest 31.2 Oscillations 1) in the north-south plane 2) in the up-down plane 3) in the NE-SW plane 4) in the NW-SE plane 5) in the east-west plane The electric field in an EM wave traveling northeast oscillates up and down. In what plane does the magnetic field oscillate? The magnetic field oscillates perpendicular to BOTH the electric field and the direction of the wave. Therefore the magnetic field must oscillate in the NW-SE plane.

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