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Waves

Waves. Do the wave!!. New Jersey Center for Teaching and Learning Progressive Science Initiative.

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Waves

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  1. Waves Do the wave!!

  2. New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org 
and is intended for the non-commercial use of 
students and teachers. These materials may not be 
used for any commercial purpose without the written 
permission of the owners. NJCTL maintains its 
website for the convenience of teachers who wish to 
make their work available to other teachers, 
participate in a virtual professional learning 
community, and/or provide access to course 
materials to parents, students and others. Click to go to website: www.njctl.org

  3. Simple Harmonic Motion www.njctl.org

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

  5. Period and Frequency Return to Table of Contents

  6. 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.

  7. 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,

  8. 1 If it takes 50 seconds for an object to travel 
around a circle 5 times, what is the period of its 
motion? Answer [This object is a pull tab]

  9. 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? Answer [This object is a pull tab]

  10. 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,

  11. 3 An object travels around a circle 50 times in ten 
seconds, what is the frequency (in Hz) of its 
motion? Answer [This object is a pull tab]

  12. 4 If an object is traveling in circular motion with a 
frequency of 7.0 Hz, how many revolutions will it 
make in 20s? Answer [This object is a pull tab]

  13. Period and Frequency Since  and then  and  

  14. 5 An object has a period of 4.0s, what is the 
frequency of its motion (in Hertz)? Answer [This object is a pull tab]

  15. 6 An object is revolving with a frequency of 8.0 
Hz, what is its period (in seconds)? Answer [This object is a pull tab]

  16. Cpo-t and f

  17. 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. Harmonic Motion

  18. 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) Vibrations

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

  20. In class on board- w/demos • Wave vs particle • Mechancalvs non-mechancal • Longitudinal vs Transverse • Spreading of waves Intro to Waves

  21. A disturbance which travels through a medium from one point in space to the others. I. Nature of a WaveA. Definition of wave

  22. 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. Properties of Waves

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

  24. 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..

  25. 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:

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

  27. 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. • Thefrequency (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. Itis the time taken for one complete oscillation(wave). It is related to frequency by T = 1/ƒUnit : s

  28. 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. Transverse Paper Activity

  29. Longitudinal wave

  30. 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

  31. 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. Longitudinal paper activity

  32. 1. Classification based on direction of vibration • according to the direction of vibration, waves are classified into : • (a) Transverse wave; • (b) Longitudinal waves.

  33. 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).

  34. a. Transverse Waves • 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.

  35. Types of Waves: Longitudinal Sound waves are longitudinal waves:

  36. 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

  37. Mechanical Waves Based on medium • 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.

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

  39. Non Mechanical Waves (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. examples X-rays, radio waves, micro-waves,etc.

  40. Categories of WavesWavesare classified into different types according to their natures :

  41. 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 -- The Wave Equation v = ƒ

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

  43. The speed of a wave equals the frequency times the wavelength. Frequency (cycles/sec) Relationship between speed, frequency, and wavelength v = f l Speed (m/sec) Wavelength (m)

  44. 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 WAVE EQUATION ACTIVITY

  45. 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

  46. 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

  47. 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

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