Wave Basics + Equation

Parts of a Wave

● Wave- a disturbance that moves from one place to another without moving matter ● Simple harmonic motion- back and forth motion (ie. a pendulum)

● Wavelength- the length completing one wave (crest to crest/trough to trough) ● Crest- the top of a wave/highest point

● Trough- the bottom of a wave/lowest point ● Oscillation- complete cycle

● Frequency- the number of events per time (cycles, vibrations, oscillations, or any repeated events)

● Period- the time required for a complete orbit (one cycle/half a wavelength) ● Amplitude- the distance from the midpoint to the maximum(crest) or to the

minimum(trough) of a wave

● Hertz- the SI unit of frequency, # of cycles per second

Practice Problems #1 and #2

#1: Identify which part of the wave is marked in the diagram shown below

#2: What is the difference between period and wave speed?

A: The period is the time it takes to complete one cycle/half a wavelength, so from a crest to the next trough. Wave speed is the time it takes to complete a full wavelength, so from one crest to the next

Wave Equations

● v= λ • f

○ wave speed/velocity= wavelength • frequency ○ meters per second= meters • Hertz (Hz)

● f= 1/p

○ frequency (Hz)= 1 ÷ period ● λ= v/f

○ wavelength= speed/frequency ○ meters= meters per second/Hz ● p= 1/f

○ period = 1 ÷ frequency (Hz)

Relationships in Waves

● the period and frequency are inversely proportional (ie. doubling the frequency will cut the period in half)

○ f = x2 and p= ÷2

● wavelength and period are directly proportional (ie. doubling the wavelength will double the period)

○ λ = x2 and p= x2

● wavelength and frequency are inversely proportional (ie. doubling the wavelength will cut the frequency in half)

Practice Problems #3 and #4

#3 Given V = 522m/s, f = 261 Hz #4 Given wavelength = 2m, period = ⅓ sec

How long is the wavelength? How fast is the wave speed?

V = λ • f p= 1/f f = 3 Hz

522 m/s = wavelength • 261 Hz V = λ • f

Wavelength = 522 m/s ÷ 261 hz V = 2 meters • 3 Hz

Standing Waves and

Harmonics

Standing Waves

●

Are an example of interference where a string is forced to

vibrate at a particular frequency

●

Node - places in a standing wave that do not move

Harmonics

- Harmonics: the harmonic of a standing

wave describes how many nodes are

present

-- Harmonic level = (n--1) central nodes

-

= # of antinodes

-- # of wavelengths = harmonic #

- Harmonics when one end is

closed and the other is open:

Solving Harmonics Problems

ex) The speed of sound is 330 m/s. You have a 0.5m pipe that is

open on both ends. What note will be the first harmonic of the pipe?

1. Draw the length given of the pipe , then draw the length of a full

wave

2. Determine the length of a full wave based on given information

3. Plug into the equation velocity equals wavelength multiplied by

frequency V=

𝝺

f

Sound

Key Ideas

What is Sound and How does it travel?

★ Sounds are longitudinal waves that come from vibrations of

matter

- It also needs MATTER to travel by collisions with neighboring

particles

- Air molecules must be present in order to transfer vibrations

★ The frequency of sound is the pitch/tone

Doppler Effect

●

Shift in the frequency of a wave sound when the wave source

and/or the receiver is moving.

Speed of Sound

★ The properties of certain materials affect the speed of

sound

- Speed of sound is not affected by the shape or

frequency of the pulses

★ In general, sound travels slowest to fastest in this order:

GASES<LIQUIDS<SOLIDS

As density

DECREASES, speed

INCREASES.

As hardness

INCREASES, speed

INCREASES

SOLIDS

As temperature

INCREASES, speed

INCREASES.

As mass

DECREASES, speed

INCREASES.

LIQUIDS/G

ASES

Decibels

-

The intensity and loudness is related to the amplitude which is

measured in decibels (dB)

- Scaled so zero is barely audible

- Decibel scale is logarithmic

- If there is an increase of 10 that means a sound is 10 times stronger.

EX: A sound level of 70 is 100 times stronger than a sound level of 50

Resonance

- Means to resound or sound again

- It needs a force to pull it back to its starting position and enough

energy to keep it vibrating.

Introduction to Light Review

Light as a Photon

❖ _{Photons are the basic unit of light & transmit electromagnetic energy} ❖ _{They are massless and travel in wave-like patterns}

Speed of light facts

❖

Light travels at a constant speed

Light as a Wave and the Electromagnetic Spectrum

❖ _{When the frequency of a light wave is doubled, the wavelength is halved} ❖ _{Different types of light are defined by changes in wave frequency}

Types of light on the EM spectrum:

● Radio waves have the longest wavelength and the lowest frequency

EM Spectrum

X rays

Gamma rays UV rays Infrared

Micr

owa

ves

Visible light Radio

Absorption, Transmission, & Reflection

❖ _{Absorption: atom absorbs light and converts it into a different energy form} ➢ _{Such as heat}

❖ _{Reflection: when light bounces off a surface}

❖ _{Transmission: When light photons hit an atom and pass on the energy.}

Color Absorption and

Transmission

Cone Cells in the Eyes

● There are cone cells in the back of the eye that receive photons

● A color is seen when photons of the appropriate frequency hit the eyes ● Each cone is set to receive a specific set of frequencies

Additive Color Mixing

- Primary colors are - Red , Blue and Green

- Adding more photons of different frequencies - Examples are tv screens and spotlights

Subtractive Color Mixing

- Primary colors are

- Yellow, Magenta and cyan

- Start with white and remove photons - Filters which remove the color are

- The color an object appears is the color it reflects

- This means that a yellow object

will appear red under red light, and green under green light. Yellow does not contain blue, so it will appear black under blue light. White objects reflect all light,

Refraction and Reflection

Reflection

Reflection - light particles bouncing off of matter

*Reflection is extremely common. In fact, everything you see is just light being reflected off of that object!

Law of Reflection - light bouncing off of a surface will

exit at the same angle it came in at

Ex) If a ray of light hit a

surface at 75°, then the light

Refraction

Waves will tend to bend towards the slower side, for example...

During a

refraction, there

will be an...

Angle of

Incidence,

Angle of

Refraction,

Lenses

Types of Lenses

Convex

●

Thickest in the middle

●

Creates real images (opposite side of object)

●

f

is opposite of object, f

is same side as object

Concave

●

Thickest at the ends

Lens Diagram

Convex Lens

Concave Lens

Lens Equation

This equation can be used to find focal length, distance to the object or the distance to

the image.

(1/d

) + (1/d

) = (1/f)

f = distance from lens to focal point

d

and d

= distance from lens to object or image

REMEMBER THE SIGNS! If the problem deals with a concave lens, f is negative. If it

is a convex lens, f is positive.

Multi Lens System

The image from the first lens

becomes the object for the second.

When using the lens

equation for multi lens

systems, remember the

d

you receive for your

first lens is not necessarily

going to be the d

for

the next lens. Use the

distance between the lenses

to find how far away your

image is from the next lens.

The Eye

Farsighted

Nearsighted

Use a convex lens to help

focus the light

Use a concave lens to help

_{focus the light}

Cause when the retina is too

Motion Relationships and

Vocab

Vocab

Quantity Symbol Unit Definition

Poition x, y, z Meter (m) Location on a coordinate system Distance d, Δx Meter (m) Measure of separation between two

positions Displacement →

d

Meter (m) Measure of separation between two positions in the same direction

Vocab

Quantity Symbol Unit Velocity _{V or}

_v̅

Acceleration _{a or a̅} m/s²

Misconception Questions

To make units work, how do you go from distance to velocity? Velocity to acceleration?

When an object is “at rest,” which quantities of motion must be equal to zero?

Misconception Questions

Can your speed change while your velocity is constant? Can your velocity change while your speed is constant?

Can your speed be constant, but still be accelerating?

Is slowing down accelerating?

Motion Relationships

As position increases, velocity and speed are positive and vice versa.

As distance from the starting point increases or decreases, displacement does the same but with a direction.

As speed increases, so does velocity. However, if velocity is negative, speed does not become negative If velocity is decreasing, the acceleration is negative

If speed is not 0, position is changing.

Motion Lecture

Position Vs. Time Graphs

Position Vs. Time graphs will be a

parabola because what comes up must come down. The slope of the graph is the velocity, the y-axis would be the position, and the x-axis would be the Time because the Time should always be the x-axis. On earth all objects will accelerate at

Equations

Vertical motion: Δx=(½)at

+vt

Horizontal motion: x=v

t

Units:Δx=change in x, a=acceleration (m/s)

,T=time

,V=velocity

Different Types of Motion

First off vertical and horizontal motion are completely independent of one another. Horizontal motion depends on its horizontal velocity, the time it takes the for the object to fall and hit the ground, and technically the acceleration but this isn’t a big deal because for all of the problems that we will be doing will use gravity on earth, which is -9.8m/s2. Vertical motion is more complicated even though it doesn’t

really use any more variables. Vertical motion relies on its original velocity, the time it takes for the object to go up and come down, and still technically

Practice Problem

Gary Busey falls off of a flying Aardvark with magnificent white wings. It’s

wingspan is 3m. Gary Busey falls for 5 seconds before he hits the ground

and shatters the universe. Gravity (if you haven’t memorized even though

you should’ve) pulls Gary Busey down with an acceleration of -9.8m/s

.

With your new found knowledge of Gary Busey calculate his final velocity,

and calculate how far he fell

Examples

Vertical motion

Equation: Δx=(½)at

+vt

Δx=(½)-9.8m/s

(5)

=(49)(5)

Δx=4.9m/s

25+(49)(5)

Δx=245-122.5

Δx=121.5 meters

Equation: a=(v

-v

/t)

9.8=(v

-0/5)

Projectile Motion

Projectile

● A projectile is any object that

moves, acted on only by gravity

● In absence of air resistance,

any object launched at an angle

will follow a parabolic motion

● For a projectile, the horizontal

motion is independent of the

vertical motion

Horizontal and Vertical Equations

Horizontal

△

X=Vx*T

● Vx is constant

● aX=0

Vertical

△

Y=1/2a(t)

+V(t)

● Vy=a*t+V(y)

● ay=gravity which is

Practice problem

△

_y=1/2at

_{+ Vi(Y)t}

80=½(-9.8)t

+ 0(vi)

80 =-4.9 t

80/-4.9 =-4.9t

/-4.9

A ball is launched with a vertical force of 80 m/s and a

horizontal force of 105 m/s. How long is the ball in the air?

16.667 = t

√16.667 = √t

t=4.082

2(4.082)=t

Things to Remember

● Time can’t be negative

● Acceleration is negative do to

gravity

Newton’s First Law

Newton’s First Law states that an object at rest will stay at rest, and an

object in motion will stay in motion unless acted upon by an external force.

Also known as inertia, when an object has the tendency to resist a change in motion

Equilibrium

Equilibrium is when all the forces that act upon an object are balanced

It is also when the motion and velocity of an object does not change

Forces are considered balanced if the force to the left is balanced by the force to the right and the upward force is balanced by the downward force. Although this does not mean that all forces are equal.

Newton’s Second Law

Force equals mass times acceleration, F=m a

This law has to do with the behavior of unbalanced forces. Since unbalanced

forces cause acceleration, acceleration depends on the mass of the object and the net force on it.

The more mass an object has, the more net force is needed to get the object to accelerate.

Inertia

-Tendency of an object to resist change in motion

-Inertia is not a force

-It’s the tendency of matter not in motion to remain at rest and matter in motion to remain in motion

-In order to overcome inertia(get the object to move) you have to apply a force

Friction

Static Friction

●

Static Friction occurs when object is stationary

●

Varies to be equal to applied force

●

Direction is opposite of applied force

●

Has a larger maximum value

Kinetic Friction

●

Occurs when an object is moving

●

Constant value

●

Direction is opposite of the motion

Examples

A stationary object will have static friction acting upon it. Static

friction is usually greater than kinetic friction. The same object, but

moving, would have kinetic friction acting upon making it easier to

move since this friction is far less than static.

Static Friction: A car gently accelerating

Walking

●

The force responsible for walking is friction

●

Person pushes the ground and stays in place the force of static

FBDs & Tension

How to Draw Free Body Diagrams

●

Represent the object as a dot

●

Draw all forces on the object pointing away from the

dot

●

Label every force

●

DO NOT DRAW FORCES PERFORMED BY THE OBJECT

●

The length of the arrow represents the strength of the

F

ɡ

= Force of gravity and it always points down no matter what

F

ɴ

= Normal Force which points in the opposite direction of gravity

and is equal in magnitude to F

ɡ

F

= Friction Force that acts parallel between two surfaces to inhibit

movement

F

= Air Resistance is a force that exist in the air and causes objects to

stay in the air

*Important*: When the object is slanted or sliding, the normal force is

perpendicular to the slant and will change.

Examples of FBDs

Tension

●

Pulling Force

●

F

●

Examples: Rope and String

Example of FBD with Tension

1. There are two

blocks that are

shown on the left.

M

is a 75 kg block

while M

is a 50 kg

block. Draw a FBD

for each of the

Free Body Diagrams Checklist

●

Gravity

●

Pushes only apply to the specific object that is being pushed

●

Each rope gets its own tension

●

If objects are touching:

○

Put in contact/normal force

○

Consider Friction

●

Consider whether objects are acceleration or not and make

Net Force & Equilibrium

Net Force

● The sum of all the forces acting on an object ■ Equation: Fnet = Mass * Acceleration

■ Equation: Fnet = (forces is the positive direction) - (forces in the negative direction)

Equilibrium

● The state when the velocity does not change ● When the net force of an object is equal to zero

Types of Friction

Friction force: force exerted by the surface; almost always opposes the direction of motion of an object

Static friction - force that keeps an object at rest and must be overcome to start moving the object.

Kinetic friction - force that acts against

Other Types of Forces

Applied force - force applied to an object or person Tension force - pulling force that comes from a rope

Normal force - support force that the ground or object pushes back perpendicular so the object isn’t falling

Newton’s Third Law

Whenever one object exerts a force on a second object, the second object exerts a force of equal magnitude, but opposite direction, on the first object.

Ex: bat hitting a ball

Ex: finger pushing on a wall

Fbat Fball

Interaction Pairs

Two forces of equal magnitude acting on two objects.

Every force is part of an interaction pair

If thing1 exerts a force on thing2, then thing2 exerts a force on thing1.

EX: I sit on the chair...the chair holds me up I push the wall...the wall pushes back.

Multi-body Forces Problems

Steps of solving

multi-body

problems about

Forces

1. Choose directions that are to be to be positive

2. Draw a separate Free Body Diagram (FBD) for

each separate object

3. On your FBD, be clear on which forces are of the

same value

4. Create an equation for Fnet for each FBD

5. Determine how the acceleration of each object

relate

6. Use ( Fnet= Mass x Acceleration )

Practice Problem:

First Step

5 kg

Second Step:

Third Step: On your

FBD, be clear on

which forces are of

the same value

5 kg 20 kg 5kg F_g F_20kg Fn Fg 20kg F_friction

Fourth Step: Create

an equation of Fnet

for each FBD

5 kg

20 kg

F

= F

- F

Fifth Step:

Determine how the

accelerations of

each object relate

5 kg

20 kg

The Accelerations are

Sixth Step: Use

Fnet= mass x

acceleration

5 kg

20 kg

F

= 20 x a

Final Step: If

required, solve

system of equation

5 kg

20 kg

F

- F

= 20a