Download Lecture17_Maxwell

Physics 7E
Prof. D. Casper
Admin
• Midterms to be returned in Thursday’s discussion sections
• Chapter 16 HW is due Thursday
• Reading
• Wednesday: Chapter 32.1 – 32.3
• Friday: Chapter 32.3 – 32.5
• Monday: Chapter 33.1 – 33.2
Doppler Effect: Moving Listener
A moving listener relative to a stationary
source will encounter wave crests at a different
frequency than they are omitted
The wave crests are spaced a distance 𝜆 apart
The moving listener encounters them at a rate
𝑣 + 𝑣𝐿 𝑣 + 𝑣𝐿
𝑣 + 𝑣𝐿
𝑓𝐿 =
= 𝑣 = 𝑓𝑆
𝜆
𝑣
𝑓𝑆
Note: positive 𝑣𝐿 means in direction from
listener toward source
Q16.8
On a day when there is no wind, you are moving toward a
stationary source of sound waves. Compared to what you
would hear if you were not moving, the sound that you
hear has
A. a higher frequency and a shorter wavelength.
B. the same frequency and a shorter wavelength.
C. a higher frequency and the same wavelength.
D. the same frequency and the same wavelength.
A16.8
On a day when there is no wind, you are moving toward a
stationary source of sound waves. Compared to what you
would hear if you were not moving, the sound that you
hear has
A. a higher frequency and a shorter wavelength.
B. the same frequency and a shorter wavelength.
C. a higher frequency and the same wavelength.
D. the same frequency and the same wavelength.
Doppler Effect: Moving Source
For moving source crests are spaced
closer together in the direction of
motion:
𝜆in front = 𝜆𝑆 − 𝑣𝑆 𝑇𝑆 =
𝑣 𝑣𝑆
−
𝑓𝑆 𝑓𝑆
𝜆in front =
𝑣 − 𝑣𝑆
𝑓𝑆
𝜆behind =
𝑣 + 𝑣𝑆
𝑓𝑆
𝑣 + 𝑣𝐿
𝑓𝐿 =
= 𝑓𝑆
𝜆behind
𝑣 + 𝑣𝐿
𝑣 + 𝑣𝑆
Positive velocity means in direction from L to S!
Q16.9
On a day when there is no wind, you are at rest and a
source of sound waves is moving toward you. Compared to
what you would hear if the source were not moving, the
sound that you hear has
A. a higher frequency and a shorter wavelength.
B. the same frequency and a shorter wavelength.
C. a higher frequency and the same wavelength.
D. the same frequency and the same wavelength.
A16.9
On a day when there is no wind, you are at rest and a
source of sound waves is moving toward you. Compared to
what you would hear if the source were not moving, the
sound that you hear has
A. a higher frequency and a shorter wavelength.
B. the same frequency and a shorter wavelength.
C. a higher frequency and the same wavelength.
D. the same frequency and the same wavelength.
The Doppler Effect and Reflections
One wrinkle that occurs in Doppler problems involves reflection
Work out the frequency of waves hitting a reflector (e.g. wall) by
treating it as a listener. Use 𝑣𝐿 for the velocity of the reflector to find
the frequency waves arrive.
Reflected waves will leave with the same frequency they arrive.
But if the wall is moving it is a moving source for anyone who hears the
reflected sound!
Complicated Example with Reflection
A bat flies at speed 𝑣𝐵 toward a truck moving with speed 𝑣𝑇 away from
the bat. The bat emits a chirp at frequency 𝑓0 which reflects off the truck
and returns to the bat. What return frequency does the bat hear?
We have to solve this problem in two parts:
1. Find the frequency of the direct sound (from bat) arriving at the wall
2. Find the frequency of the reflected sound (from wall) arriving at the bat
Bat Example (1)
For the first part, we have a moving source (the bat) and the truck which
reflects the sound is treated as a moving listener.
The bat is moving in the direction of the truck…is 𝑣𝑆 positive or negative?
Positive is always defined as the direction from listener to source. The source
velocity is therefore negative.
The truck is moving away from the bat…is 𝑣𝐿 positive or negative?
Positive is always defined as the direction from listener to source. The
listener velocity is away from the source, so 𝑣𝐿 is also negative.
The frequency of the sound arriving at the truck is therefore:
𝑣 − 𝑣𝑇
𝑓refl = 𝑓0
𝑣 − 𝑣𝐵
Bat Example (2)
For the reflected sound, we have a moving source (the truck) and a
moving listener (the bat). The truck emits reflected sound at the
frequency we found a moment ago.
The truck is now the source, and the bat is now the listener. Is 𝑣𝑆 now
positive or negative?
Positive is always the direction from listener to source. The truck is
moving in the direction from bat to truck, so 𝑣𝑆 is now positive.
Is 𝑣𝐿 now positive or negative?
The listener (bat) is moving toward the source, so 𝑣𝐿 is also positive.
𝑣 + 𝑣𝐵
𝑣 − 𝑣𝑇 𝑣 + 𝑣𝐵
𝑓final = 𝑓refl
= 𝑓0
𝑣 + 𝑣𝑇
𝑣 + 𝑣𝑇 𝑣 − 𝑣𝐵
Electromagnetic Waves
In this chapter, you should learn:
• Why there are both electric and
magnetic fields in a light wave
• How the speed of light is related to
the fundamental constants of
electricity and magnetism
• How to describe the propagation of
a sinusoidal electromagnetic wave
• What determines the amount of
power carried by an
electromagnetic wave
• How to describe standing
electromagnetic waves
Maxwell’s Equations (#1 and #2)
Gauss’ Law (for Electricity):
𝑄𝑒𝑛𝑐𝑙
∮ 𝐸 ⋅ 𝑑𝐴 =
𝜖0
(Electric field lines begin on positive
charges and end on negative charges)
Gauss’ Law (for Magnetism):
∮ 𝐵 ⋅ 𝑑𝐴 = 0
(There are no isolated magnetic charges)
Maxwell’s Equations (#3)
Faraday’s Law:
𝑑Φ𝐵
∮ 𝐸 ⋅ 𝑑𝑙 = −
𝑑𝑡
(A changing magnetic field creates
an electric field)
Maxwell’s Equations (#4)
Ampere’s Law (Incomplete):
∮ 𝐵 ⋅ 𝑑 𝑙 = 𝜇 0 𝑖𝑐
(A magnetic field is generated by
an electric current…)
Ampere’s Law (Complete):
𝑑Φ𝐸
∮ 𝐵 ⋅ 𝑑 𝑙 = 𝜇0 𝑖𝑐 + 𝜖0
𝑑𝑡
(… or a changing electric field!)
Electromagnetic Waves
An oscillating or accelerating electric charge will radiate energy as a
disturbance in the electric (and magnetic) fields
According to Maxwell’s equations, such a disturbance in the fields
propagates with the speed of light…because it is light!
The expected behavior was confirmed experimentally by Heinrich Hertz
The Electromagnetic Spectrum
Visible light spans a very narrow band of frequencies, compared to full
spectrum of electromagnetic radiation
Properties of Electromagnetic Waves
(in vacuum)
Maxwell’s Equations require:
• The wave travels with a fixed speed
1
𝑐=
≈ 3 × 108 m/s
𝜖0 𝜇0
and both 𝐸 and 𝐵 obey the wave equation
• The wave is transverse; both 𝐸 and 𝐵 are
perpendicular to the wave’s direction of
propagation
• The 𝐸 and 𝐵 fields are perpendicular to each
other
• There is a fixed ratio between the magnitudes
of 𝐸 and 𝐵: 𝐸 = 𝑐𝐵
No physical medium is necessary!
Plane Waves
We will often make the approximation that
the waves we are dealing with are plane
waves.
For a plane wave, if we pick any plane
perpendicular to the direction the wave is
moving, we assume that the values of 𝐸 are
the same at every point in that plane and
the values of 𝐵 are the same at every point
in that plane.
This is a good approximation for waves far
from their source
Sinusoidal Electromagnetic Waves