Transcript Lecture_19
Chapter 16 Sound Copyright © 2009 Pearson Education, Inc. 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 2) frequency will not change 3) frequency will decrease 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 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. A longer pipe means that the standing wave in the bottle would have a longer wavelength. Because the wave speed remains the same, and we know that v = f l, then we see that the frequency has to be lower. Follow-up: Why doesn’t the wave speed change? ConcepTest 16.9 Interference 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? 1) intensity increases 2) intensity stays the same 3) intensity goes to zero 4) impossible to tell A B L ConcepTest 16.9 Interference 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? 1) intensity increases 2) intensity stays the same 3) intensity goes to zero 4) impossible to tell 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. A Follow-up: What if you move back by 4 m? B L 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. Copyright © 2009 Pearson Education, Inc. 16-7 Doppler Effect Emitted at t T t 0 If we can figure out what the change in the wavelength is, we also know the change in the frequency. l v sT l ' v vs v f f f' 1 v v vs f f' t T v 1 f ' f f v vs 1 vs v Copyright © 2009 Pearson Education, Inc. 16-7 Doppler Effect The change in the frequency is given by: If the source is moving away from the observer: Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. 16-7 Doppler Effect We find, for an observer moving toward a stationary source: And if the observer is moving away: 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? 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? 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! Basic point: if source and receiver moving closer – f’ > f if source and receiver moving apart – f’ < f Copyright © 2009 Pearson Education, Inc. ConcepTest 16.11a Doppler Effect I 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? 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 ConcepTest 16.11a Doppler Effect I 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? 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 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? 16-8 Shock Waves and the Sonic Boom If a source is moving faster than the wave speed in a medium, waves cannot keep up and a shock wave is formed. The angle of the cone is: Copyright © 2009 Pearson Education, Inc. Chapter 31 Maxwell’s Equations and Electromagnetic Waves Copyright © 2009 Pearson Education, Inc. 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 Copyright © 2009 Pearson Education, Inc. Units of Chapter 31 • Measuring the Speed of Light • Energy in EM Waves; the Poynting Vector • Radiation Pressure • Radio and Television; Wireless Communication Copyright © 2009 Pearson Education, Inc. E&M Equations to date Gauss' Law: E dA Qenc 0 dB Faraday's Law: E d dt Ampere's Law: Bd 0 I enc Two for the electric field; only one for the magnetic field – not very symmetric! Copyright © 2009 Pearson Education, Inc. ConcepTest 31.1a 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? EM Waves I 1) the plastic loop 2) the copper loop 3) voltage is same in both Plastic Copper ConcepTest 31.1a 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: d % N B dt The change in flux is the same (and N is the same), so the induced emf is the same. EM Waves I 1) the plastic loop 2) the copper loop 3) voltage is same in both Plastic Copper 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): Qmag 0 Copyright © 2009 Pearson Education, Inc. mag B dA Q 0 enc 0 E&M Equations to date - updated E dA Qenc 0 mag B dA Q 0 enc 0 dB E d dt Bd Copyright © 2009 Pearson Education, Inc. 0 I enc E&M Equations to date - updated E dA Qenc 0 mag B dA Q 0 enc No effect since RHS identically zero dB E d dt Bd 0 I enc dQ dQ mag mag Now, I suggests I 0 dt dt Copyright © 2009 Pearson Education, Inc. These two not pretty, i.e., not symmetric E&M Equations to date – more updated E dA Qenc 0 mag B dA Q 0 enc mag d B I enc E d dt 0 Bd ??? 0 I enc Wouldn’t it be nice if we could replace ??? with something? Copyright © 2009 Pearson Education, Inc. 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. Bd 0 I encl Copyright © 2009 Pearson Education, Inc. 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: Copyright © 2009 Pearson Education, Inc. 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: Copyright © 2009 Pearson Education, Inc. 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-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. 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 μ0), and is sometimes called the displacement current: where 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: Qenc E dA 0 mag B dA Q 0 enc d B I emag nc E d dt 0 dE B d 0 0 dt 0 I enc Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. 31-4 Production of Electromagnetic Waves Oscillating charges will produce electromagnetic waves: 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: Copyright © 2009 Pearson Education, Inc. 31-4 Production of Electromagnetic Waves Far from the source, the waves are plane waves: Copyright © 2009 Pearson Education, Inc. 31-4 Production of Electromagnetic Waves The electric and magnetic waves are perpendicular to each other, and to the direction of propagation. 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: 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 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: . 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 . 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, 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 108 m/s – precisely equal to the measured speed of light. Copyright © 2009 Pearson Education, Inc. 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: 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 E0 = 2.0 V/m. Write vector expressions for E and B as functions of position and time. Copyright © 2009 Pearson Education, Inc. 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. 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 1014 Hz. 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. Copyright © 2009 Pearson Education, Inc. ConcepTest 31.2 Oscillations 1) in the north-south plane The electric field in an EM wave traveling northeast oscillates up and down. In what plane does the magnetic field oscillate? 2) in the up-down plane 3) in the NE-SW plane 4) in the NW-SE plane 5) in the east-west plane ConcepTest 31.2 Oscillations 1) in the north-south plane The electric field in an EM wave traveling northeast oscillates up and down. In what plane does the magnetic field oscillate? 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 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.