Copyright © 2009 Pearson Education, Inc. Chapter 16 Sound

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 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 longer pipe longer wavelength v = f frequency has to be lower 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, then we see that the frequency has to be lower. ConcepTest 16.6c ConcepTest 16.6c Pied Piper III Follow-up: Why doesn’t the wave speed change?

Speakers A and B emit sound waves of = 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? L A B 1) intensity increases 2) intensity stays the same 3) intensity goes to zero 4) impossible to tell ConcepTest 16.9 ConcepTest 16.9 Interference

L A B = 1 m2.5 m2.5 out of phasedestructive interference If = 1 m, then a shift of 2.5 m corresponds to 2.5, which puts the two waves out of phase, leading to destructive interference. The sound intensity will therefore go to zero. Speakers A and B emit sound waves of = 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 ConcepTest 16.9 ConcepTest 16.9 Interference Follow-up: What if you move back by 4 m?

Copyright © 2009 Pearson Education, Inc. The Doppler effect occurs when a source of sound is moving with respect to an observer 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.

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 Doppler Effect

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

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 Doppler Effect

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

Copyright © 2009 Pearson Education, Inc 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 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 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

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 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 observer C The number of wave fronts hitting observer C per unit time is greatest—thus the observed frequency is highest there. ConcepTest 16.11a ConcepTest 16.11a Doppler Effect I Follow-up: Where is the frequency lowest?

Copyright © 2009 Pearson Education, Inc. 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: 16-8 Shock Waves and the Sonic Boom

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

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

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

Copyright © 2009 Pearson Education, Inc. E&M Equations to date Two for the electric field; only one for the magnetic field – not very symmetric!

ConcepTest 31.1aEM Waves I Plastic Copper 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? 1) the plastic loop 2) the copper loop 3) voltage is same in both

Faraday’s law says nothing about the material: change in flux is the same induced emf is the same The change in flux is the same (and N is the same), so the induced emf is the same. ConcepTest 31.1aEM Waves I Plastic Copper 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? 1) the plastic loop 2) the copper loop 3) voltage is same in both

Copyright © 2009 Pearson Education, Inc 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):

Copyright © 2009 Pearson Education, Inc. E&M Equations to date - updated

Copyright © 2009 Pearson Education, Inc. E&M Equations to date - updated No effect since RHS identically zero These two not pretty, i.e., not symmetric

Copyright © 2009 Pearson Education, Inc. E&M Equations to date – more updated Wouldn’t it be nice if we could replace ??? with something?

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

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

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

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 Changing Electric Fields Produce Magnetic Fields; Ampère’s Law and Displacement Current

Copyright © 2009 Pearson Education, Inc 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

Copyright © 2009 Pearson Education, Inc 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:

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 Production of Electromagnetic Waves

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

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

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

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

Copyright © 2009 Pearson Education, Inc 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 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 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 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 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 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.

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

Copyright © 2009 Pearson Education, Inc 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.

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

Copyright © 2009 Pearson Education, Inc 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 Hz.

Copyright © 2009 Pearson Education, Inc 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.

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