# Wave Basics + Equation

## Full text

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### 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

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### 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

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### 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)

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### 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)

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### 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

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## Sound

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### Light as a Photon

Photons are the basic unit of light & transmit electromagnetic energyThey are massless and travel in wave-like patterns

### Light travels at a constant speed

of 300,000,000 m/s ( 3x108) ❖ The speed of light passing through materials is slower than light in empty

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### Light as a Wave and the Electromagnetic Spectrum

When the frequency of a light wave is doubled, the wavelength is halvedDifferent 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

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### EM Spectrum

X rays

Gamma rays UV rays Infrared

Micr

owa

ves

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### Absorption, Transmission, & Reﬂection

Absorption: atom absorbs light and converts it into a different energy formSuch as heat

Reﬂection: when light bounces off a surface

Transmission: When light photons hit an atom and pass on the energy.

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### 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

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- Primary colors are - Red , Blue and Green

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

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### Subtractive Color Mixing

- Primary colors are

- Yellow, Magenta and cyan

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

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- 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,

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### 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!

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### Refraction

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

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1

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object

image

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image

object

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### 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

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### Vocab

Quantity Symbol Unit Velocity V or

### v̅

+- m/s

Acceleration a or a̅ m/s²

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### 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?

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### Misconception Questions

Can your speed be constant, but still be accelerating?

Is slowing down accelerating?

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### 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.

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### 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

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2

x

2

(seconds)

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### 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

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2

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2

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f

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### 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

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### 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.

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### 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.

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### 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

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### 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

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### 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

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### 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

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### 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

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### 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.

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### 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 )

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5 kg

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### the same value

5 kg 20 kg 5kg Fg F20kg Fn Fg 20kg Ffriction

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5 kg

20 kg

net20kg

push

friction

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5 kg

20 kg

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5 kg

20 kg

net20kg

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5 kg

20 kg

push

friction

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