Vincent Selhorst-Jones

Intro to Waves

Slide Duration:

Section 1: Motion
Math Review

16m 49s

Intro
0:00
The Metric System
0:26
Distance, Mass, Volume, and Time
0:27
Scientific Notation
1:40
Examples: 47,000,000,000 and 0.00000002
1:41
Significant Figures
3:18
Significant Figures Overview
3:19
Properties of Significant Figures
4:04
How Significant Figures Interact
7:00
Trigonometry Review
8:57
Pythagorean Theorem, sine, cosine, and tangent
8:58
Inverse Trigonometric Functions
9:48
Inverse Trigonometric Functions
9:49
Vectors
10:44
Vectors
10:45
Scalars
12:10
Scalars
12:11
Breaking a Vector into Components
13:17
Breaking a Vector into Components
13:18
Length of a Vector
13:58
Length of a Vector
13:59
Relationship Between Length, Angle, and Coordinates
14:45
One Dimensional Kinematics

26m 2s

Intro
0:00
Position
0:06
Definition and Example of Position
0:07
Distance
1:11
Definition and Example of Distance
1:12
Displacement
1:34
Definition and Example of Displacement
1:35
Comparison
2:45
Distance vs. Displacement
2:46
Notation
2:54
Notation for Location, Distance, and Displacement
2:55
Speed
3:32
Definition and Formula for Speed
3:33
Example: Speed
3:51
Velocity
4:23
Definition and Formula for Velocity
4:24
∆ - Greek: 'Delta'
5:01
∆ or 'Change In'
5:02
Acceleration
6:02
Definition and Formula for Acceleration
6:03
Example: Acceleration
6:38
Gravity
7:31
Gravity
7:32
Formulas
8:44
Kinematics Formula 1
8:45
Kinematics Formula 2
9:32
Definitional Formulas
14:00
Example 1: Speed of a Rock Being Thrown
14:12
Example 2: How Long Does It Take for the Rock to Hit the Ground?
15:37
Example 3: Acceleration of a Biker
21:09
Example 4: Velocity and Displacement of a UFO
22:43
Multi-Dimensional Kinematics

29m 59s

Intro
0:00
0:07
Scalars and Vectors
0:08
A Note on Vectors
2:12
Indicating Vectors
2:13
Position
3:03
Position
3:04
Distance and Displacement
3:35
Distance and Displacement: Definitions
3:36
Distance and Displacement: Example
4:39
Speed and Velocity
8:57
Speed and Velocity: Definition & Formulas
8:58
Speed and Velocity: Example
10:06
Speed from Velocity
12:01
Speed from Velocity
12:02
Acceleration
14:09
Acceleration
14:10
Gravity
14:26
Gravity
14:27
Formulas
15:11
Formulas with Vectors
15:12
Example 1: Average Acceleration
16:57
Example 2A: Initial Velocity
19:14
Example 2B: How Long Does It Take for the Ball to Hit the Ground?
21:35
Example 2C: Displacement
26:46
Frames of Reference

18m 36s

Intro
0:00
Fundamental Example
0:25
Fundamental Example Part 1
0:26
Fundamental Example Part 2
1:20
General Case
2:36
Particle P and Two Observers A and B
2:37
Speed of P from A's Frame of Reference
3:05
3:22
Acceleration Shows the Change in Velocity
3:23
Acceleration when Velocity is Constant
3:48
Multi-Dimensional Case
4:35
Multi-Dimensional Case
4:36
Some Notes
5:04
Choosing the Frame of Reference
5:05
Example 1: What Velocity does the Ball have from the Frame of Reference of a Stationary Observer?
7:27
Example 2: Velocity, Speed, and Displacement
9:26
Example 3: Speed and Acceleration in the Reference Frame
12:44
Uniform Circular Motion

16m 34s

Intro
0:00
Centripetal Acceleration
1:21
Centripetal Acceleration of a Rock Being Twirled Around on a String
1:22
Looking Closer: Instantaneous Velocity and Tangential Velocity
2:35
Magnitude of Acceleration
3:55
Centripetal Acceleration Formula
5:14
You Say You Want a Revolution
6:11
What is a Revolution?
6:12
How Long Does it Take to Complete One Revolution Around the Circle?
6:51
Example 1: Centripetal Acceleration of a Rock
7:40
Example 2: Magnitude of a Car's Acceleration While Turning
9:20
Example 3: Speed of a Point on the Edge of a US Quarter
13:10
Section 2: Force
Newton's 1st Law

12m 37s

Intro
0:00
Newton's First Law/ Law of Inertia
2:45
A Body's Velocity Remains Constant Unless Acted Upon by a Force
2:46
Mass & Inertia
4:07
Mass & Inertia
4:08
Mass & Volume
5:49
Mass & Volume
5:50
Mass & Weight
7:08
Mass & Weight
7:09
Example 1: The Speed of a Rocket
8:47
Example 2: Which of the Following Has More Inertia?
10:06
Example 3: Change in Inertia
11:51
Newton's 2nd Law: Introduction

27m 5s

Intro
0:00
Net Force
1:42
Consider a Block That is Pushed On Equally From Both Sides
1:43
What if One of the Forces was Greater Than the Other?
2:29
The Net Force is All the Forces Put Together
2:43
Newton's Second Law
3:14
Net Force = (Mass) x (Acceleration)
3:15
Units
3:48
The Units of Newton's Second Law
3:49
Free-Body Diagram
5:34
Free-Body Diagram
5:35
Special Forces: Gravity (Weight)
8:05
Force of Gravity
8:06
Special Forces: Normal Force
9:22
Normal Force
9:23
Special Forces: Tension
10:34
Tension
10:35
Example 1: Force and Acceleration
12:19
Example 2: A 5kg Block is Pushed by Five Forces
13:24
Example 3: A 10kg Block Resting On a Table is Tethered Over a Pulley to a Free-Hanging 2kg Block
16:30
Newton's 2nd Law: Multiple Dimensions

27m 47s

Intro
0:00
Newton's 2nd Law in Multiple Dimensions
0:12
Newton's 2nd Law in Multiple Dimensions
0:13
Components
0:52
Components
0:53
Example: Force in Component Form
1:02
Special Forces
2:39
Review of Special Forces: Gravity, Normal Force, and Tension
2:40
Normal Forces
3:35
Why Do We Call It the Normal Forces?
3:36
Normal Forces on a Flat Horizontal and Vertical Surface
5:00
Normal Forces on an Incline
6:05
Example 1: A 5kg Block is Pushed By a Force of 3N to the North and a Force of 4N to the East
10:22
Example 2: A 20kg Block is On an Incline of 50° With a Rope Holding It In Place
16:08
Example 3: A 10kg Block is On an Incline of 20° Attached By Rope to a Free-hanging Block of 5kg
20:50

42m 5s

Intro
0:00
Block and Tackle Pulley System
0:30
A Single Pulley Lifting System
0:31
A Double Pulley Lifting System
1:32
2:59
Example 1: A Free-hanging, Massless String is Holding Up Three Objects of Unknown Mass
4:40
Example 2: An Object is Acted Upon by Three Forces
10:23
Example 3: A Chandelier is Suspended by a Cable From the Roof of an Elevator
17:13
Example 4: A 20kg Baboon Climbs a Massless Rope That is Attached to a 22kg Crate
23:46
Example 5: Two Blocks are Roped Together on Inclines of Different Angles
33:17
Newton's Third Law

16m 47s

Intro
0:00
Newton's Third Law
0:50
Newton's Third Law
0:51
Everyday Examples
1:24
Hammer Hitting a Nail
1:25
Swimming
2:08
Car Driving
2:35
Walking
3:15
Note
3:57
Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 1
3:58
Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 2
5:36
Example 1: What Force Does the Moon Pull on Earth?
7:04
Example 2: An Astronaut in Deep Space Throwing a Wrench
8:38
Example 3: A Woman Sitting in a Bosun's Chair that is Hanging from a Rope that Runs Over a Frictionless Pulley
12:51
Friction

50m 11s

Intro
0:00
Introduction
0:04
Our Intuition - Materials
0:30
Our Intuition - Weight
2:48
Our Intuition - Normal Force
3:45
The Normal Force and Friction
4:11
Two Scenarios: Same Object, Same Surface, Different Orientations
4:12
6:36
Friction as an Equation
7:23
Summing Up Friction
7:24
Friction as an Equation
7:36
The Direction of Friction
10:33
The Direction of Friction
10:34
A Quick Example
11:16
Which Block Will Accelerate Faster?
11:17
Static vs. Kinetic
14:52
Static vs. Kinetic
14:53
Static and Kinetic Coefficient of Friction
16:31
How to Use Static Friction
17:40
How to Use Static Friction
17:41
Some Examples of μs and μk
19:51
Some Examples of μs and μk
19:52
A Remark on Wheels
22:19
A Remark on Wheels
22:20
Example 1: Calculating μs and μk
28:02
Example 2: At What Angle Does the Block Begin to Slide?
31:35
Example 3: A Block is Against a Wall, Sliding Down
36:30
Example 4: Two Blocks Sitting Atop Each Other
40:16
Force & Uniform Circular Motion

26m 45s

Intro
0:00
Centripetal Force
0:46
Equations for Centripetal Force
0:47
Centripetal Force in Action
1:26
Where Does Centripetal Force Come From?
2:39
Where Does Centripetal Force Come From?
2:40
Centrifugal Force
4:05
Centrifugal Force Part 1
4:06
Centrifugal Force Part 2
6:16
Example 1: Part A - Centripetal Force On the Car
8:12
Example 1: Part B - Maximum Speed the Car Can Take the Turn At Without Slipping
8:56
Example 2: A Bucket Full of Water is Spun Around in a Vertical Circle
15:13
Example 3: A Rock is Spun Around in a Vertical Circle
21:36
Section 3: Energy
Work

28m 34s

Intro
0:00
Equivocation
0:05
Equivocation
0:06
Introduction to Work
0:32
Scenarios: 10kg Block on a Frictionless Table
0:33
Scenario: 2 Block of Different Masses
2:52
Work
4:12
Work and Force
4:13
Paralleled vs. Perpendicular
4:46
Work: A Formal Definition
7:33
An Alternate Formula
9:00
An Alternate Formula
9:01
Units
10:40
Unit for Work: Joule (J)
10:41
Example 1: Calculating Work of Force
11:32
Example 2: Work and the Force of Gravity
12:48
Example 3: A Moving Box & Force Pushing in the Opposite Direction
15:11
Example 4: Work and Forces with Directions
18:06
Example 5: Work and the Force of Gravity
23:16
Energy: Kinetic

39m 7s

Intro
0:00
Types of Energy
0:04
Types of Energy
0:05
Conservation of Energy
1:12
Conservation of Energy
1:13
What is Energy?
4:23
Energy
4:24
What is Work?
5:01
Work
5:02
Circular Definition, Much?
5:46
Circular Definition, Much?
5:47
Derivation of Kinetic Energy (Simplified)
7:44
Simplified Picture of Work
7:45
Consider the Following Three Formulas
8:42
Kinetic Energy Formula
11:01
Kinetic Energy Formula
11:02
Units
11:54
Units for Kinetic Energy
11:55
Conservation of Energy
13:24
Energy Cannot be Made or Destroyed, Only Transferred
13:25
Friction
15:02
How Does Friction Work?
15:03
Example 1: Velocity of a Block
15:59
Example 2: Energy Released During a Collision
18:28
Example 3: Speed of a Block
22:22
Example 4: Speed and Position of a Block
26:22
Energy: Gravitational Potential

28m 10s

Intro
0:00
Why Is It Called Potential Energy?
0:21
Why Is It Called Potential Energy?
0:22
Introduction to Gravitational Potential Energy
1:20
Consider an Object Dropped from Ever-Increasing heights
1:21
Gravitational Potential Energy
2:02
Gravitational Potential Energy: Derivation
2:03
Gravitational Potential Energy: Formulas
2:52
Gravitational Potential Energy: Notes
3:48
Conservation of Energy
5:50
Conservation of Energy and Formula
5:51
Example 1: Speed of a Falling Rock
6:31
Example 2: Energy Lost to Air Drag
10:58
Example 3: Distance of a Sliding Block
15:51
Example 4: Swinging Acrobat
21:32
Energy: Elastic Potential

44m 16s

Intro
0:00
Introduction to Elastic Potential
0:12
Elastic Object
0:13
Spring Example
1:11
Hooke's Law
3:27
Hooke's Law
3:28
Example of Hooke's Law
5:14
Elastic Potential Energy Formula
8:27
Elastic Potential Energy Formula
8:28
Conservation of Energy
10:17
Conservation of Energy
10:18
You Ain't Seen Nothin' Yet
12:12
You Ain't Seen Nothin' Yet
12:13
Example 1: Spring-Launcher
13:10
Example 2: Compressed Spring
18:34
Example 3: A Block Dangling From a Massless Spring
24:33
Example 4: Finding the Spring Constant
36:13
Power & Simple Machines

28m 54s

Intro
0:00
Introduction to Power & Simple Machines
0:06
What's the Difference Between a Go-Kart, a Family Van, and a Racecar?
0:07
Consider the Idea of Climbing a Flight of Stairs
1:13
Power
2:35
P= W / t
2:36
Alternate Formulas
2:59
Alternate Formulas
3:00
Units
4:24
Units for Power: Watt, Horsepower, and Kilowatt-hour
4:25
Block and Tackle, Redux
5:29
Block and Tackle Systems
5:30
Machines in General
9:44
Levers
9:45
Ramps
10:51
Example 1: Power of Force
12:22
Example 2: Power &Lifting a Watermelon
14:21
Example 3: Work and Instantaneous Power
16:05
Example 4: Power and Acceleration of a Race car
25:56
Section 4: Momentum
Center of Mass

36m 55s

Intro
0:00
Introduction to Center of Mass
0:04
Consider a Ball Tossed in the Air
0:05
Center of Mass
1:27
Definition of Center of Mass
1:28
Example of center of Mass
2:13
Center of Mass: Derivation
4:21
Center of Mass: Formula
6:44
Center of Mass: Formula, Multiple Dimensions
8:15
Center of Mass: Symmetry
9:07
Center of Mass: Non-Homogeneous
11:00
Center of Gravity
12:09
Center of Mass vs. Center of Gravity
12:10
Newton's Second Law and the Center of Mass
14:35
Newton's Second Law and the Center of Mass
14:36
Example 1: Finding The Center of Mass
16:29
Example 2: Finding The Center of Mass
18:55
Example 3: Finding The Center of Mass
21:46
Example 4: A Boy and His Mail
28:31
Linear Momentum

22m 50s

Intro
0:00
Introduction to Linear Momentum
0:04
Linear Momentum Overview
0:05
Consider the Scenarios
0:45
Linear Momentum
1:45
Definition of Linear Momentum
1:46
Impulse
3:10
Impulse
3:11
Relationship Between Impulse & Momentum
4:27
Relationship Between Impulse & Momentum
4:28
Why is It Linear Momentum?
6:55
Why is It Linear Momentum?
6:56
Example 1: Momentum of a Skateboard
8:25
Example 2: Impulse and Final Velocity
8:57
Example 3: Change in Linear Momentum and magnitude of the Impulse
13:53
Example 4: A Ball of Putty
17:07
Collisions & Linear Momentum

40m 55s

Intro
0:00
Investigating Collisions
0:45
Momentum
0:46
Center of Mass
1:26
Derivation
1:56
Extending Idea of Momentum to a System
1:57
Impulse
5:10
Conservation of Linear Momentum
6:14
Conservation of Linear Momentum
6:15
Conservation and External Forces
7:56
Conservation and External Forces
7:57
Momentum Vs. Energy
9:52
Momentum Vs. Energy
9:53
Types of Collisions
12:33
Elastic
12:34
Inelastic
12:54
Completely Inelastic
13:24
Everyday Collisions and Atomic Collisions
13:42
Example 1: Impact of Two Cars
14:07
Example 2: Billiard Balls
16:59
Example 3: Elastic Collision
23:52
Example 4: Bullet's Velocity
33:35
Section 5: Gravity
Gravity & Orbits

34m 53s

Intro
0:00
Law of Universal Gravitation
1:39
Law of Universal Gravitation
1:40
Force of Gravity Equation
2:14
Gravitational Field
5:38
Gravitational Field Overview
5:39
Gravitational Field Equation
6:32
Orbits
9:25
Orbits
9:26
The 'Falling' Moon
12:58
The 'Falling' Moon
12:59
Example 1: Force of Gravity
17:05
Example 2: Gravitational Field on the Surface of Earth
20:35
Example 3: Orbits
23:15
Example 4: Neutron Star
28:38
Section 6: Waves
Intro to Waves

35m 35s

Intro
0:00
Pulse
1:00
Introduction to Pulse
1:01
Wave
1:59
Wave Overview
2:00
Wave Types
3:16
Mechanical Waves
3:17
Electromagnetic Waves
4:01
Matter or Quantum Mechanical Waves
4:43
Transverse Waves
5:12
Longitudinal Waves
6:24
Wave Characteristics
7:24
Amplitude and Wavelength
7:25
Wave Speed (v)
10:13
Period (T)
11:02
Frequency (f)
12:33
v = λf
14:51
Wave Equation
16:15
Wave Equation
16:16
Angular Wave Number
17:34
Angular Frequency
19:36
Example 1: CPU Frequency
24:35
Example 2: Speed of Light, Wavelength, and Frequency
26:11
Example 3: Spacing of Grooves
28:35
Example 4: Wave Diagram
31:21
Waves, Cont.

52m 57s

Intro
0:00
Superposition
0:38
Superposition
0:39
Interference
1:31
Interference
1:32
Visual Example: Two Positive Pulses
2:33
Visual Example: Wave
4:02
Phase of Cycle
6:25
Phase Shift
7:31
Phase Shift
7:32
Standing Waves
9:59
Introduction to Standing Waves
10:00
Visual Examples: Standing Waves, Node, and Antinode
11:27
Standing Waves and Wavelengths
15:37
Standing Waves and Resonant Frequency
19:18
Doppler Effect
20:36
When Emitter and Receiver are Still
20:37
When Emitter is Moving Towards You
22:31
When Emitter is Moving Away
24:12
Doppler Effect: Formula
25:58
Example 1: Superposed Waves
30:00
Example 2: Superposed and Fully Destructive Interference
35:57
Example 3: Standing Waves on a String
40:45
Example 4: Police Siren
43:26
Example Sounds: 800 Hz, 906.7 Hz, 715.8 Hz, and Slide 906.7 to 715.8 Hz
48:49
Sound

36m 24s

Intro
0:00
Speed of Sound
1:26
Speed of Sound
1:27
Pitch
2:44
High Pitch & Low Pitch
2:45
Normal Hearing
3:45
Infrasonic and Ultrasonic
4:02
Intensity
4:54
Intensity: I = P/A
4:55
Intensity of Sound as an Outwardly Radiating Sphere
6:32
Decibels
9:09
Human Threshold for Hearing
9:10
Decibel (dB)
10:28
Sound Level β
11:53
Loudness Examples
13:44
Loudness Examples
13:45
Beats
15:41
Beats & Frequency
15:42
Audio Examples of Beats
17:04
Sonic Boom
20:21
Sonic Boom
20:22
Example 1: Firework
23:14
Example 2: Intensity and Decibels
24:48
Example 3: Decibels
28:24
Example 4: Frequency of a Violin
34:48
Light

19m 38s

Intro
0:00
The Speed of Light
0:31
Speed of Light in a Vacuum
0:32
Unique Properties of Light
1:20
Lightspeed!
3:24
Lightyear
3:25
Medium
4:34
Light & Medium
4:35
Electromagnetic Spectrum
5:49
Electromagnetic Spectrum Overview
5:50
Electromagnetic Wave Classifications
7:05
7:06
Microwave
8:30
Infrared and Visible Spectrum
9:02
Ultraviolet, X-rays, and Gamma Rays
9:33
So Much Left to Explore
11:07
So Much Left to Explore
11:08
Example 1: How Much Distance is in a Light-year?
13:16
Example 2: Electromagnetic Wave
16:50
Example 3: Radio Station & Wavelength
17:55
Section 7: Thermodynamics
Fluids

42m 52s

Intro
0:00
Fluid?
0:48
What Does It Mean to be a Fluid?
0:49
Density
1:46
What is Density?
1:47
Formula for Density: ρ = m/V
2:25
Pressure
3:40
Consider Two Equal Height Cylinders of Water with Different Areas
3:41
Definition and Formula for Pressure: p = F/A
5:20
Pressure at Depth
7:02
Pressure at Depth Overview
7:03
Free Body Diagram for Pressure in a Container of Fluid
8:31
Equations for Pressure at Depth
10:29
Absolute Pressure vs. Gauge Pressure
12:31
Absolute Pressure vs. Gauge Pressure
12:32
Why Does Gauge Pressure Matter?
13:51
Depth, Not Shape or Direction
15:22
Depth, Not Shape or Direction
15:23
Depth = Height
18:27
Depth = Height
18:28
Buoyancy
19:44
Buoyancy and the Buoyant Force
19:45
Archimedes' Principle
21:09
Archimedes' Principle
21:10
22:30
22:31
Example 1: Rock & Fluid
23:47
Example 2: Pressure of Water at the Top of the Reservoir
28:01
Example 3: Wood & Fluid
31:47
Example 4: Force of Air Inside a Cylinder
36:20
Intro to Temperature & Heat

34m 6s

Intro
0:00
Absolute Zero
1:50
Absolute Zero
1:51
Kelvin
2:25
Kelvin
2:26
Heat vs. Temperature
4:21
Heat vs. Temperature
4:22
Heating Water
5:32
Heating Water
5:33
Specific Heat
7:44
Specific Heat: Q = cm(∆T)
7:45
Heat Transfer
9:20
Conduction
9:24
Convection
10:26
11:35
Example 1: Converting Temperature
13:21
Example 2: Calories
14:54
Example 3: Thermal Energy
19:00
Example 4: Temperature When Mixture Comes to Equilibrium Part 1
20:45
Example 4: Temperature When Mixture Comes to Equilibrium Part 2
24:55
Change Due to Heat

44m 3s

Intro
0:00
Linear Expansion
1:06
Linear Expansion: ∆L = Lα(∆T)
1:07
Volume Expansion
2:34
Volume Expansion: ∆V = Vβ(∆T)
2:35
Gas Expansion
3:40
Gas Expansion
3:41
The Mole
5:43
Conceptual Example
5:44
7:30
Ideal Gas Law
9:22
Ideal Gas Law: pV = nRT
9:23
p = Pressure of the Gas
10:07
V = Volume of the Gas
10:34
n = Number of Moles of Gas
10:44
R = Gas Constant
10:58
T = Temperature
11:58
A Note On Water
12:21
A Note On Water
12:22
Change of Phase
15:55
Change of Phase
15:56
Change of Phase and Pressure
17:31
Phase Diagram
18:41
Heat of Transformation
20:38
Heat of Transformation: Q = Lm
20:39
Example 1: Linear Expansion
22:38
Example 2: Explore Why β = 3α
24:40
Example 3: Ideal Gas Law
31:38
Example 4: Heat of Transformation
38:03
Thermodynamics

27m 30s

Intro
0:00
First Law of Thermodynamics
1:11
First Law of Thermodynamics
1:12
Engines
2:25
Conceptual Example: Consider a Piston
2:26
Second Law of Thermodynamics
4:17
Second Law of Thermodynamics
4:18
Entropy
6:09
Definition of Entropy
6:10
Conceptual Example of Entropy: Stick of Dynamite
7:00
Order to Disorder
8:22
Order and Disorder in a System
8:23
The Poets Got It Right
10:20
The Poets Got It Right
10:21
Engines in General
11:21
Engines in General
11:22
Efficiency
12:06
Measuring the Efficiency of a System
12:07
Carnot Engine ( A Limit to Efficiency)
13:20
Carnot Engine & Maximum Possible Efficiency
13:21
Example 1: Internal Energy
15:15
Example 2: Efficiency
16:13
Example 3: Second Law of Thermodynamics
17:05
Example 4: Maximum Efficiency
20:10
Section 8: Electricity
Electric Force & Charge

41m 35s

Intro
0:00
Charge
1:04
Overview of Charge
1:05
Positive and Negative Charges
1:19
A Simple Model of the Atom
2:47
Protons, Electrons, and Neutrons
2:48
Conservation of Charge
4:47
Conservation of Charge
4:48
Elementary Charge
5:41
Elementary Charge and the Unit Coulomb
5:42
Coulomb's Law
8:29
Coulomb's Law & the Electrostatic Force
8:30
Coulomb's Law Breakdown
9:30
Conductors and Insulators
11:11
Conductors
11:12
Insulators
12:31
Conduction
15:08
Conduction
15:09
Conceptual Examples
15:58
Induction
17:02
Induction Overview
17:01
Conceptual Examples
18:18
Example 1: Electroscope
20:08
Example 2: Positive, Negative, and Net Charge of Iron
22:15
Example 3: Charge and Mass
27:52
Example 4: Two Metal Spheres
31:58
Electric Fields & Potential

34m 44s

Intro
0:00
Electric Fields
0:53
Electric Fields Overview
0:54
Size of q2 (Second Charge)
1:34
Size of q1 (First Charge)
1:53
Electric Field Strength: Newtons Per Coulomb
2:55
Electric Field Lines
4:19
Electric Field Lines
4:20
Conceptual Example 1
5:17
Conceptual Example 2
6:20
Conceptual Example 3
6:59
Conceptual Example 4
7:28
8:47
8:48
Why Does It Work?
9:33
Electric Potential Energy
11:40
Electric Potential Energy
11:41
Electric Potential
13:44
Electric Potential
13:45
Difference Between Two States
14:29
Electric Potential is Measured in Volts
15:12
Ground Voltage
16:09
Potential Differences and Reference Voltage
16:10
Ground Voltage
17:20
Electron-volt
19:17
Electron-volt
19:18
Equipotential Surfaces
20:29
Equipotential Surfaces
20:30
Equipotential Lines
21:21
Equipotential Lines
21:22
Example 1: Electric Field
22:40
Example 2: Change in Energy
24:25
Example 3: Constant Electrical Field
27:06
Example 4: Electrical Field and Change in Voltage
29:06
Example 5: Voltage and Energy
32:14
Electric Current

29m 12s

Intro
0:00
Electric Current
0:31
Electric Current
0:32
Amperes
1:27
Moving Charge
1:52
Conceptual Example: Electric Field and a Conductor
1:53
Voltage
3:26
Resistance
5:05
Given Some Voltage, How Much Current Will Flow?
5:06
Resistance: Definition and Formula
5:40
Resistivity
7:31
Resistivity
7:32
Resistance for a Uniform Object
9:31
Energy and Power
9:55
How Much Energy Does It take to Move These Charges Around?
9:56
What Do We Call Energy Per Unit Time?
11:08
Formulas to Express Electrical Power
11:53
Voltage Source
13:38
Introduction to Voltage Source
13:39
Obtaining a Voltage Source: Generator
15:15
Obtaining a Voltage Source: Battery
16:19
Speed of Electricity
17:17
Speed of Electricity
17:18
Example 1: Electric Current & Moving Charge
19:40
Example 2: Electric Current & Resistance
20:31
Example 3: Resistivity & Resistance
21:56
Example 4: Light Bulb
25:16
Electric Circuits

52m 2s

Intro
0:00
Electric Circuits
0:51
Current, Voltage, and Circuit
0:52
Resistor
5:05
Definition of Resistor
5:06
Conceptual Example: Lamps
6:18
Other Fundamental Components
7:04
Circuit Diagrams
7:23
Introduction to Circuit Diagrams
7:24
Wire
7:42
Resistor
8:20
Battery
8:45
Power Supply
9:41
Switch
10:02
Wires: Bypass and Connect
10:53
A Special Not in General
12:04
Example: Simple vs. Complex Circuit Diagram
12:45
Kirchoff's Circuit Laws
15:32
Kirchoff's Circuit Law 1: Current Law
15:33
Kirchoff's Circuit Law 1: Visual Example
16:57
Kirchoff's Circuit Law 2: Voltage Law
17:16
Kirchoff's Circuit Law 2: Visual Example
19:23
Resistors in Series
21:48
Resistors in Series
21:49
Resistors in Parallel
23:33
Resistors in Parallel
23:34
Voltmeter and Ammeter
28:35
Voltmeter
28:36
Ammeter
30:05
Direct Current vs. Alternating Current
31:24
Direct Current vs. Alternating Current
31:25
Visual Example: Voltage Graphs
33:29
Example 1: What Voltage is Read by the Voltmeter in This Diagram?
33:57
Example 2: What Current Flows Through the Ammeter When the Switch is Open?
37:42
Example 3: How Much Power is Dissipated by the Highlighted Resistor When the Switch is Open? When Closed?
41:22
Example 4: Design a Hallway Light Switch
45:14
Section 9: Magnetism
Magnetism

25m 47s

Intro
0:00
Magnet
1:27
Magnet Has Two Poles
1:28
Magnetic Field
1:47
Always a Dipole, Never a Monopole
2:22
Always a Dipole, Never a Monopole
2:23
Magnetic Fields and Moving Charge
4:01
Magnetic Fields and Moving Charge
4:02
Magnets on an Atomic Level
4:45
Magnets on an Atomic Level
4:46
Evenly Distributed Motions
5:45
Unevenly Distributed Motions
6:22
Current and Magnetic Fields
9:42
Current Flow and Magnetic Field
9:43
Electromagnet
11:35
Electric Motor
13:11
Electric Motor
13:12
Generator
15:38
A Changing Magnetic Field Induces a Current
15:39
Example 1: What Kind of Magnetic Pole must the Earth's Geographic North Pole Be?
19:34
Example 2: Magnetic Field and Generator/Electric Motor
20:56
Example 3: Destroying the Magnetic Properties of a Permanent Magnet
23:08
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Intro to Waves

• There are three main categories of waves:
• Mechanical Waves: These travel through a material medium.
• Electromagnetic Waves: EM waves do not require a material medium to exist.
• Matter or Quantum Mechanical Waves: These describe the motion of elemental particles (electrons, protons, etc.) on the atomic level. We won't investigate them in this course.
• We also classify waves based on how they move:
• Transverse Waves: The particles of the wave move perpendicular to the motion of the wave.
• Longitudinal Waves: The particles of the wave move parallel to the motion of the wave. This is done through compression and rarefaction (expansion), i.e., the wave is transmitted by pressure changes.
• We describe a wave with the following characteristics:
• Amplitude (A): How tall the wave is at its maximum height.
• Wavelength (λ): The distance between "repeating" points on the wave, such as top-to-top.
• Wave speed (v): How fast the wave is moving.
• Period (T): The time it takes to go through a full oscillation.
• Frequency (f): The number of oscillations that occur per second. [The unit for this is the hertz (Hz) where 1 Hz = [1/1s]. Thus, f = [1/T] and T = [1/f].]
• Because speed, frequency, and wavelength are all related, v = λf .
• We can find the height (or pressure differential if it's a longitudinal wave) with the following equation:
 y(x,t) = Asin(kx − ωt).
• x is the horizontal location we are considering.
• t is the time we are looking at the wave.
• k is the angular wave number and is connected to the wavelength:
 k = 2πλ .
• ω is the angular frequency and is connected to the period (which is connected to the frequency):
 ω = 2πT ⇔     ω = 2π·f.

Intro to Waves

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Pulse 1:00
• Introduction to Pulse
• Wave 1:59
• Wave Overview
• Wave Types 3:16
• Mechanical Waves
• Electromagnetic Waves
• Matter or Quantum Mechanical Waves
• Transverse Waves
• Longitudinal Waves
• Wave Characteristics 7:24
• Amplitude and Wavelength
• Wave Speed (v)
• Period (T)
• Frequency (f)
• v = λf
• Wave Equation 16:15
• Wave Equation
• Angular Wave Number
• Angular Frequency
• Example 1: CPU Frequency 24:35
• Example 2: Speed of Light, Wavelength, and Frequency 26:11
• Example 3: Spacing of Grooves 28:35
• Example 4: Wave Diagram 31:21

Transcription: Intro to Waves

Welcome back to Educator.com Today we’re going to be talking about an introduction to waves.0000

We’re going to finally get an understanding of how waves work and they have an incredibly large presence in our daily lives.0005

Waves are way for one object or location to have energy transferred to another object or location.0011

That seems like a really large definition and it is. It’s not the only way for energy to be transferred but it a motion of energy from location to location.0018

It also has a lot of other effects and we’ll be investigating some of those.0028

There are many different kinds of waves and you’re constantly around them.0032

Some basic examples that you’re being currently being exposed to: sound and light.0036

Also any vibrating strings, waves in water, and the list goes way on.0041

There’s all sorts of other things, seismic waves in the ground, vibration along a steel pipe.0046

There’s quantum motion in waves, though we won’t be getting into that.0052

Waves make up a fundamental part of the universe and nature around us.0055

To begin with, let’s imagine the idea of a pulse. Imagine you’ve tied one end of a string to a wall, so it’s tied over here and you pull the string taunt.0061

Then you whip it, really suddenly, once. You whip it hard, what’s going to happen?0072

Well you’re going to create a pulse of energy that’s going to be sent down the string.0077

As the energy might be here, we’ll have a sort of raised up area and then as time goes on, not long time probably, it’s going to move to here and then it’ll move to here then it’ll move to here until eventually it hits the wall.0081

So that pulse of energy will be sent down the string and it’ll keep moving down the string towards the wall.0095

We whip it once and we move the energy, the energy that we put into our whip gets transmitted down the string.0099

Some of it goes into heat and other things, we won’t actually be investigating the energy, we will just be investigating the motion of waves.0105

There is definitely a change of energy from a location to another location.0111

You transmit that motion down the line into the wall.0119

Do the same situation but this time you start whipping the string up and down regularly, creating multiple pulses at even time intervals.0122

Some of these pulses are pointing up and some of these pulses are pointing down. What’s going to happen then? You’re creating a wave.0128

Instead we’ve got one pulse here and one pulse here but they form together to make a continuous wave shape. The whole thing makes a wave.0133

Once again, as time moves on, the things going to slide over and the whole thing will move farther along the line and get closer to the wall.0141

As time goes on, the thing shifts forward an amount. It has a constant velocity moving towards wherever it’s moving towards.0150

We’ve created a wave, there is a number of characteristics about the wave. Some of these drawings aren’t quite perfect but the important things is that waves have regularity.0159

It’s the fact that we can always trust it to get to the same height or pressure differential as we’ll talk about much later in sound.0168

We can always trust it to get to the same levels every amount that it goes.0173

Once it goes through one oscillation, one period of itself, it manages to repeat all the same effects.0178

So looking at one snapshot, the right chunk snapshot, it can look just like another chunk snapshot, can look just like another chunk snapshot.0184

That’s when the important ideas of waves, the fact that we’ve got regularity, something we can trust is going to be regular coming down the line.0191

There are three main categories of waves.0199

Mechanical waves are the waves that you probably have the most familiarity with at this point.0202

These are the waves that travel through any sort of material medium.0206

Common examples, the most common one that we’re all used too, sound waves.0209

Every time you hear something, if you hear a big bass drum get kicked at a concert and you feel those vibrations in your chest, in your body, that’s actually another form of sound waves.0212

They are just a very low frequency, so they’re able to vibrate your entire body.0223

Another type would be water waves. Waves on the top of waters is another form of waves.0228

Seismic waves, waves in the motion of the Earth. Things that cause earthquakes, these are all different forms of waves and different propagations of energy.0234

Electrometric waves, EM waves, don’t require material medium to exist.0244

We’re also exposed to these constantly, but you might have less of an intuitive understanding of them.0248

Examples of this is radio waves, the visible light that you’re currently seeing from the screen, X-rays.0254

Anything that has, that is, is light, is a part of the electrometric spectrum, but we’ll talk about that more.0258

That’s a little bit difficult to understand, because light has a whole bunch of special properties that really affect the nature of the universe in incredibly strong ways.0267

That’s going to be its on special section. We’ll very lightly touch the surface of that.0277

But for now, we can just think of it as light.0281

Finally, matter or quantum mechanical waves. These are waves that describe the motion of elemental particles, like the electron, the proton, or even smaller, the quark or the photon on the atomic level.0284

They’re very important to modern physics. They have a whole big impact and what we understand now and where our research is going currently.0296

We’re not going to be investigating them in this course. They behave a little bit differently than the classical waves we’re going to be studying.0302

They’re going to be more challenging to understand, so that’s something we’re going to save a future course.0307

Alright, in addition to the previous categories, the mechanical waves, EM waves, and mater waves.0313

We won’t be talking about mater waves. Mechanical waves are the ones we most understand.0320

They’re the ones that have motion medium. EM waves, they sort of come with their own medium.0325

In addition to the previous categories, we can also classify waves based on how they move.0329

Transverse waves. The particles of the waves move perpendicular to the motion of the waves.0334

If we got something that would normally be a flat line like the surface of the sea.0339

Then we’ve got a wave, an undulating curve on top of it that causes the surface of that sea to move up and down depending on the location of the wave.0344

That’s going to be a transverse wave. It’s happening transverse to the motion, it’s happening perpendicular to the motion of the wave.0353

Examples include a vibrating string, EM waves, any waves in water; not any waves, sorry you can also have sound waves in water.0361

Waves that we’re used to seeing in water. There is a huge varieties of things like this.0369

If you were to knock on a pipe, you’d also once again…if you were to shake a pipe, you’d get waves. If you were to knock on a pipe, you’d get sound waves.0375

Longitude in the waves. The particles of the wave move parallel to the motion of the waves.0387

So this a little bit harder to see and we’ll get the chance to get a better visual understand of this once we get to sound.0390

The particles of the wave move parallel to the motion of the wave. This done through compression and rarefaction, expansion.0395

So if we got two particles like this and remember they’re charged particles so they don’t like getting to close to each other normally.0401

The wave is going to be transmitted by pressure changes. If one particle pushes towards the other one for a moment, a brief moment, they’ll be together and push back away from one another.0407

That pressure wave will wind up getting transmitted all the way through.0418

A pressure front and once they push away from each other, we’ll have a rarefaction of area and they’ll wind up getting pushed back together again by the next pressure front coming through.0423

Pressure changes will transmit the information, will transmit the energy. The motion is being caused by pressure changes.0431

Most common examples is sound. But it also exists in certain kinds of seismic waves.0439

Alright, let’s investigate the wave more deeply. Here’s an okay drawing of how a wave looks.0446

This is a general sinusoidal wave and we can treat most waves as sinusoidal.0451

Meaning it comes from sin, as in the sin function that looks like just like this when you graph it out.0456

First off, amplitude. How tall the wave is at its maximum height.0464

In this case, the amplitude would show up right here. We’d get A there.0469

Somewhere else we’d see it here, we’d see it also right here. Anytime we see the maximum height.0472

What about down here? Well down here, it’s also going to be a height of A.0477

Instead if we were to look at it from an absolute point of view it’s going to show up at –A, although the length will be A.0482

Amplitude is the absolute value of you location from the medium location.0489

Its how far up or down you go, but it’s always going to wind up being a positive number.0495

How tall the wave is at its maximum height is amplitude. A.0499

Wave length, the distance between repeating points on the wave, such as top to top.0504

Remember, one of the important qualities of the wave is that it repeats itself after a certain amount of time.0508

If we go from here to here, notice that this entire area here looks just like this entire area here.0513

Just like this entire area to the front of it and this entire area to the front of it looks the same.0523

And if fact, if we were to go all the way through, we’d wind up getting all the same information.0528

It’s going to look like the exact same thing from the wave length point of view.0532

When you get a one wave length, the distance that it takes to do an oscillation in the wave, you’re going to see repeating points.0537

Everything will wind up repeating. If we go from top to top, we’ll have a wave length.0545

The guy that we use to call out wave length is lambda. Lambda is another Greek letter, he gets thrown around now in waves, he becomes very important.0553

He’s pronounced lambda and spelled in case you’re curious, lambda. Lambda. Lambda is the guy.0561

What some other repeating points on this? What about from here to here?0569

Well that isn’t going to wind up being lambda because notice how this section right here is doing something different than this section right here.0573

If we wanted to say, look from this point, we’d have to go all the way to here because know we’ve got just to the right of it.0582

It’s going up a bit and just to the right of it over here it’s going up a bit.0588

So from here to here would also be another example of lambda.0592

We could do to this from anything as long as we wound up being at the same height and we went through the right amount to wind up having it experience the same affects inside the wave.0597

We’re able to get one wave length. The important part about a wave length is that after you go that distance everything repeats in the wave.0607

More characteristics. Waves speed, how fast the wave is moving.0615

Remember this whole thing is moving forward at some speed. We’ve got some velocity that it’s got.0619

After one second it will be that many meters farther ahead.0625

For velocities and meters per second, we take that and one second later it will be that much velocity meters ahead.0630

Remember the wave is moving along. And as this moves forward we’re going to wind up seeing more of it coming out of it.0638

There is always more wave that’s going to be put in. Either it’s too the left outside of where we’re looking or it gets whipped into place by the motion of whatever is creating the wave.0645

The wave continues out on either side, and the whole thing moves forward.0656

Period. The period is the time it takes to go through a full oscillation.0664

Remember if we got some speed V, that this whole thing has, we’re going to be able to get from here to here and we’ll have a repartition.0668

Now one way is we could change the location we’re looking, but we could also fix the location that we’re looking here.0678

We’d be able to see that T later. We start here, say we start here, but T later because of the velocity will wind up showing up there.0684

If you notice, the velocity times the period is always going to wind up equaling the wave length.0698

Because the amount of time that it takes, if the velocity goes this way and T later is how long it takes to go through a single oscillation, the period is how long it takes from wave peak to get to another wave peak.0708

Or one point on the wave to get to its corresponding twin point on the wave.0721

That’s going to wind up having to be the wave length right? That’s what the definition of the wave length is.0727

We can think of it as a movement, the time that we’ve allowed it to move, and has given us a repetition, a period.0732

Or we could think of it as how far different we’ve seen in the distance that we’re looking in the wave, has given us a repetition on the wave.0740

So we’ve got the velocity times the time that it takes for the period is going to equal that wave length because they’ve got to be equivalent.0747

Frequency, the number of oscillation’s that occur per second.0754

Say we’ve got some period. T is equal to the period right? So in here…it’s gets from here to here if we’re looking from some single place.0759

If we fix our gaze here, so fix our gaze on this blue line, this blue dash line and we look up, we’re going to see this point here.0775

T time later will see the red dot above us. T time later the red dot will have moved to where the blue dot is.0783

If that’s the case, we can ask, alright so, it takes T many seconds and T could a larger number, greater than one or T can be a small number that’s well less than one.0791

We could ask, if it takes us T many seconds to get a repetition in the wave, how many repetitions are we going to get every second?0805

How many oscillations are we going to have per second? How many wave peaks are we going to have per second?0814

Well if that’s the case we’re going to need something that measures per second and that’s where the hertz comes in.0820

That’s one hertz equals one per second. One over one second. So that means the frequency is equal to one second divided by the period.0825

The period, so if we have something is the period of T=0.2 seconds then that means the frequency is going to be 5 because in one second we managed to have 0.2 seconds occur five times.0836

Frequency is the inverse of the period. And the period is equal to the inverse of the frequency.0854

Anytime we want one for the other, we just flip it and we’re able to get the answer.0859

One divided by the other and we take reciprocal and we’ll get it.0863

That’s because the fact we’re looking for long it takes to get from one like point on the wave to another point.0866

How long it takes for a single oscillation to occur is going to also be if we divide one second by how long it takes we’ll get the number of times we get an oscillation.0873

If we have the number of times oscillation happens in a second and we divide one second by those numbers of oscillations, we’ll get how long it takes each oscillation to occur.0882

Finally because speed, frequency, and wave length are all deeply related, we’re going to have the fact that velocity is equal to lambda times frequency.0892

Which is equivalent to velocity times time equals lambda. Remember we know that velocity that we’re moving, times the time it takes to from peak to peak has to be equal to lambda.0900

We’ve got the same thing going on here since V=λf. Well if we divide by F on both sides, we get v/f=λ. Which 1/f=t, so we get vt=λ.0914

So these are equivalent expressions. Why is V=λf make sense? Well if we’ve got lambda distance here, this is lambda…distance.0926

And we know that time, in one second we’re going to see the frequency occur. So if we see ten oscillations in one second, then how much distance have we covered?0939

We’ve covered ten oscillations to each oscillation as one wave length, then ten times the wave length.0949

So the frequency, the number of oscillations we occur, that occur in one second, we have in one second, times how long each one of those oscillations is, is going to be the velocity since we can just divide by one second.0955

Velocity is equal to lambda, the distance, times frequency, which comes in one of our seconds. So we’ve got meters per second.0967

Great. Wave equation, finally we can talk about if want to know the height of a point on a wave.0975

We’ll need to know two inputs. The horizontal location x and the time we’re looking at the wave.0982

Here’s just a quick sketch of a wave. If we got some wave like this, we could either look at this location x or maybe we want to look at this location x.0987

We’re going to get totally different results for that. However, what happens if then we also say, one of them is T=1?0999

What happens when we look at T=2? Well then the entire wave is going to have slid over some amount.1006

We’re going to have the same wave, but it’s going to have slid over and we’re going to get totally different answers for each one of those x’s.1013

That means, the time that we’re looking and also the location on the wave that we’re looking matters.1021

We’ve got a two variable function, we’ve got an equation that’s going to be based off of two variables that give us that dependent variable, that why, what output value.1027

Notice that one other thing about this, if we only care about the point where the wave originates, the very beginning point, x=0, we can simplify this because we can just knock out that x term.1037

We can make it simple at A times sin of omega T. Now, at this point you’re probably wondering what k and omega is, that’s a great question, we’re about to answer it.1046

Our equation is Y of x,t equals a, amplitude, times sin of kx minus omega t and quantity.1056

So before we can use our equation we’re going to define what k and omega mean.1065

K is the angler wave number and it causes our function to give the same value for every wave length lambda.1070

Now remember, in case you don’t remember some of the stuff from trig, every time sin of 2π times any number, n.1075

Where n equals -2, -1, 0, 1, 2… on either side. Any integer number.1085

Sin of 2π repeats, the whole thing repeats, no matter what we’ve got added to that inside of it, we’re going to wind up getting the same answer.1096

Because what we’ve done, whenever we do 2π, we’ve lapped the circle. And we’ve winding up starting here and we lap the circle, then we’re still going to get the same answer.1103

If we lap the circle in the other direction twice it doesn’t matter, we’re going to the same answer as long as we land at the same point.1113

As long as we change by things of 2π we’re going to have the same thing show up.1119

Which makes a lot of sense because on our wave, as long as we change by some wave length distance, we’re going to have all the same stuff show up.1124

If we change by one wave length and we’re using sin, we’re going see inside of it, a factor of 2π show up.1132

So for every wave length we change, we show up by 2π, that’s why we get k here.1140

Because if k is equal to 2π/λ and then we move over by 2λ amount, well the lambdas cancel out and we get 4π, which is equal to 2π times some n.1146

So we’re going to see the exact same thing as if we hadn’t shifted over, which is exactly what makes sense.1159

When we shift over by some wave length amount, it shouldn’t have an effect on what we would have seen otherwise.1164

Shifting over by a wave length is no different from the point of view of what value we’re going to see for the height or the pressure differentials that we’ll talk about later in sound.1168

Same basic ideas going for omega. Omega is the angler frequency and it causes our function to give the same value for every period time. So every period, big T.1178

Omega, not sure if I said, I don’t think I said, this guy right here, is once again another Greek letter and its pronounced omega. O M E G A.1187

You’re probably seen his bigger brother at some point. Capital Omega is that guy but this is lowercase omega.1201

Back to the thing at hand. Omega is the angler frequency and it cause our function to give the same value for every period.1209

Remember once again, every time we pass one period of time, as long as we’re looking at the same location, we should experience no difference right?1216

Every time you go through one period you’ve gone through one entire oscillation, so the wave just looks the same to you from that point of view.1224

As long as you wait 1T to look, everything is going to be the same.1230

So if we plug in omega for 2π over T. And then we hit it with some time that is factor of a period, 3t. Those t’s cancel out and we get something that is just going to get canceled out by sin.1234

We’re going to care about the other information inside of there. So as long as we wind up shifting some amount by a period, it’s not going to have an effect.1246

Let’s look at a slightly more complex example. We’re not going to see the time be just a factor of the period.1256

What if we look at t=1 and t=1+t? So if we look at that then we can say, let’s make it easy on ourselves, we’ll look at just generally…we’ll look at the same location x.1260

X is going to be fixed, otherwise we wouldn’t wind up seeing the periodic nature of the oscillations reoccur.1276

So our two values is going to be, our function is going to be y=a(sin)kx. And what’s k? We’ve got as 2π/λx - ω2π/. x t. The time.1282

If plug in t=1, we’ll plug in t=1 over here so t=1, we’re going to get y is equal to a(sin)2π/λ whatever x we’d chosen minus 2π/tx1, so there we are. That’s what we’re going to wind up seeing.1305

What happens when we plug in 1 plus one more period of time? Well we’re going to hope that we’re going to see the exact same value.1328

We’ll plug that one over here, we’ve got y=a times sin of 2πλ times x minus, now what…times one plus t, we’ll get 2π over t plus just 2π right?1334

So if that’s the case then we’ve got y=a sin 2π λ x - 2π/t - 2π.1358

This part right here winds up being the exact same as this part right here.1371

The only part that’s different is this here, but remember since we’re dealing with sin, since we’ve moved just one more 2π, we’re some location.1379

Then we just spin it around and boom we wind up being at the exact same location because we’ve moved by -2π.1389

So this location here, this stuff all here, is our real location. So if wind up shifting things by one whole period, even if we start at some time that isn’t a whole thing of a period, the way we’ve got this set up.1396

Since we’re using sin, a regular periodic function, we’ve got the fact we’re able to make those oscillations occur in our mathematics, our algebra, is able to support our visual oscillations.1409

We move a period temporally in algebra, we wind up moving that same full length time, so we see the exact thing.1422

The exact same would happen if we used k, if we used…if we moved x around and this sort of thing, but this is just to illustrate that the math here is really working and why it is.1430

We’ve got to make sure that 2π over t is able to handle a motion of a period as causing no effect to the values we’ll get out. Same thing with the motions of a wave length.1439

That’s why that 2π comes in, is because sins, sins natural period is 2π right? Its period before it repeats is 2π.1448

So we have to have a way to have those two periods, the period of the wave we’re working with and the period of the natural function we’re working with to be able to communicate with each other and that’s what this is all about.1456

Then finally, if we have 2π/t since over t is the same thing as times frequency, we get omega is also equal to 2π times the frequency, as simple as that.1465

Finally we’re ready to work on some examples. If we have a CPU on some device that has a frequency of 1 gigahertz, then we’ve got a frequency equals 1 gigahertz.1476

How many hertz is that? Well it goes, kila, mega, giga. So 10^3, 10^6, 10^9.1487

So 1 gigahertz becomes 1x10^9 hertz.1494

What’s the time that it would take to complete a single cycle? So if we want to know what the period is, then we remember the fact that frequency equals 1 over t.1501

T equals 1 over f. If want to know the period, t equals 1 over 1 gigahertz. 1x10^9.1512

Which becomes 10^-9, which is the same thing as mila, micro, nano. So we get one nanosecond is how long it takes.1523

There are 10^9 nanoseconds in a single second, which makes sense because 10^9, there has to be 10^9 nanoseconds because each of those cycles has to be complete for it to be able a whole frequency of 10^9 cycles completing.1524

So CPU, we’ve got the same, it’s not directly a wave in the same way, but we’ve got the fact that it’s having repetitive things happen.1539

Its going through cycles, it’s cycling through data. We’re able to talk about it in terms of frequency and in terms of periods just like we do with waves.1566

If the speed of light is velocity 3x10^8 meters per second, mighty fast. And you receive a wave with a wave length of 500 nanometers. Very small wave length. What is its frequency?1573

Speed of light is v=3x10^8 meters per second and you receive a wave with a wave length of 500 nanometers. We already know what v is, v is here.1588

So 500 nanometers is the wave length, right? The wave length equals 500 nanometers, which is the same thing as nana, 10^-9, 500x10^-9 meters.1598

If we want to know what its frequency is, we remember that velocity is equal to the frequency times lambda.1611

The frequency times lambda has to give us the velocity because that’s how much distance has been covered.1620

Wave length is a chuck of distance and frequency is how many times you have those chunks distance in one second to we cover. Frequency times wave length.1625

We cover fxλ and that gives us our v.1634

v=fxλ, so v/λ=f, so if we want to know what f is. F is going to be equal to 3x10^8/500x10^-9.1637

We plug that into a calculator and we get 6x10^14 hertz. That’s a giant frequency compared to the stuff that we’re used to seeing in sound.1655

For light though that’s pretty reasonable and you’re probably seeing a color pretty close to that.1666

6x10^14 hertz is a receivable for the human eye, it’s something in the visual spectrum and I think, don’t hold me to this, it’s probably pretty close to either yellow, green, or blue, somewhere in that sort of range.1671

Probably a little bit closer to the blue, green or blue. Anyway, that’s something that your eye is actually really able to see and so as opposed to seeing a numerical frequency data when we look at something.1687

We don’t say “Oh, that frequency is that”. We see a color. We’ve got these other ways of interpreting the information that the universe is sending to us.1697

It is a real thing, we are getting real information here just like when we go to some height, we’re really at a height but we can measure that height and periodically we’re able to measure the frequency we see in periodically.1704

If you’re driving a car going 30 meters per second and the car beings to run over a rumble strip, rumble strips are these evenly spaced grooves used to alert drivers, so little down grooves in the road like this.1716

So when a tire rolls over it, the tire falls in the up and down motion, winds up jostling the driver and they notice something, or they’re accidentally swerving off to the side, they notice that they’re swerving off to the side or if they’re coming up on some toll, they notice that they’re coming up to some toll.1733

It’s just something to alert drivers. If the strip vibrates your car at 98 hertz, what’s the spacing of the grooves?1747

First off, I’d like to point out that this isn’t technically a wave. Just like in #1 we weren’t technically working with a wave, but we can still apply many of the concepts.1754

In this case, the wave speed, we know the velocity of the car is equal to 30 meters per second.1762

While the wave might not be moving, the way it’s experiencing the wave is moving. In another way we could consider the tire is still, and the wave is the thing moving.1771

From your point of view you can’t really tell who’s moving when you’re inside of the car, although we look at our scenery and we can easily tell.1783

But you know, we can’t be sure who’s the thing that’s moving. It’s possible the road is the thing moving. So you can take it as the wave moving underneath you.1789

Once again, we’re not getting full repartition quite the same, maybe. But we’re not necessarily thinking it purely in terms of wave lengths, but that isn’t the issue.1796

We can expand a lot of these ideas to more things.1806

So we’re running over some rumble strips and it’s moving by us at 30 meters per second, either because the cars moving, or because it’s moving relative to us.1810

If the strip vibrates your car or bounces you up and down 98 hertz or 98 times per second, what the spacing of the grooves got to be?1818

It’s the exact same thing, if it manages to bump us up and down 98 times in a second and the wave length is the spacing of the strips. The spacing of the grooves is going to be the wave length.1827

How far they spread apart, then the 30 meters per second that we experience has got to be that number of times that the wave length times how many times they show up in a second.1838

Velocity is equal to the frequency times lambda. So we plug in our numbers and if we want to know what lambda, is we’re going to have the velocity divided by the frequency.1849

We plug in our numbers 30 meters per second divided by a frequency of 98 hertz and we get 0.306 meters.1860

There we are, the spacing of those grooves is about a third of a meter which makes a lot of sense if you’ve ever looked at them on the street.1872

Example four. Use the following diagram to give an equation describing the wave in the diagram.1882

Now to begin with, lets point out, we just want to remember y equals a, the amplitude, times sin, the function that allows us to have periodicity, allows us to have oscillations occur algebraically.1887

kx - ω x t. So x, the location we are in the wave. T the time that we’re looking at the wave. Omega is the factor that allows us to handle the fact that periods cause repetitions.1901

K is the fact that allows us to handle that wave lengths cause repetitions. To begin with, we know that the period is equal to 0.02 seconds.1915

We know that amplitude is equal 0.5 meters. Okay, great. What is this here?1927

Well that is not equal to the wave length. Remember, if we look just to the right of this point, and look just to the right of this point. We should see the exact same thing.1935

We don’t see the exact same thing, it’s going down over. If we go over here though, we will see it.1944

And because its sin wave, it’s evenly spaced out throughout, we know that 3.5 meters isn’t going to be the wave length, but it’s going to be half the wave length because it’s in one of the dips.1950

So the wave length over 2, so that means that our wave length is equal to 7 meters.1961

That’s all the data that we wind up needing. Now we want to solve for what k has to be.1968

K is equal to 2π/λ, so k is equal to 2π/7. Omega is equal 2π over the period.1972

By the way, k, we’re throwing around k a lot. I never mentioned this but k is not the same k as when we’re dealing with springs. It’s a different k, we’re using it to mean a totally different thing at this point.1985

The k that we’re using in this stuff is different than the k we used before. Just like how little t and big t don’t necessarily mean the same thing. We can even wind up using the same letter for different things, and we have know contextually what we’re talking about.1999

Sorry, I made that assumption, but that’s actually a really important thing. You don’t want to get confused and think that springs and waves necessarily have to do with each other every time. It’s not that same spring constant we were talking about before.2011

Totally different use of k. Anyway back to the problem. Omega is equal to 2π divided by the period.2024

If we know the period is, 2π/0.02 seconds and that will wind up giving us 100π.2030

Simple as this at this point, we just plug in all of our numbers. Y is equal to that amplitude, 0.5 meters times sin, of the numbers 2π/7x-ω100π times the time that we’re looking.2039

That right here is our answer. Simple as that. So we just want to be able to analyze the diagram.2065

One of the most important things to pay attention to the fact that wave length has to be not just some distance where you get the same point, but some distance where you get a point that means the exact same thing.2071

That if you look just a little bit further on and a little bit further behind you’re going to see a full repetition.2083

It’s not just the same point, because the same point occurs at any horizontal thing, except for the very tops and bottoms.2089

These pairs of points are not enough to determine a wave length. What you need is to reach is to reach a little bit farther and look here.2097

The very top to top because tops themselves only occur once every wave length.2104

Whereas middles occur twice. Same with bottoms, you can go from the bottom to the bottom and the top to the top.2111

That’s normally the easiest thing to measure, but if you’re measuring from the middle to the middle, this isn’t enough.2117

You need to also go to here. Okay, great. I hope you enjoyed that, I hope that made sense, waves are a whole bunch of big ideas, but we’re going to…2123

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