Physics 1C · 2011-11-30 · Sound waves are longitudinal waves traveling through a medium. ......
Transcript of Physics 1C · 2011-11-30 · Sound waves are longitudinal waves traveling through a medium. ......
Physics 1C Class Review
"All good things must come to an end.”
--Proverb
Outline
CAPE evaluations
Give an Overview of the topics
covered
Try to give some examples
Things We Have Learned 1) Simple Harmonic Motion:
For a mass on a spring, the force on the mass will
be given by:
In general, anything that exhibited simple harmonic
motion:
F F restoring constant displacement
The periods of SHM
can be:
Tspring 2m
k
Tpend 2L
g
Problem
A spring stretches 0.300m when a 0.300kg mass
is hung from it. Determine the spring constant.
Draw a force diagram for the mass when it is first hung on
the spring:
mass Fgravity, Earth on mass
Frestoring, spring on mass
Since the mass is in equilibrium:
Frestoring Fg
+y
kx = mg
k = mg/x = .300kg*9.8m/s2/.150m = 9.8kg/s2
Things We Have Learned 2) Waves:
Waves were a disturbance in a medium created by
a source.
We represent a traveling wave with a sine wave.
vwave
T fWe could relate wavelength
and frequency by:
Things We Have Learned 3) Sound:
Sound waves are longitudinal waves traveling
through a medium.
Sound waves interfere (here k, w, and A are the
same): y1+y2 = 2A cos (f/2) sin (kx - wt + f/2)
fo f s
vsound vo
vsound vs
When the source or the observer is
moving, the frequency will change:
Standing waves occur under wave
reflection such that nodes and anti-
nodes are created:
Things We Have Learned 4) Reflection and Refraction:
When light moves between two
different media, the light will be
refracted at an angle given by:
1 1
When light is reflected off of a
surface it will be reflected at an
angle given by:
Remember that all angles are
measured with respect to the normal!
n1 sin1 n2 sin2
Refraction Example
Light travels from air (n=1.0) to a glass with
n=1.3 and then to a plastic with n=1.5.
Describe the path of the ray as it changes
from one medium to the next.
Answer
Draw schematic
Consider each interface
separately
1
2
3
n = 1.0
n = 1.3
n = 1.5
First Interface Light travels from air (n=1.0) to a glass with
n=1.3. Which way will light bend? By how
much if the angle of incidence is 45?
Snell’s law :
n1 sin 1 = n2 sin 2
2 = sin-1 [(n1 /n2) sin 1]
2 = 33
1
n = 1.0
n = 1.3 2 Any reflection? What is
angle of reflection? Any
phase change?
Does wavelength change?
1'
Second Interface Input to second interface is the output from
the first. What is appropriate angle of
incidence?
2
3
n = 1.3
n = 1.5
2 = 33
Snell’s law :
n2 sin 2 = n3 sin 3
3 = sin-1 [(n2 /n3) sin 2]
3 = 28
Any reflection? What
happens?
Does wavelength change?
Thin Films Light travels from air (n=1.0) to a glass with
n=1.3 and then to a plastic with n=1.5. Do the
reflected rays interfere constructively?
1
2
1' Consider each interface
What leads to constructive
interference?
Phase shift at first
interface?
Phase shift at second
interface?
Path length difference?
2t = n’
n = 1.0
n = 1.3
n = 1.5
t
Things We Have Learned 5) Mirrors and Lenses:
Mirrors use the reflection of light
to divert the light rays.
Lenses use the refraction of
light to divert the light rays.
1
p
1
q
1
f
M h
h
q
p
Ray diagrams
may be useful:
Sign conventions
are important
Thin Lens Equation Example
An object is placed 15cm to the left of a
diverging lens that has a focal length of 10cm.
Describe what the resulting image will look
like (i.e. image
distance,
magnification...).
Answer
The coordinate system
defined.
The center of the lens
is the origin.
Object
N F
Image
Thin Lens Equation Answer
First, turn to the thin lens equation:
where the negative sign means that the
image is on the same side of the lens as the
object (i.e. the left side of the lens).
The magnification of the object will be:
1
p
1
q
1
f
Thin Lens Equation Image is: diminished (|M| = 0.40 < 1).
Upright (M = +0.40 > 0).
Virtual (q = –6.0cm < 0; same side as
object).
Located about
halfway between the
near focal point and
the lens (q = –6.0cm,
f = –10cm).
Object
N F
Image
Things We Have Learned 6) Wave Interference:
The wave nature of light leads to interference effects.
These can be caused by a path length difference or a
phase shift.
Double slit interference was due
to a path length difference.
m dsinThin film interference was due to
both:
2nt m1
2 Con. for 1
phase change
Des. for 1
phase change For m = 0, 1, 2...
Things We Have Learned 7) Electromagnetic Waves:
Electromagnetic waves are transverse waves with
electric and magnetic fields
perpendicular to the
direction of motion.
They carry energy and
momentum.
E = hf
p = E/c Polarization.
I Io cos2
Things We Have Learned 8) Quantum Physics:
Light exhibits wave-particle duality.
Experiments such as the photoelectric effect and the
Compton effect demonstrate the particle nature of
light.
Experiments like double-slit interference and Bragg’s
X-ray scattering demonstrate the wave nature of light.
En nhf
deBroglie hypothesized that all matter
also could have wave properties.
Light is also quantized into
discrete units known as photons.
h
p
h
mv
Clicker Question CR-1 • A star in the sky appears to be blue. The
temperature of this star must be:
A) higher than that of the sun.
B) lower than that of the sun
C) equal to that of the sun.
D) about that of the earth.
Things We Have Learned 9) Atomic Physics:
Emission spectral lines were always at particular
wavelengths for certain elements.
Bohr took this information and decided the atom must be
quantized (just about everything in it was).
rn n2 2
mekee2
2
i
2
f
Hn
1
n
1R
1
E tot 1
2ke
e2
n2ao
13.6 eV
n2
Quantum mechanics starts with the principal quantum
number, n, but also includes other quantum numbers (ℓ,
mℓ, ms).
Things We Have Learned 10) Nuclear Physics:
Rutherford’s thin-foil experiment demonstrated that
the nucleus is small and dense.
Stable nuclei can be categorized by the amount of
binding energy per nucleon they have.
Q m c2 minitial m final c2
Sunset pictures courtesy David Vier
Clicker Question CR-2 In a single-slit diffraction experiment, as the width of
the slit is made smaller, the width of the central
maximum of the diffraction pattern:
A) becomes smaller.
B) becomes wider.
C) remains the same.
D) There will be no
diffraction pattern on the
screen since the
apparatus and screen
distance are set up for a
particular width.
Finals Week Information
Clicker points will be posted online (hopefully) by
Monday.
Recall that clicker points are awarded by
answering questions (1 pt per question) and by
answering correctly (1 additional pt per question).
Clicker questions are worth up to 5 % (extra)
So there are two possible points per clicker
question.
Rainbow pictures courtesy David Vier
ALMOST THE END
Final is Monday, 8am – 11am in this room (2722 York).
There will be 27 questions with 3 extra credit problems.
Bring a Scantron, your ID, and write your proper quiz code number on your form.
For the most part, every chapter will be represented on the final.
Forrest will be holding a problem session during the Friday lecture time.
Sunset pictures courtesy David Vier
THE END
“Go forth and slay dragons.”
--Roderick Reid
Thank you for your
attention
Sunset pictures courtesy David Vier