Lecture 19
2d standing wave patterns
some math (f(x-vt) & wave equation)
some more math (gradient operator)
Maxwells equations
Monday, February 25, 13
Exam
Physics 340 midterm I: distribution
5
histogram
median
mean
mean+/-
histogram
4
3
2
1
0
0
20
40
60
Physics 340 Homework Assignment #3
Sept. 28, Due Oct. 5 (in class)
Reading: Chapter 17 and 18
Problems:
1) Text (17.110) Rods made of copper, brass and steel are welded together to form a Y shaped
figure. The cross-sectional area of each rod is 2 cm2. The
Physics 340 Homework Assignment #3 Solution
1) Text (17.110) Rods made of copper, brass and steel are welded together to form a Y shaped
figure. The cross-sectional area of each rod is 2 cm2. The free end of the Cu rod is maintained at
100oC and the free
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Lenses, Optical systems
1. The eye has the job of focusing light from objects at distances from
about = 25 cm to objects very far, = , onto the retina, at the
back of the eye. The image distance is the diameter of the eyeball,
= +2
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Properties of matter: Heat capacities
Constants: = 273.15 + , 1atm= 101,000 Pa, = 6.02 1023 /mol, =
8.31 Jmol K, = 1.38 1023 J/K, 1u = 1.67 1027kg.
1. In the troposphere, the part of the atmosphere that extends from the surface to a
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1. What would you expect for the interference pattern from the following wedge formed
from glass placed on top of a mirror, illuminated with light of wavelength ?
Mirror
2. An experiment is conducted in which red light is diffracted
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Constants: = 273.15 + , = 334kJ/kg for water, 1atm= 101kPa
09-30: The Carnot cycle and second law
1. A refrigerator moves heat from cold to warm. Is this a violation of the second law of
thermodynamics? Why?
2. Here are some propose
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09-26: Heat, Work and the first law
Constants: = 273.15 + , 1atm= 101,000 Pa, = 6.02 1023 /mol, =
8.31 Jmol K, = 1.38 1023 J/K.
1. An ideal gas undergoes a thermodynamic process of two isobaric and two isothermal
steps as shown in t
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10-24 Beats, Doppler and Interference
1. Two sources of waves, A and B, produce waves in phase with one another, so that a
peak leaves each source at the same moment. If = 3/2. Find all positions along
the horizontal line between A
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Radiation and Conduction 09-14
1. A building has 4 walls, each with area 40 m2, which are insulated with R-values of
3.5 m2 K/W insulation (about R-19 in imperial units). The interior of the building is
20 C and the outside air is -
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Constants: = 273.15 + , 1atm= 101,000 Pa, = 8.31 Jmol K
09-30: heat engines and cyclic processes
1. A gasoline engine takes in 14,100 J and delivers 3400 J of work per cycle. The heat is
obtained by burning gasoline with a heat of c
Physics 340: Heat,
Waves and Light
25 Geometric
Optics: Mirrors and
Lenses
25-1
Class Items
Exams to be returned Friday.
New homework assignment posted tonight. Due a week from Friday.
Read chapter 34 on geometric optics for today and Friday.
25-2
Images
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Ideal Gas and Gas Kinetics 09-15
Constants: = 273.15 + , 1atm= 101,000 Pa, = 6.02 1023 /mol, =
8.31 Jmol K.
1. If the pressure of an ideal monatomic gas is increased while the number of moles is
kept constant, what happens to the av
1
Instructor: Jianming Qian
Due: January 19, 2017
Physics 340 (Winter17): Homework Assignment #02
(ideal gas, heat capacity, kinetic theory)
Homework 2.1
A long cylinder of length L and cross section A consists of two halves connected in the middle. One h
1
Instructor: Jianming Qian
Due: January 12, 2017
Physics 340 (Winter17): Homework Assignment #01
(Temperature and heat, phase changes, heat capacity and transfer)
Homework 1.1
A typical doughnut contains 2.0 g of protein, 15.0 g of carbohydrates, and 6.0
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Thermal Stress and Heat Capacity 09-09
1. Mercury was used in thermometers because its a good thermal conductor and it has a
high . A 0.200-cm3 glass bulb is filled with Hg at 20C. How
much mercury flows from the bulb into the threa
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Heat conduction 09-12
1. Put a piece of paper and a piece of metal on the table. Let them sit for a minute or
two.
a) Are they at the same temperature? Why?
b) Touch them briefly with your finger. Which feels colder? How do you reco
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09-23: Heat, Work and Internal Energy
Constants: = 273.15 + , 1atm= 101,000 Pa, = 6.02 1023 /mol, =
8.31 Jmol K, = 1.38 1023 J/K.
An ideal gas undergoes a thermodynamic process of two isobaric and two isothermal
steps as shown in th
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Lenses, Mirrors
1. An object is 18.5 cm from the center of a spherical silvered-glass Christmas tree
ornament 6.00 cm in diameter. What is the position of its image? What is the
magnification?
2. Have you even noticed a water drop m
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1. Revisit the muon question. Suppose a muon is created in the upper atmosphere,
= 0, = 0, in our reference frame and also lets take = 0, = 0 in the frame of
the muon. The speed of the muon is 0.999 c. Lets suppose that the muon ha
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10-14: Mechanical Waves
1. Show that any function (,)=() will satisfy the wave equation:
2
2 y ( x, t )
2 y ( x, t )
.
=
v
t 2
x 2
2. A certain transverse wave is described by
(, ) = 6mm cos 2
26 3.7 102
Determine the waves (a) a
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1. Two very narrow slits are spaced 2.00 m and are placed 50.0 cm from a screen.
What is the distance between the first and second dark lines of the interference pattern
when the slits are illuminated with coherent light with a wave
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Constants: = 273.15 + , = 334kJ/kg and = 4.186 kJ/ kg-K for water,
1atm= 101kPa
10-04: Entropy
1. A 4.50-kg block of ice at 0.00C falls into the ocean and melts. The average
temperature of the ocean is 3.50C, including all the deep
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Maxwell Equations and Electromagnetic Waves
1. Start with an electric field given by (, ) = 0 cos( ).
a. Calculate
(, ) = 0 cos( ) , satisfies the Maxwell equation =
b. Show that
1
if 0 = 0 . (Since = , this implies that 0 = 0 /.
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1. Why is a diffraction grating better at measuring wavelength than a two slit setup?
2. A laser beam of wavelength 632.8 nm shines at the reflective side of a CD. Tracks of
tiny pits are spaced 1.60 m apart on a CD. For what angles
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Light Polarization
1. In the demonstration the electric field is polarized along the x-axis.
a. What is the direction of the magnetic field for electromagnetic
waves propagating toward you (+z direction)?
b. Waves are also propagati
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1. Take moving with a speed = 0.6 in the + direction. Find the coordinates in
of the following
a. = 4m, = 0.
b. = 1.8 108 m, = 1s.
2. In the laboratory two protons approach each other, each with speed 0.99c. What is
the speed of on
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1. The lifetime of a muon is = 2.2. We receive radiation from the sun as muons.
Muons are created in the upper atmosphere as high energy particles from the sun hit
the atmosphere. The atmosphere is about 10 km thick. Travelling at 0
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1 amu = 1.66 1027 kg. Also, = 8.314 J/mol-K
10-19 Sound
1. Air is about 80% N2 and 20% O2. Atmospheric pressure is about 101 kPa at room
temperature.
a. What is /?
b. What is the density, ?
c. A very loud, even damaging, sound inten