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**(Feimer's Physics Page)**

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**Study Of Waves, Energy, Light, and Sound**

**Waves and Energy:** Energy can be transferred by waves as
well as by the transfer of matter. It is the former that this page addresses..

**Categories of Waves:**

**1. Mechanical Waves:** This type of wave requires a medium (material)
to travel through. Examples of such waves would be waves on a jump
rope, a slinky, surface waves on water, and sound waves.

**2. Electromagnetic Waves:** This type of wave requires no
medium (substance) to travel through. Visible Light and X-rays are
examples of two kinds of electromagnetic waves.

**Three General Types of Waves:**

**1. Transverse Wave:** This type of wave causes the particles
in a medium to vibrate perpendicular to the direction in which the the
wave moves. Two examples are that of waves sent along a jump rope or along
a spring such as a slinky.

**2. Longitudinal Wave:** This type of wave causes the particles
in a medium to vibrate parallel to the direction in which the wave moves.
Two examples are a compression wave moving along a spring (produced by
compressing and then releasing a few coils of a spring) and a sound wave.

**3. Surface Wave:** This type of wave has characteristic of both
the transverse wave and the longitudinal wave. Surface waves cause particles
on the surface of a medium to move both horizontally and vertically in
sort of a rolling, circular motion as the wave moves forward. An example
are the surface waves moving across a body of water.

**More Facts about waves:** A medium vibrates in response to
a wave moving along through the material, but the medium itself does not
move with the wave. A pulse is a single disturbance in the medium. A single
ripple spreading out across a pond would be an example of a single pulse.
A wave train is a series of pulses at regular intervals. A series of waves
rolling up on a shore is an example of a wave train.

**Common Terminology and Measurements: ** A wave crest is the
highest point on a transverse wave or the point of maximum compression
on a longitudinal wave. A wave trough is the lowest point on a transverse
wave or the point of least compression on a longitudinal wave. The
wavelength of a wave is the distance between corresponding points on consecutive
waves. The wave height of a wave is the maximum displacement of the
wave from the rest or equilibrium position. The period of a wave
is the time required for one complete wave to pass a single point.
The frequency of a wave is the number of waves passing a given point per
second. (Remember that 1 wave / second is 1 Hz (1 Hertz)) The
velocity of a wave is the speed and direction of the wave. The equation
to find the velocity of the wave is v = f l
. (f is the symbol for the frequency for the wave and l
is the symbol for the wavelength of the wave.)

**A Comparison of two waves:**

Wave 1: A wave with a frequency of 2 Hz and a wavelength of 4
m / wave has a

period of 0.5 seconds per wave and a velocity of 8 m/s.

Wave 2: A wave with a frequency of 4 Hz and a wavelength of 2
m / wave has a

period of 0.25 seconds per wave and a velocity of 8 m/s.

Example problem: A wave having a wavelength of 0.1 m moves past
a point in 0.25 seconds.

Calculate the speed of the wave.

G: T = 0.25 s, l = 0.1 m

F: The speed of the wave

E: v = f l.

S: v = (1 / 0.25 s)(0.1 m)

A: v = 0.4 m/s

**Wave Pulses at Boundaries:** The junction of two media is
referred to as a boundary. A wave pulse reaching a boundary is often
partially reflected and partially transmitted. When a pulse encounters
a new medium at a boundary that is more rigid or dense than the medium
it has been already traveling through the reflected pulse is inverted.
If the new medium is less rigid or dense the reflected pulse is not inverted.

**Superposition of Waves:** When two or more waves meet they
pass through one another and the displacements of the waves affect each
other in either an additive or subtractive way. This is referred to as
wave interference. The positioning of one wave upon another is called
the super positioning of one wave on top of another. The result can
be either constructive or destructive interference. Constructive
interference occurs when wave crests meet producing a single crest larger
than either wave individually. Destructive interference occurs when
two waves meet and a crest and a trough come together canceling the wave
pulses passing through each other at that point.

**Standing Waves:** To understand a standing wave consider
the following idea. Attach one end of a jump rope or a long spring
to a wall or doorknob. Hold the other end in your hand. Begin by
sending a series of waves down the rope or spring. Pulses will be
reflected back towards you when the waves your are generating reach the
wall or the doorknob. If you adjust the motion of your hand, you
can get the wave you are generating and the wave being reflected synchronized
so that the waves overlap perfectly. When this is accomplished you
will see points along the rope (or spring) that remain stationary.
These appear to be about every half wavelength and are called nodes.
Between these nodes the rope (or spring) appear to be experiencing maximum
displacement from the rope's (or spring's) rest position. These points
of maximum amplitude are called anti nodes. A wave that appears to
remain stationary with visible nodes and anti nodes being observed is called
a standing wave.

**Properties of Waves:**

**1. Reflection:** The law of reflection says that the angle
at which a wave approaches a barrier is equal to the angle at which the
wave is reflected. Angles are measured from a line perpendicular
to the reflective surface.

**The Law of Reflection: ** The angle of reflection = the angle
of incidence

**2. Refraction:** The law of refraction says that as a wave
crosses a boundary between two media of different densities the wave changes
direction. When light approaches a boundary between two transparent
media the angle of incidence formed between the normal and the incoming
light ray is different from the angle of refraction formed between the
normal and the light ray continuing through the new media. The relationship
between the two angles is defined by Snell's Law.

**Snell's Law: ** n = the sine of the angle of incident / the
sine of the angle of refraction. n is the index of refraction for
individual transparent materials. When a light ray crosses a boundary
between a low dense material like air into a more dense material like glass,
the light ray is bent towards the normal. If a light ray moves from
a more dense material like glass into a less dense material like air the
light ray is bent away from the normal.

**3. Diffraction:** This is the bending of a wave around a
barrier placed in the waves path. This explains how light and sound
waves can be detected on the opposite side of a barrier such as a wall
sitting in the path of the waves.

**Electromagnetic Radiation: ** An electrical and magnetic disturbance
which travels through space in the form of a wave. Electromagnetic
radiation can travel through the vacuum of space. In a vacuum it
travels at about 186,000 miles / second.

The Electromagnetic Spectrum: Listed from highest energy to lowest energy

**Gamma Rays**: Given off in nuclear reactions. Used to see inside
concrete supports. Used to treat cancer.

**X-rays**: Used in medicine to see dense masses like bones
which cast shadows on the film used to take pictures.

**Ultra-violet light**: Causes sunburn. Blocked by the ozone
layer. Sterilizes surgeries. Used in forensic science.

**Visible light**: Many application. The most significant is in laser
technologies from laser scalpels to communication.

**Infra-red rays**: Heat rays. Used to keep food warm. Used
in remote controls.

**Microwaves**: Used to cook food. Used to send large
quantities of data in the communication industries.

**Radio waves**: Used for TV. Used for AM and FM radio.
Used in all sorts of radio communication and in radar.

According to the equation E = h f, The energy of a wave varies
directly with the frequency of the wave.

According to the equation v = f l.,
The frequency of a wave varies inversely with the wavelength of a wave.

Visible light too can be arranged from highest energy to lowest energy.

**V**iolet
**I**ndigo
**B**lue
**G**reen
**Y**ellow
**O**range
**R**ed

To remember the colors from low to high energy remember ROY G BIV

**Colors seen in objects we look at are dependent upon wavelengths
(colors) absorbed and transmitted.**
**When we see that an object is yellow, it is because the material
that the object is made out of absorbs other colors of light, but not yellow.
Yellow is the color that is reflected off of the object and reaches our
eyes.**

**Snell's Law: **Refraction is described as the bending of
light as light rays cross from one transparent substance into another.
This bending occurs at the boundary. Snell's law tells us that there
is a relationship between the angle if incidence and the angle of refraction.
This relationship says that there is a value called the index of refraction,
symbol n, for every transparent substance. This value is equal to
the ratio of the sine of the angle of incidence to the sine of the angle
of refraction. The equation is written as n = sin i / sin r.
The determination of the angles is based on rays of light passing from
a vacuum into a transparent material.

**Example: **A ray of light traveling through air is incident
upon a sheet of crown glass at an angle of 30 degrees. What is the
angle of refraction.

The equation to be used is n(i) sin qi =
n(r) sin qr, where n(i) is the index of refraction

The substitution is 1.00 (sin 30 deg) = 1.52 (sin qr)

Sin qr = 1.00 (sin 30 deg) / 1.52 = 0.329

The answer is qr = 19.2 deg

**Focusing light with concave mirrors:** Light can be focussed
by using concave mirrors. Spherical concave mirrors can be used to
accomplish this, but do have one drawback. They do not produce as crisp
an image as a parabolic mirror. However, if a little fuzziness is
ok, then a spherical concave mirror will work just fine. A spherical
concave mirror has a center of curvature and will have a measure of its
radius defining its degree of curvature.

The equation used to determine the location of an image produced by
the mirror using light from an object is 1/f = 1 / di + 1 /
do, where: f is the focal length of the mirror, which is the distance between
the focal point and the mirror, the focal length of the mirror is always
one half of the radius of the mirror,

di is the distance the image is from the mirror, also called the location
of the image,

do is the distance the object is from the mirror, also called the location
of the object.

The equation used to determine the size and orientation of an image
produced by the mirror is hi / ho = -di / do

where hi is the height of the image and ho is the height of the object.

The use of the negative sign in the above equation is a means of indicating
that the image is, itself, inverted.

Texts usually show the equation with a negative sign in it so the answer
describes the inverted nature of the image being produced.

This equation is called the magnification equation, because the magnification
resulting from the use of the mirror is defined by the ratio hi / ho. As
an equation it is written as m = hi / ho

**Example:** An object 2 cm high is 30.0 cm in front of a concave
mirror. The radius of the mirror is 20 cm. Determine the location
of the image and determine the size of the object.

The equation to be used to find the location is 1/f = 1
/ di + 1 / do

The equation is changed to 1 / di = 1 / f - 1 / do

The substitution is 1 / di = 1 / 10 cm - 1 / 30 cm

The common denominator yields 1 / di = 3 / 30 cm - 1 / 30 cm = 2 /
30 cm

The answer is di = 15 cm / 2 = 15 cm

The equation used to find the size of the image is hi / ho = di / do

The cross multiplying and the division yields hi = ho di / do

The substitution is hi = 2 cm (15 cm) / 30 cm = 1 cm

**Focussing light with convex lenses: ** The focussing of light
rays using convex lenses uses the same equations as the focussing of light
with concave mirrors does. All variable symbols are also the same. Study
the text book examples of these two scenarios for more practice.