Pendulum
Terms
• Period
• Sine curve
• Simple harmonic motion
Equation
• 𝑇 = 2π 𝐿/𝑔
•
http://www.youtube.com/watch?v=P-Umre5Np_0
Spider Problem
A spider swings in the breeze from a silk thread
with a period of 0.6 seconds. How long is the
spiders strand of silk?
Answer:
𝑇 = 2π 𝐿/𝑔
Rearrange equation 𝑇 2 = 4π2 𝐿/𝑔
𝐿=
𝑔𝑇 2 10∗0.62
=
=0.09m
2
2
4π
4π
What Is A Wave?
A WAVE is a disturbance which causes energy to be
transported from one location to another, without a transfer
of mass.
There are two different classifications of waves:
Mechanical Waves
Electromagnetic Waves (EM)
Mechanical Waves
Waves are produced by a disturbance in a physical
medium.
The MEDIUM is the material through which the waves
travel.
The medium moves or oscillates back and forth,
which causes energy to be transported from one
location to another.
Examples of mechanical waves include ocean waves,
sound waves, and earthquake waves. What would be
the mediums for these waves?
Electromagnetic (EM) Waves
EM waves are created by oscillating electric and magnetic
fields.
EM waves require no medium to travel through.
EM waves include such things as Light, X-Rays, Ultraviolet,
Radio waves, and Infrared.
We’ll discuss EM Waves in more detail later.
Waves
Parts of a wave
• Crest
• Trough
• Amplitude
• Wave length
• Frequency
• Period
• Velocity of a wave
A sound wave with a frequency of 262 Hz has a
wavelength of 1.29 m. What is the wave
speed?
V=fλ
V = (262 Hz)(1.29 m)
V = 338 m/s
Radio station Problem
Radio station WKLB in Boston broadcasts at a
frequency of 99.5 MHz. What is the wavelength of
the radio waves emitted by WKLB?
Standing Wave
Nodes
Anti Nodes
Mechanical Waves Review
Symbols and Units:
• Wavelength: λ (lambda) measured in m
• Frequency: f measured in Hz (1/s)
• Period: T measured in s
• Wave speed: v measured in m/s
• Amplitude: A measured in m
Equations:
• T=time/wave and f=# waves/time
• T=1/f and f=1/T
• v= λ/T OR v= λf
Bell Ringer
Ultra sound with a frequency of 4.25 MHz can be
used to produce images of the human body. If the
speed of sound in the body is the same as in salt
water (1500 m/s), What is the wavelength of the
pressure wave in the body?
V=fλ
V/f=λ
λ = (1500 m/s)/(4.25x106Hz)
λ = 3.5 x 10-4 m
Three Types of Waves
1. Transverse Waves- The particles of the medium
move perpendicular to the wave motion.
2. Longitudinal Waves- The particles of the medium
move parallel to (along the direction of) the wave
motion.
3. Surface Waves- The particles of the medium move
both parallel and perpendicular to the wave
motion.
Transverse Waves
Motion of wave
Motion of medium
Motion of medium
Motion of wave
Notice the medium moves up and down,
while the wave moves horizontally. The
highest point is called the crest. The
lowest point is called the trough.
Longitudinal Waves
Motion of wave
Motion of medium
Motion of medium
Here, the medium vibrates back and forth, parallel
to the direction that the wave moves. The regions
where the medium is compressed closest together
are called compressions. The regions in between,
where the medium is stretched far apart are called
rarefactions.
Surface Waves
Motion of Wave
Surface waves occur at the surface of water or other materials. The particles of
the medium travel in a circular fashion, which is a combination of transverse and
longitudinal.
Wave Pulse
A wave pulse occurs if a single disturbance
travels along a medium.
Take a rope or spring, and give a quick jerk to
one side, and then return it, you will create a
wave pulse!
Traveling Waves
If you create a wave pulse continuously, you
will get a traveling wave.
The source of the disturbance vibrates, causing
a steady stream of wave pulses.
This is called a traveling wave.
Doppler effect
Doppler effect: The apparent change in frequency
due to the motion of the source (or receiver)
Example: Fire engine speeding by
Shifting
Red shift: A decrease of apparent frequency.
Blue shift: An increase of apparent frequency.
http://www.youtube.com/watch?v=hVApTLE7Csc
Bow waves
Bow waves: 2D wave generated by an object moving
faster on a wave surface then the waves speed.
When a boat moves faster then the waves speed, ideally it
produces a wave pattern as shown below.
Sonic Booms
Shock waves: 3D wave generated by an object moving
faster in a substance then the waves speed.
Sonic booms: When an aircraft goes fast then the
speed of sound. (330m/s)
http://www.youtube.com/watch?v=6o0zmafxTmE
Bell Ringer
The lowest frequency we can hear is about 20 Hz.
Calculate the wavelength associated with this frequency
for sound that travels at 340 m/s. How long is this in feet?
Sound
What is sound: All sounds are produced by the vibrations of material objects.
So can sound travel through liquids?
How about solids?
Pitch- Same as frequency but is subjective.
Infrasonic- Below the hearing of humans 20 Hz
Ultrasonic- Above the hearing of humans 20,000 Hz
Speed of Sound: 330 m/s (738 mil/hr) in air at 0°C
Sound travels faster through denser material
So does sound travel through water faster?
How about metals?
Loudness
Decibel (dB): This is the intensity of sound
It is logarithmic. Meaning that
it goes up in powers of ten.
Hearing starts with zero dB and
goes till threshold of pain at 120 dB
Natural Frequency and Resonance
Natural frequency: It is the natural frequency an object will vibrate at.
Almost all objects have a natural frequency that it will vibrates at.
Resonance: When frequency of a forced vibration on an object matches the
object’s natural frequency, a dramatic increase in amplitude occurs.
http://www.youtube.com/watch?v=3mclp9QmCGs
Interference
Interference- When two waves combined to make a new waves
Constructive interference- When 2 waves in phase add to make a larger wave
Destructive interference- When 2 waves out of phase add to cancel out the
waves and make no wave
http://www.youtube.com/watch?v=J_xd9hUZ2AY
http://homepages.ius.edu/kforinas/physlets/waves/waves.html
Interference patterns
Beats
When two frequencies are close to each other but are off by a small
frequency they create interference that is called beats.
You can calculate the beats by subtracting the two frequencies from each
other and you will get how many beats there are per second.
Single source online generator
http://www.audiocheck.net/audiofrequencysignalgenerator_sinetone.php
Bell Ringer
The first violinist plays a G note (196.0 Hz) and the second
violinist attempts to plays the same note but hears beats
4 beats per second.
• What are the two frequencies she could be playing at?
• If second violinist tighten the string a little bit and then
hear 5 beats are they sharp or flat?
• (i.e. above or below the first violins frequency).
History of Light
Ancients thought of light
Olaus Roemer (1675) – Jupiter's moon Io experiment
Albert Michelson (1880) Octagonal Mirror experiment
Michelson-Morley Light travels on Aether.
http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/mmexpt6
.htm
Theorist
Date
Idea
Theory
Socrates &
Plato
400 BC
Light originates in the eyes; particles traveled to objects and
return to the eyes enabling sight.
Empedocles
400 BC
Objects give off waves of light; the waves reach your eyes
enabling you to see them.
Wave
Newton
mid 1600s
Studied color; created rainbow from white light; light can
divide into pieces of color.
Particle
Huygens
mid 1600s
Light is a source of spherical waves; the waves reach your eye
allowing you to see.
Wave
Young
early 1800s
Light produces interference; light waves overlap one another
enabling sight.
Wave
Einstein
early 1900s
Light travels as photons; the photoelectric effect is the release
of energy we see as light.
Particle
Particle
Light
Speed of light is constant through space: 3.0 x10 8m/s (67,108,089 mile/hour)
symbolized by C
If light were to travel for a year how far would it go?
Answer:
V=d/t  Vt=d
d= 300,000 m/s * 1 year
𝑑=
300,000 𝑘𝑚
365 𝑑𝑎𝑦 24 ℎ𝑟 3600 𝑠𝑒𝑐
x 1 yr x
𝑥
𝑥
𝑠𝑒𝑐
1 𝑦𝑟
1 𝑑𝑎𝑦
1 ℎ𝑟
D=9.5x1012 km or 9,500,000,000,000 or 9.5 quadrillion kilometer
The distance light travels in one year is a light-year.
Light is produced by vibrating electrons
Quantum mechanics says that light is both a waves and a particle
Photons are the massless packets of light.
Electromagnetic waves: a self propagating wave of magnetic and electric
fields
Electromagnetic spectrum: The range of the electromagnetic waves.
(see next slide)
Memorize the spectrum
Shadows
Transparent: When light can travel through a object with out being altered
or blocked
Opaque: when light is absorbed with out reemission and thus allows no light
through it.
Different materials can be transparent with certain frequencies but are
opaque with other frequencies. Example is the Earth’s atmosphere is
transparent to visible light by opaque to infrared light.
Shadows (cont.)
Ray: A thin beam of light. Can be thought of as a line.
Any beam of light is full of rays
Shadow: places that light rays can not reach
Umbra: total shadow, where light rays are stopped by an edge of an object.
Penumbra: partial shadow, when some of the light is blacked but other light
sources fill in.
Polarization
Light travels in transverse waves. This is shown by polarization.
Polarization is allowing only certain direction of light.
This is how they do 3D movies
Optical Illusions
http://www.youtube.com/watch?v=7WXW2bBWBEg
Bell Ringer
Alpha Centauri is the nearest star to us, if its 4.2 Light years away how far in
kilometers is the nearest star ?
C=d/t=3x108 m/s
C*t=d
(3.0𝑥106 𝑘𝑚/𝑠)(4.2𝑦𝑟𝑠)(
365 𝑑𝑦 24 ℎ𝑟 60 𝑚𝑖𝑛 60 𝑠
)(
)(
)(
)
1 𝑦𝑟
𝑑𝑦
ℎ𝑟
𝑚𝑖𝑛
3.9x1014km
To give you an idea how large that is, it is about 270,00
times the distance from the sun to the Earth.
Color
Spectrum- When light is spread out into its different colors.
Like a prism does to sun light.
White light- Under white light objects appear white and colored objects
appear there color. It reflexes all colors of light and absorbs none. Because
white light reflexes all colors of light it is not really a color but is all colors
Black- is similar to white in that it is not a color itself but is the absences of
light. Objects appear black when they absorb light of all colors of light.
Reflection of color
Because all objects absorb some kind of natural frequency (talked about in
previous chapters) all objects will absorb a specific frequency. The
frequencies that are reflected will depend on the kind of light shone on it.
What are the colors
that reflected on this
flower?
Color by transmission
Transparent objects depends on the color of the light is transmits.
Red piece of glass appears of red because it absorbs all the colors
of white light except red.
Pigments- materials in an object that
selectively absorbs colored light.
Sun light
Mixing Colored Light
The three colors that make up the Primary
Colors are red, green, and blue. They can be
mixed in any proportion to make any color.
When you mix colors you get:
• Red + Green = Yellow
• Red + Blue = Magenta
• Blue + Green = Cyan
• Yellow + Blue = White
When you mix two colors together to
produce white they are called
complementary colors.
• Magenta + Green = White
• Cyan + Red = White
Mixing Colored Pigments
The mixing of paints and dyes is an entirely different process from the mixing of
colored light.
Because pigments reflect colored light we
use the Subtractive primary colors .
http://www.youtube.com/watch?v=ygUch
cpRNyk
Color Subtraction
Pigments
Absorbs
Reflects
Red
Blue, Green
Red
Green
Blue, Red
Green
Blue
Red, Green
Blue
Yellow
Blue
Red, Green
Cyan
Red
Green, Blue
Magenta
Green
Red, Blue
Why is the Sky Blue
When white light travels through the atmospheres shorter wavelength gets
scattered the most, allowing longer light to travel through it. This I causes
the sky to appear blue.
Why Is The Sunset Red?
Because light has to travel through more atmosphere the closer to sunset,
blue wavelengths are scatted more causing a red hue.
What Is The Color Of Water
Why is really clear water cyan in color?
Water molecules absorbed red light and the complementary color or red is cyan.
So cyan is reflected.
Colored Spectrum
When gases are electrified they emits a specific color. (aka neon lights)
When white light goes through a small slit the light is refracted and sped out
into a rainbow. This is called Spectroscopy and the instrument is called
spectroscope.
But when electrified gases go through the spectroscope line appear because
the atoms electrons move in certain way emitting specific colors.
Different spectral lines
for different elements