Lecture PowerPoint
Chapter 11
Physics: Principles with
Applications, 6th edition
Giancoli
© 2005 Pearson Prentice Hall
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11-7 Wave Motion
A wave travels
along its medium,
but the individual
particles just move
up and down.
11-7 Wave Motion
All types of traveling waves transport energy.
Study of a single wave
pulse shows that it is
begun with a vibration
and transmitted through
internal forces in the
medium.
Continuous waves start
with vibrations too. If the
vibration is SHM, then the
wave will be sinusoidal.
11-7 Wave Motion
Wave characteristics:
• Amplitude, A
• Wavelength, λ
• Frequency f and period T
• Wave velocity
1
f 
T
(on formula sheet)
11-8 Types of Waves: Transverse and
Longitudinal
The motion of particles in a wave can either be
perpendicular to the wave direction (transverse) or
parallel to it (longitudinal).
11-8 Types of Waves: Transverse and
Longitudinal
Sound waves are longitudinal waves:
11-8 Types of Waves: Transverse and
Longitudinal
Earthquakes produce both longitudinal and
transverse waves. Both types can travel through
solid material, but only longitudinal waves can
propagate through a fluid – in the transverse
direction, a fluid has no restoring force.
Surface waves are waves that travel along the
boundary between two media.
11-11 Reflection and Transmission of Waves
When waves reach the boundary between two media, they
are partially reflected and partially transmitted. The
difference in the media determines the amount reflected.
A wave hitting an
obstacle will be
reflected (a), and its
reflection will be
inverted. A wave
reaching the end of its
medium, but where the
medium is still free to
move, will be reflected
(b), and its reflection
will be upright.
11-11 Reflection and Transmission of Waves
A wave encountering a denser medium will be partly
reflected and partly transmitted; if the wave speed is
less in the denser medium, the wavelength will be
shorter.
11-11 Reflection and Transmission of Waves
Two- or three-dimensional waves can be
represented by wave fronts, which are curves
of surfaces where all the waves have the same
phase.
Lines perpendicular to
the wave fronts are
called rays; they point in
the direction of
propagation of the wave.
11-11 Reflection and Transmission of Waves
The law of reflection: the angle of incidence
equals the angle of reflection.
11-12 Interference; Principle of Superposition
The superposition principle says that when two waves
pass through the same point, the displacement is the
arithmetic sum of the individual displacements.
In the figure below, (a) exhibits destructive interference
and (b) exhibits constructive interference.
11-12 Interference; Principle of Superposition
These figures show the sum of two waves. In (a)
they add constructively; in (b) they add
destructively; and in (c) they add partially
destructively.
11-13 Standing Waves; Resonance
Standing waves occur
when both ends of a
string are fixed. In that
case, only waves which
are motionless at the
ends of the string can
persist. There are nodes,
where the amplitude is
always zero, and
antinodes, where the
amplitude varies from
zero to the maximum
value.
11-13 Standing Waves; Resonance
The frequencies of the
standing waves on a
particular string are called
resonant frequencies.
They are also referred to as
the fundamental and
harmonics.
11-14 Refraction
If the wave enters a medium where the wave
speed is different, it will be refracted – its wave
fronts and rays will change direction.
We can calculate the angle of
refraction, which depends on
both wave speeds:
(11-20)
11-14 Refraction
The law of refraction works both ways – a wave
going from a slower medium to a faster one
would follow the red line in the other direction.
Water waves refract as they approach the shore.
(a) Soldier analogy to derive (b) law of refraction for
waves.
11-15 Diffraction
When waves encounter
an obstacle, they bend
around it, leaving a
“shadow region.” This is
called diffraction.
11-15 Diffraction
The amount of diffraction depends on the size of
the obstacle compared to the wavelength. If the
obstacle is much smaller than the wavelength,
the wave is barely affected (a). If the object is
comparable to, or larger than, the wavelength,
diffraction is much more significant (b, c, d).
12-1 Characteristics of Sound
Sound can travel through any kind of matter,
but not through a vacuum.
The speed of sound is
different in different
materials; in general, it is
slowest in gases, faster in
liquids, and fastest in solids.
The speed depends
somewhat on temperature,
especially for gases.
12-1 Characteristics of Sound
Loudness: related to intensity of the sound
wave
Pitch: related to frequency.
Audible range: about 20 Hz to 20,000 Hz; upper
limit decreases with age
Ultrasound: above 20,000 Hz; see ultrasonic
camera focusing below
Infrasound:
below 20 Hz
12-4 Sources of Sound: Vibrating Strings
and Air Columns
A tube open at both ends (most wind instruments)
has pressure nodes, and therefore displacement
antinodes, at the ends.
12-5 Quality of Sound, and Noise;
Superposition
So why does a trumpet sound different from a
flute? The answer lies in overtones – which ones
are present, and how strong they are, makes a
big difference.
The plot below shows frequency spectra for a
clarinet, a piano, and a violin. The differences in
overtone strength are apparent.
12-6 Interference of Sound Waves; Beats
Sound waves interfere in the same
way that other waves do in space.
12-6 Interference of Sound Waves; Beats
Waves can also interfere in time, causing a
phenomenon called beats. Beats are the slow
“envelope” around two waves that are relatively
close in frequency.
12-7 Doppler Effect
The Doppler effect occurs when a source of
sound is moving with respect to an observer.
12-7 Doppler Effect
As can be seen in the previous
image, a source moving toward an
observer has a higher frequency
and shorter wavelength; the
opposite is true when a source is
moving away from an observer.
12-7 Doppler Effect
If we can figure
out what the
change in the
wavelength is, we
also know the
change in the
frequency.
12-8 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:
(12-5)
12-8 Shock Waves and the Sonic Boom
Shock waves are analogous to the bow waves
produced by a boat going faster than the wave
speed in water.
12-8 Shock Waves and the Sonic Boom
Aircraft exceeding the speed of sound in air will
produce two sonic booms, one from the front
and one from the tail.
Production of Electromagnetic Waves
The electric and magnetic waves are
perpendicular to each other, and to the
direction of propagation. EM waves are waves
of fields, not matter. Accelerating electric
charges give rise to EM waves.
Light as an Electromagnetic Wave and the
Electromagnetic Spectrum
Light was known to be a wave; after producing
electromagnetic waves of other frequencies, it
was known to be an electromagnetic wave as
well.
The frequency of an electromagnetic wave is
related to its wavelength:
v  f
(On formula sheet)
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.
Light: Geometric Optics
Is the picture on p. 632 right side up?
23-1 The Ray Model of Light
Light very often travels in straight lines. We
represent light using rays, which are straight
lines emanating from an object. This is an
idealization, but is very useful for geometric
optics.
23-2 Reflection; Image Formation by a
Plane Mirror
Law of reflection: the angle of reflection
(that the ray makes with the normal to a
surface) equals the angle of incidence.
23-2 Reflection; Image Formation by a
Plane Mirror
When light reflects from a rough surface, the law
of reflection still holds, but the angle of
incidence varies. This is called diffuse reflection.
23-2 Reflection; Image Formation by a
Plane Mirror
With diffuse reflection, your eye sees
reflected light at all angles. With specular
reflection (from a mirror), your eye must be in
the correct position.
23-2 Reflection; Image Formation by a
Plane Mirror
What you see when you look into a plane (flat)
mirror is an image, which appears to be behind
the mirror.
23-2 Reflection; Image Formation by a
Plane Mirror
This is called a virtual image, as the light does
not go through it. The distance of the image
from the mirror (di) is equal to the distance of
the object from the mirror (do).
In a real image, light passes through the
image. This could appear on a screen or on
film. Curved mirrors and lenses can produce
real images. An example is a movie projector
lens. It produces a real image on the screen.
What is the minimum height of the mirror, and how high must its
lower edge be above the floor, if she is to be able to see her whole
body? Does this result depend on the person’s distance from the
mirror?
23-3 Formation of Images by Spherical
Mirrors
Spherical mirrors are shaped like sections of
a sphere, and may be reflective on either the
inside (concave) or outside (convex).
A convex mirror gives a wide field of view. A concave mirror gives
a magnified image.
23-3 Formation of Images by Spherical
Mirrors
Rays coming from a faraway object are
effectively parallel.
23-3 Formation of Images by Spherical
Mirrors
Parallel rays striking a
spherical mirror do not
all converge at exactly
the same place if the
curvature of the mirror is
large; this is called
spherical aberration. In
other words, a spherical
mirror will not make as
sharp an image as a
plane mirror.
23-3 Formation of Images by Spherical
Mirrors
If the curvature is small, the focus is much more
precise; the focal point is where the rays
converge.
23-3 Formation of Images by Spherical
Mirrors
Using geometry, we find that the focal length is
half the radius of curvature:
(on formula sheet)
Spherical aberration can be avoided by
using a parabolic reflector; these are more
difficult and expensive to make, and so are
used only when necessary, such as in
research telescopes.
23-3 Formation of Images by Spherical
Mirrors
We use ray diagrams to determine where an
image will be. For mirrors, we use three key
rays, all of which begin on the object:
1. A ray parallel to the axis; after reflection it
passes through the focal point
2. A ray through the focal point; after reflection
it is parallel to the axis
3. A ray perpendicular to the mirror; it reflects
back on itself
23-3 Formation of Images by Spherical
Mirrors
Is the image real or
virtual? Why?
23-3 Formation of Images by Spherical
Mirrors
The intersection of these three rays gives the
position of the image of that point on the
object. To get a full image, we can do the
same with other points (two points suffice for
many purposes).
23-3 Formation of Images by Spherical
Mirrors
Geometrically, we can derive an
equation that relates the object
distance, image distance, and
focal length of the mirror:
(on formula sheet )
d=s
23-3 Formation of Images by Spherical
Mirrors
We can also find the magnification (ratio of
image height to object height).
(on formula sheet)
The negative sign indicates that the image is
inverted. This object is between the center of
curvature and the focal point, and its image is
larger, inverted, and real.
23-3 Formation of Images by Spherical
Mirrors
If an object is outside the center of curvature of a
concave mirror, its image will be inverted,
smaller, and real.
23-3 Formation of Images by Spherical
Mirrors
If an object is inside the focal point, its image
will be upright, larger, and virtual.
23-3 Formation of Images by Spherical
Mirrors
For a convex mirror,
the image is always
virtual, upright, and
smaller.
23.3 Formation of Images by Spherical
Mirrors
Problem Solving: Spherical Mirrors
1. Draw a ray diagram; the image is where the rays
intersect.
2. Apply the mirror and magnification equations.
3. Sign conventions: if the object, image, or focal point is
on the reflective side of the mirror, its distance is
positive, and negative otherwise. Magnification is
positive if image is upright, negative otherwise.
4. Check that your solution agrees with the ray diagram.
23.4 Index of Refraction
In general, light slows somewhat when
traveling through a medium. The index of
refraction of the medium is the ratio of the
speed of light in vacuum to the speed of light
in the medium:
(on formula sheet)
23.5 Refraction: Snell’s Law
Light changes direction when crossing a
boundary from one medium to another. This is
called refraction, and the angle the outgoing ray
makes with the normal is called the angle of
refraction.
23.5 Refraction: Snell’s Law
Refraction is what makes objects halfsubmerged in water look odd.
23.5 Refraction: Snell’s Law
The angle of refraction depends on the indices
of refraction, and is given by Snell’s law:
(on formula sheet)
The goggles appear to be above where they really are.
23.6 Total Internal Reflection; Fiber Optics
If light passes into a medium with a smaller
index of refraction, the angle of refraction is
larger. There is an angle of incidence for which
the angle of refraction will be 90°; this is called
the critical angle:
(on formula sheet)
23.6 Total Internal Reflection; Fiber Optics
If the angle of incidence is larger than this,
no transmission occurs. This is called total
internal reflection.
23.6 Total Internal Reflection; Fiber Optics
Binoculars often use total internal reflection;
this gives true 100% reflection, which even the
best mirror cannot do.
23.6 Total Internal Reflection; Fiber Optics
Total internal reflection is also the principle
behind fiber optics. Light will be transmitted
along the fiber even if it is not straight. An image
can be formed using multiple small fibers.
23.7 Thin Lenses; Ray Tracing
Thin lenses are those
whose thickness is small
compared to their radius
of curvature. They may
be either
(a)converging (one that is
thicker in the center than
it is at the edge).
(b)diverging (one that is
thicker at the edge than it
is in the center).
23.7 Thin Lenses; Ray Tracing
Parallel rays are
brought to a focus by
a converging lens.
23.7 Thin Lenses; Ray Tracing
A diverging lens (thicker at the edge than in
the center) make parallel light diverge; the
focal point is that point where the diverging
rays would converge if projected back.
23.7 Thin Lenses; Ray Tracing
The power of a lens is the inverse of its focal
length.
Lens power is measured in diopters, D.
1 D = 1 m-1
23.7 Thin Lenses; Ray Tracing
Ray tracing for thin lenses is similar to that for
mirrors. We have three key rays:
1. This ray comes in parallel to the axis and exits
through the focal point.
2. This ray comes in through the focal point and
exits parallel to the axis.
3. This ray goes through the center of the lens
and is undeflected.
23.7 Thin Lenses; Ray Tracing
The image is real
and inverted.
23.7 Thin Lenses; Ray Tracing
For a diverging lens, we can use the same
three rays; the image is upright and virtual.
23.8 The Thin Lens Equation; Magnification
The thin lens equation is the same as the
mirror equation:
23.8 The Thin Lens Equation; Magnification
The sign conventions are slightly different:
1. The focal length is positive for converging lenses
and negative for diverging.
2. The object distance is positive when the object is on
the same side as the light entering the lens (not an
issue except in compound systems); otherwise it is
negative.
3. The image distance is positive if the image is on the
opposite side from the light entering the lens;
otherwise it is negative.
4. The height of the image is positive if the image is
upright and negative otherwise.
23.8 The Thin Lens Equation; Magnification
The magnification formula is also the same
as that for a mirror:
(23-9)
The power of a lens is positive if it is
converging and negative if it is diverging.
23.8 The Thin Lens Equation; Magnification
Problem Solving: Thin Lenses
1. Draw a ray diagram. The image is located
where the key rays intersect.
2. Solve for unknowns.
3. Follow the sign conventions.
4. Check that your answers are consistent with
the ray diagram.
23.9 Combinations of Lenses
In lens combinations, the image formed by the
first lens becomes the object for the second
lens (this is where object distances may be
negative).
24.3 Interference – Young’s Double-Slit
Experiment
If light is a wave, interference effects will be
seen, where one part of wavefront can interact
with another part.
One way to study this is to do a double-slit
experiment:
24.3 Interference – Young’s Double-Slit
Experiment
If light is a wave,
there should be
an interference
pattern.
24.3 Interference – Young’s Double-Slit
Experiment
The interference occurs because each point on
the screen is not the same distance from both
slits. Depending on the path length difference,
the wave can interfere constructively (bright
spot) or destructively (dark spot).
24.3 Interference – Young’s Double-Slit
Experiment
We can use geometry to find the conditions for
constructive and destructive interference:
(on formula sheet)
d is the distance between the slits and theta is
the angle with the horizontal.
24.4 The Visible Spectrum and Dispersion
The index of refraction of a material varies
somewhat with the wavelength of the light. This
variation in refractive index is why a prism will
split visible light into a rainbow of colors.
24.4 The Visible Spectrum and Dispersion
Actual rainbows are created by dispersion in tiny
drops of water.
24.8 Interference by Thin Films
Another way path lengths can differ, and
waves interfere, is if the travel through
different media.
If there is a very thin film of material – a few
wavelengths thick – light will reflect from both
the bottom and the top of the layer, causing
interference.
This can be seen in soap bubbles and oil
slicks, for example.
24.8 Interference by Thin Films
At A, part of the light is
reflected and part is
transmitted and reflected
at B. The part reflected at
B must travel farther. If
this path difference is a
whole # of wavelengths,
there will be constructive
interference. If it is a half
# of wavelengths, there
will be destructive
interference. Depending
on the thickness of the
oil, different bright colors
will be seen.