Remember: Each student will be allowed bathroom privileges twice a six weeks. Plan accordingly. You must sign out AND in AND include your destination whenever you leave my room, whether to RR, Clinic, Office etc.

Welcome Back! Pick up notes packet and warm up sheet

3/16 Warm Up #1

What is the unit for force? For displacement?

Begin working on SHM WS I

3/17 Warm Up #2

What is the definition of period? of frequency?

If you were absent yesterday, pick up notes, new warm up Sheet, and SHM WS I

3/18

SHM WS I and WS II due end of class today

From test: adjust and use as a warm up

A water wave with the speed of 5 m/s and a frequency of 10 waves per minute hits the shore. If you are 200 m out from shore how many waves will you see between you and the shore?

Formulas

kxFs

k

mTs 2

g

lTp 2

fT /1Tf /1

fv

What do the following all have in common?

Swing, pendulum, vibrating string

They all exhibit forms of periodic motion.

Periodic Motion:When a vibration or

oscillation repeats itself over the same path

A specific form of periodic motion in which the restoring force is proportional to distance from the equilibrium position.

Simple _________ Motion (SHM):Harmonic

Objects that exhibit SHM

Spring Systems* Pendulums* Circular Motion Waves

Sound, Light, Pressure

Definitions

Period – Time required for one complete cycle T =(sec/cycle) measured in seconds

Frequency - Number of complete cycles in a period of time ( f =(cycle/sec) measured in Hertz

Amplitude – Displacement from the equilibrium position. It is a measure of energy

Definitions

Equilibrium Position - The center of motion; the place at which no forces act.

Displacement - The distance between the center (equilibrium position) and location of the spring, pendulum, or wave at any time.

Example 1A fishing bobber moves up and down 24

times in 1 minute. A: What is its period?B: What is its frequency?C: What is the relationship between Period and Frequency?

Example 1A: What is its period?T = sec/cycleT = 60 sec/ 24 “bobs”T = 2.5 seconds

Example 1B: What is its frequency?

f = Cycles/Secf = 24 “bobs”/60 sec f =0.4 Hz

Example 1C: What is the relationship between Period and Frequency?T = sec/cycle f = Cycles/Sec

They are reciprocals of each other!

1/0.4 Hz = 2.5 sec1/2.5 seconds = 0.4 Hz

Tf /1fT /1

SHM and Springs

Demo Vertical spring What is the natural state for the spring? What causes it to be stretched or

compressed? What causes it to return to its natural

state?

SHM and Springs

Compare various springs How are they different? What does that mean?

Horizontal Springs

It has a mass of some kind attached to a spring.

This spring is stretched and released. This causes the entire system to oscillate. (move back and forth)

Springs

So the equation for force of a spring is as follows:

FS = kx

(Hooke’s Law)FS: the force supplied by the spring

K: the spring constant (depends on how the spring is made)

x: displacement of the spring from its equilibrium position

Hooke’s Law Fspring: magnitude of the distorting or

restoring force in Newtons K: spring constant or force constant

(stiffness of a spring) in Newtons per meter (N/m)

x: displacement from equilibrium in meters

kxFS

If time

Simple harmonic motion - Physics Flash Animations

Application in Engineering and design

beyond springs and rubber bands Chairs Floors Anything that flexes and provides an

upward support force

Example 2 I have a slinky with a spring constant of 130 N/m.

With what force do I need to pull it to stretch the slinky from its equilibrium position for the following displacements?

A. 0.1m:B. 0.5 m:C. What is the relationship between Force and

displacement?D. How would the required force (to displace the

mass 0.1m) change if the spring constant was doubled?

kxFS

Example 2

I have a slinky with a spring constant of 130 N/m. With what force do I need to pull it in order to stretch the slinky from its equilibrium position for the following displacements?

A. 0.1 m Fs = (130N/m) (0.1m) = 13 NB. 0.5 m Fs = (130N/m) (0.5m) = 65 NC. What is the relationship between Force and

displacement? Directly ProportionalD. How would the required force (to displace the mass

0.1m) change if the spring constant was doubled? Fs = (260N/m) (0.1m) = 26 N

Spring Constant is directly proportional to F

kxFS

Period on a Spring

If we stretch a spring with a mass and release it, it will oscillate.

This is SHM!

What is the period of this

Motion?

Period on a Spring

The period of a spring system is given by the equation below:

T – the period of motionm – Mass of the body attachedk – spring constant

k

mTs 2

Period

What is the relationship between mass and period of a spring?

What is the relationship between spring strength (Think spring constant) and period of a spring?

Remember that period is always in seconds!

Example 3 What is the mass of my car if the shocks

have a spring constant of 6000 N/m and it oscillates with a period of 2 seconds when I hit a bump in the road?

m= (6000 N/m)(2 s)2/4π2

m = 607.9 kg

k

mTs 2

2

2

4skT

m

What is the difference between period and frequency?

Formulas Calculating Period and Frequency

ond

cyclesf

cycles

ondsT

sec

sec

T = period or time for one revolution or cycle (sec)

f = number of revolutions or cycles per second (Hz or sec-1)

Let’s take a jump!

http://departments.weber.edu/physics/amiri/director/DCRfiles/Energy/bungee4s.dcr

Out of chaos, comes order. The scientific explanation notwithstanding , this is some neat  stuff to watch     

    Harvard  built a device with a series of fifteen pendulums in a row,  each one of them slightly longer than its neighbor.     The  pendulums were set into motion and the result was captured on  video.  The  patterns that appear in this short video are fascinating to  watch and to think about.  Prepare  to be captivated by this simple device !

Click on the  below link but before starting the video, READ the complete  explanation.  Fascinating.   I  want one !

http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80863&pageContentId=icb.pagecontent341734&state=maximize&view=view.do&viewParam_name=indepth.html#a_icb_pagecontent341734

Refer to your definitions and answer

A. The ____________________ is the time of one complete vibration.

B. The ____________________ of vibratory motion is the number of vibrations per second.

C. The frequency is the ____________________ of the period.

An object suspended so that it can swing back and forth about an axis is called a ___________________.

An ideal is one where all mass is considered to be concentrated in the __________.

A pendulum exhibits SHM. bob

pendulum

The Pendulum Formula

T = period (s)l = length (m)g = acceleration

due to gravity (m/s2)

g

lTp 2

Refer to the pendulum formula and answer the following statements:

How does mass affect period? What is the relationship between

length and period? What is the relationship between

acceleration of gravity and period?

Refer to the pendulum formula and answer the following statements:

How does mass affect period? It doesn’t! What is the relationship between length and

period? period is directly proportional to the square

root of its length What is the relationship between

acceleration of gravity and period? period is indirectly proportional to the

square root of the acceleration of gravity

Example 4:

What is the period of a pendulum thatis 0.35 m long at sea level?

g

lTp 2

2^/8.9

35.02

sm

mTp

sec19.1pT

Example 5:

• The frequency of a moving pendulum measures 23 oscillations per 4.3 secs. Determinethe length of the pendulum.• First determine period• 0.187 sec• Rearrange pendulum formula to solve for

length

• l = 0.00868 m

2

2

4gT

l

Example 6:

How do the periods of two pendulums compare if one has a measure of 25 cm and the other has a measure of 100 cm?

Example 6:

How do the periods of two pendulums compare if one has a measure of 25 cm and the other has a measure of 100 cm?

.25 m T = 1sec1.0 m T = 2sec

Refer to the formula for calculation of period

If one knew the length and period, what could one calculate?

GRAVITY!!!!

2

24

T

lg

Tl

g2

REVIEW: What does period of a pendulum depend on?

The period of the pendulum is directly proportional to the square root of the length and inversely proportional to the square root of the acceleration due to gravity.

The longer the pendulum, the greater the period.

Refer to the formula for calculation of period

If one knew the length and period, what could one calculate?

GRAVITY!!!!

2

24

T

lg

Tl

g2

pendulum wave appletvibrating spring wave

applet

WAVES

Demo

What is a wave (continuous wave)?

A repeating and periodic disturbance that transfers energy from one place to another

They are an energy transport system

WAVES TRANSPORT ENERGY NOT MATTER!!!

What is a pulse?

A pulse is a single non repeated disturbance

Types of WavesTypes of Waves

Waves are classified byWaves are classified by

1) The 1) The use of a mediumuse of a medium or not to or not to carry the energy carry the energy

2) The 2) The way they vibrateway they vibrate relative relative to the motion of the waveto the motion of the wave

Medium required to transfer energy

Referred to as Mechanical Waves can be transmitted through solids,

liquids, and gases. they can not travel through space Examples include: sound waves and

water waves.

The particles in a wave vibrate however they do NOT move along with the wave, only the wave front itself moves on.

Medium NOT required to transfer energy

Referred to as Electromagnetic Waves (Non Mechanical)

are able to transmit energy through a vacuum as well as solids, liquids, and gases.

They can travel through space: NO medium required

Examples of electromagnetic waves include cosmic, gamma, x-ray, ultraviolet,

visible light, infrared, microwave, radio All waves on the EM Spectrum

All e/m wavesAll e/m waves travel travel through free space at a through free space at a speed of approximatelyspeed of approximately

3.00 x 103.00 x 1088 m/s or 186,000 m/s or 186,000 miles/sec.miles/sec.

This speed is known as This speed is known as the speed of light the speed of light cc..

ELECTROMAGNETIC WAVESELECTROMAGNETIC WAVES

Categorize on direction of particle movement

Longitudinal Transverse

Types of Wave MotionLongitudinal and Transverse WaveMotion

Transverse

Compressional (Longitudinal)

Transverse Waves

Vibration is perpendicular (up & down) to the direction the wave is moving. ex. light waves, snakey

Direction of Wave

Motion of Molecules

Transverse Wave Diagrams

Longitudinal (Compressional) Waves vibration is parallel to the direction of

the wave. These waves require a medium (such as air or water) through which to travel.

ex. Sound waves (looks like a spring)

Direction of Wave

Direction of Movement

Cont’d

Rarefaction

Compression Wavelength

Longitudinal Waves: Anatomy

Rarefaction: region in which the particles are spread out

Compression: region in which the particles are close together

A wavelength: composed of a complete rarefaction and a complete compression.

Common Wave Properties

Frequency and period are inversely related. T=1/f

Calculating Wave Speed: v = f

Where v = wave speed in m/s f = frequency in Hz

= the wavelength in meters.

Which wave has the longest wavelength?

Which wave has the greatest frequency?

What is the relationship between f and λ when velocity held constant?

inversely related

IMPORTANT

The speed of the wave however depends solely on the medium through which a wave is traveling

The frequency of the wave is determined by the motion of the vibration of the source and the speed of a wave changes when it moves from one medium to another, therefore, the wavelength must change in response when the wave moves into a different medium.

The equation v=d/t can also be applied.

Ex 7

A tuning fork with a frequency of 583 Hz is vibrated, generating a sound wave. Measurements indicate that the wavelength of the sound wave being generated by the tuning fork is 0.59 m long. Calculate the speed of sound in air using this information.

Ex 8: What is the frequency of a Neon-Helium laser that emits light of a wavelength of 6.0x10-7m? Assume the speed of light (which is the speed of all EM waves) is 3.0x108m/s.

Answer: 5.0x1014 Hz

Ex 9: A water wave travels 94.6m in 0.285 seconds. What is the velocity of the wave?Use v = d/t332 m/s

How can you tell…

How much energy a wave is going to have?

Energy and Amplitude

The rate at which energy is transferred by a wave depends on the _________ of the wave.

Energy of a wave IS NOT related to the speed of the wave.

amplitude

Which wave has greatest amplitude?

What is wrong here?

Example: Measurements show that the wavelength of a sound wave in a certain material is 18.0 cm. The frequency of the wave is 1900 Hz. What is the speed of the sound wave?

λ = 0.18 mf = 1900 Hz

v = λ f = 0.18 (1900) = 342 m/s

Wave Behavior at Boundaries

Reflection Refraction Diffraction Interference

Waves at Boundaries

Remember speed of a wave depends on:

the medium the wave is passing through

not the energy that created the vibrations. Energy only determines amplitude

What is this?

Reflection

Reflection is the bouncing back of a wave at a boundary.

Law of ReflectionLaw of Reflection

the the angle of incidenceangle of incidence is is equalequalto the to the angle of reflectionangle of reflection

Sound can also be reflectedSound can also be reflected

Reflected sounds are Reflected sounds are EchoesEchoes

Does reflection just apply to lights and mirrors?

Reflection

A reflected sound wave is called an echo.

The wave equation v = f as well as the equation v = d/t can both be used for sound waves.

Reflection from a Free end (Dense to less Dense Boundary)

Reflection from a Closed end (less Dense to more Dense)

What the heck????

http://www.youtube.com/watch?v=8T8G_4H_TNg

What is Refraction?

Refraction

Refraction is the change in direction of a wave at a boundary as it passes from one medium to another due to the change in wave speed.

The speed changes however the frequency stays the same.

This means that the wavelength must change.

For refraction to occur, For refraction to occur,

the wave mustthe wave must change speedchange speed

and must enter the and must enter the new medium at an new medium at an oblique angleoblique angle..

Refraction occurs Refraction occurs because wave because wave speed speed changeschanges in in different materialsdifferent materials

In medium 2, the wave travels In medium 2, the wave travels slower than in medium 1. This slower than in medium 1. This change in speed causes a bending change in speed causes a bending toward the normal of the wave. This toward the normal of the wave. This behavior is important in lensesbehavior is important in lenses

Refraction

Air Glass

DiffractionDiffractionthethe spreadingspreading of a of a

wavewavearound a barrier oraround a barrier orthrough an openingthrough an opening

In order for diffraction to In order for diffraction to occur, the opening or edge occur, the opening or edge must be much smaller than must be much smaller than the incident wave the incident wave

These These images are images are created by a created by a ripple tankripple tank

Diffraction

Double Slit Diffraction

Results in constructive and destructive interference

adding waves

Interference

the result of the superposition of two or more waves, i.e. two or more waves occupy the same place at the same time.

constructive vs. destructive interference

Interference can be either constructive (build) or destructive (cancel).

Depends on how the waves overlap

Constructive interference

•waves align in sync or in phase•displacement is in same direction•Resultant wave has greater amplitude than orignal waves.

Destructive interference

•waves are out of sync(out of phase)•displacement is in opposite direction•Resultant wave has smaller amplitude than orignal waves•Total destruction if waves of equal amplitudes meet 180O out of phase

ConstructiveConstructiveresults in a larger amplitudelarger amplitude

Types of InterferenceTypes of Interference

DestructiveDestructiveresults in a smaller amplitudesmaller amplitude

constructive vs. destructive interference

According to superposition, the displacement of the medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves.

If an wave with an amplitude of +8cm has constructive interference with a wave with an amplitude of +6cm, the resulting amplitude is

+14cm

InterferenceInterference

ExamplesExamples

Superposition Principle Superposition Principle

the displacement of the medium when two or the displacement of the medium when two or more waves pass through it at the same time more waves pass through it at the same time is the is the algebraic sumalgebraic sum of the displacements of the displacements causedcausedby the individual wavesby the individual wavesThese two wave pulses are moving towards each other. What will happen when they are on top of each other?

Notice that wave A has an amplitude of 2, while wave B has an amplitude of 1.Both of the wave pulses are erect, so we say that they have positive values As they come together in the middle, both of them are pulling upwards…

NOTE: They are still two separate waves, they just happen to be in the same spot at the same time.

They will continue moving on and look exactly the way they looked before they hit each other.

This is an example of Constructive Interference.

When they are directly over each other, they are both shoving particles up together, so the two waves become one big wave with an amplitude of 3 for an instant.

Notice that A and B are still the same amplitude, but now B is inverted.

For a moment the two wave pulses become one smaller wave pulse with an amplitude of (+2 + -1 = +1) positive one. This is Destructive Interference

These two wave pulses are going to collide. What will happen?

And after they pass…And after they pass…

node vs antinode

node: a point in a medium that is completely undisturbed when a wave passes.

Antinode: the point of maximum displacement; it can be either a crest or a trough

Standing Wave: A result of interference

Created when two periodic waves of equal amplitude and wavelength travel in the opposite direction.

the nodes and antinodes of a wave are in a constant position.

as the frequency of the wave increases, the number of nodes and antinodes increases in the same amount of space.