Waves Do the wave!!

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Simple Harmonic Motion

Table of Contents SHM and UCM Click on the topic to go to that section Period and Frequency Spring Pendulum Simple Pendulum

Period and Frequency Return to Table of Contents

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? [This object is a pull tab] Answer

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? [This object is a pull tab] Answer

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? [This object is a pull tab] Answer

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

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)? [This object is a pull tab] Answer

6 An object is revolving with a frequency of 8.0 Hz, what is its period (in seconds)? [This object is a pull tab] Answer

* 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. repeats * 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:

* Amplitude * Wavelength ( ) * Frequency (f) * Period (T) * Wave velocity (v) A wave is usually described by the following terms : 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 to make one complete cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. It is the time taken for one complete oscillation(wave). It is related to frequency by T = 1/ƒ Unit : s

* 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 motion- using 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 See animation

* Flip side of transverse wave model * create a longitudinal wave – draw slinky-like model * Label parts * 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. Water waves, pulse in a stretched string,transverse wave demonstrator. Examples

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. Examples Sound, or a spring oscillating up and down

* A material medium is necessary for the transmission for mechanical waves. Mechanical waves cannot travel through vacuum. * Due to forces on particles in the “medium” that are next to each other, the disturbance is transmitted from one layer to the next through the medium.

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

* 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 :

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

U sing the Wave Equation 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 ? Then the period of this wave is ??? Period T = 1/ƒ T = 1/5.0 or 0.2 s = 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 The unit of ‘m’ cancel out—and you are left with 5.0/s which is 5.0 Hz

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

* Calculate the wave equation using graph paper model activity * Sine curve- draw 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 B Answer

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? 4 m/s B Answer

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

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.

 What happens when one pulse is on top of the string and the other is on the bottom?  When the pulses meet in the middle, they cancel each other out.  During destructive interference, waves add up to make a wave with smaller or zero amplitude.