Do the wave!!

New Jersey Center for Teaching and Learning
Progressive Science Initiative
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Period and Frequency
SHM and UCM
Spring Pendulum
Simple Pendulum
Table of Contents
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SHM and Circular Motion
There is a deep connection between Simple Harmonic Motion (SHM) and Uniform Circular
Motion (UCM).
Simple Harmonic Motion can be thought of as a one- dimensional projection of Uniform Circular
Motion.
All the ideas we learned for UCM, can be applied to SHM...we don't have to reinvent them.
So, let's review circular motion first, and then extend what we know to SHM.
Click here to see how circular motion relates to simple harmonic motion.

Period
The time it takes for an object to complete one trip around a circular path is called its Period.
The symbol for Period is "T"
Periods are measured in units of time; we will usually use seconds (s).
Often we are given the time (t) it takes for an object to make a number of trips (n) around a circular path. In that case,

1 If it takes 50 seconds for an object to travel around a circle 5 times, what is the period of its motion?

2 If an object is traveling in circular motion and its period is 7.0s, how long will it take it to make 8 complete revolutions?

Frequency
The number of revolutions that an object completes in a given amount of time is called the frequency of its motion.
The symbol for frequency is "f"
Periods are measured in units of revolutions per unit time; we will usually use 1/seconds (s-
1). Another name for s-1 is Hertz (Hz). Frequency can also be measured in revolutions per minute (rpm), etc.
Often we are given the time (t) it takes for an object to make a number of revolutions (n). In that case,

3 An object travels around a circle 50 times in ten seconds, what is the frequency (in Hz) of its motion?

4 If an object is traveling in circular motion with a frequency of 7.0 Hz, how many revolutions will it make in 20s?

Period and Frequency
Since and then and

5 An object has a period of 4.0s, what is the frequency of its motion (in
Hertz)?

6 An object is revolving with a frequency of 8.0 Hz, what is its period (in seconds)?

* Cpo-t and f

*
• A wave is an oscillation that travels.
• A ball floating on water can oscillate up and down in harmonic motion.
• The surface of the water oscillates in response and the oscillation spreads outward from where it started.

Vibrational Motion
*
Vibration: in a general sense, anything that switches back and forth, to and fro, side to side, in and out, off and on, loud and soft, or up and down is vibrating. A vibration is a wiggle in time.
* Wave: a wiggle in both space and time is a wave. A wave extends from one place to another.
*
Vibrations and waves: the source of all waves is something that is vibrating. Waves are propagations of vibrations throughout space.
* Harmonic motion occurs when a vibration repeats and is converted (no energy input is needed to continue the motion)
*

Properties of Periodic Motion
• Cycle: A cycle is a unit of motion that repeats.

* In class on board- w/demos
* Wave vs particle
* Mechancal vs non-mechancal
* Longitudinal vs Transverse
* Spreading of waves
*

*
*
A disturbance which travels through a medium from one point in space to the others.

*
* Energy is transferred from one place to another in a wave motion.
* Motion of the medium (particles of the medium) is usually periodically vibratory.
* Only the shape or form of wave travels, not the medium.

Wave Motion
A wave travels along its medium, but the individual particles just move up and down.

Wave Motion
All types of traveling waves transport energy.
Study of a single wave pulse shows that it is begun with a vibration and transmitted through internal forces in the medium.
Continuous waves start with vibrations too..

Wave Motion
Wave characteristics : use string and glue to create a wave- include the following label and define each characteristic.
Amplitude, A
Wavelength, λ
Crest
Trough
Rest line
Define the following:

A wave is usually described by the following terms :
*
Amplitude
*
Wavelength (

)
*
Frequency ( f )
*
Period (T)
*
Wave velocity (v)
Each term will be explained….

* The amplitude is the maximum displacement of the medium from its equilibrium position(rest line).
The amplitude of a wave refers to the distance from the equilibrium point (or ½ the distance from highest to lowest point of vibration)
* The wavelength
(  ) is the minimum distance between two points which are in phase.
*
The frequency (ƒ) is the number of complete oscillations
(waves)made in one second. The frequency of a wave refers to how many
“waves” pass by a point in a given amount of time (usually a second)
Unit : Hz
* The period
(T) The period of a wave is the time for a wave to make one complete cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. It
Unit : s is the time taken for one complete oscillation(wave). It is related to frequency by T = 1/ƒ

*
Use construction paper- string -glue
* create a transverse wave
*
Label parts
*
Crest‘- highest part off rest of transverse wave
* Trough-lowest part off rest of transverse wave
* Amplitude-maximum displacement off rest
* Wavelength-distance between two points –crest to crest
* Frequency- to how many “waves” pass by a point in a given amount of time (usually a second) the entire sheet is one second
* Period-time for a wave to make one complete cycle.
*

*

* Graphing harmonic motionusing paper and string
* When oscillations are small, the motion is called simple harmonic motion (shm) and can be described by a simple sine curve.
* See animation

*
Flip side of transverse wave model
* create a longitudinal wave – draw slinky-like modelLabel parts
*
Equilibrium line- rest line
*
Compression-Crest- particles – highest density
*
Rarefaction -Trough-particles stretched
*
Amplitude-maximum displacement off rest-compression to rest
*
Wavelength-distance between two points –compression to compression
*
Frequency- to how many “waves” pass by a point in a given amount of time (usually a second) the entire sheet is one second
*
Period-time for a wave to make one complete cycle.

*
• according to the direction of vibration, waves are classified into :
(a) Transverse wave;
(b) Longitudinal waves.

Types of Waves: Transverse and Longitudinal
The motion of particles in a wave can either be perpendicular to the wave direction (transverse) or parallel to it (longitudinal).

*
*
The waveform appears in the shape of sine curve.
*
A wave in which the motions of the matter particles are perpendicular to the direction of propagation of the wave itself.
Examples Water waves, pulse in a stretched string,transverse wave demonstrator .

Types of Waves: Longitudinal
Sound waves are longitudinal waves:

*
*
A wave in which the motions of the matter particles are in the same direction as the wave propagation .
Sound , or a spring oscillating up and down
Examples

*
*

*
Mechanical waves – require a medium to carry the energy
* ie: gas liquid solid.
* air, water, metal plumbing carries sound

(Electromagnetic Waves)
* Material medium is not essential for propagation. e/m waves travel through vacuum.
* Disturbance of electric and magnetic fields travelling through space.
* All electromagnetic waves are transverse waves .
X-rays, radio waves, micro-waves,etc.
examples

Categories of Waves
Waves are classified into different types according to their natures :
WAVES
Mechanical waves Electromagnetic waves
Transverse waves Longitudinal waves Transverse waves

The wave velocity is the displacement traveled by the wave in one second ……....
The wave velocity (v) is related to frequency and wavelength by --
The Wave Equation v = ƒ 

*
*
The speed of a wave equals the frequency times the wavelength.
Speed (m/sec) v = f 
Frequency (cycles/sec)
Wavelength (m)

U sing the Wave Equation
Example
:
A travelling wave of wavelength 0.6m moves at a speed of 3.0 m/s. What is the period of this wave ?
 = 0.6 m, v = 3.0 m/s
f = ?
By using the wave equation, v = ƒ 
ƒ = v/ 
f = (3.0 m/s)/(0.6 m)
ƒ = 5.0 Hz
Then the period of this wave is ???
Period T = 1/ƒ
T = 1/5.0 or 0.2 s

* Calculate the wave equation using graph paper model activity
*
Sine curvedraw 1,2,4,5,10, 20 waves – each wave has an amplitude of 2 blocks to crest and 2 blocks to trough.
CALCULATE:
*
Frequency-period
* wavelength
* Wave speed
*

1 What is the wave speed if the period of a wave is 4 seconds and the wavelength is 1.8 m?
7.2 m/s
Answer
B

2 A fisherman noticed that a float makes 30 oscillations in 15 seconds. The distance between to consecutive crests is 2 m. What is the wave speed?

3 What is the wavelength of a wave trveling with a speed of 6 m/s and a period of 3s?
18 m/s

A.Reflection- The bouncing back of a wave when it meets a surface or boundary i.
Echo- is a reflection of sound waves
B.Diffraction – bending of a wave around an object i.
Sound waves around a door
AM waves are longer and travel around a building
FM waves are shorter and can’t move around
E. Refraction – bending of a wave as it passes from one medium to another i. waves travel at different speeds when passing through different mediums
Demo pencil in a beaker – light travels faster in air than water

 Constructive interference happens when waves add up to make a larger amplitude.
 Suppose you make two wave pulses on a stretched string.
 One comes from the left and the other comes from the right.
 When the waves meet, they combine to make a single large pulse.

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