2. Physics: Simple Harmonic Motion, Waves and Energy CHHS Physics Mr. Puckett

3. What is a Wave? Where have you seen or felt waves in your life? – Oceans, lakes, stadium crowds, earthquakes, jump ropes, sound, pendulums… A wave is a vibration or wiggle in time and space. It transfers energy. The back and forth motion of a wave or pendulum is called simple harmonic motion (SHM)

4. Waves and Energy: WAVES are nature's way of transferring energy without transferring matter. Waves are made from vibrations in molecules and energy. – Examples range from sound and waves in water, to waves in light and electromagnetic force.

5. WAVE DIAGRAM

6. Energy in Simple Harmonic Motion in Nature. The Potential and Kinetic Energy we have studied is best examined by looking at simple harmonic motion. (SHM) SHM is the oscillatory motion that results when an elastic material is subjected to the restoring force of an ideal spring. We will examine springs and pendulums

7. Conservation of Mechanical Energy Without friction, total mechanical energy remains constant. ½ mv f 2 + mgh f = ½ mv o 2 + mgh o

8. SHM Vocabulary: Period- The time required to complete one oscillatory cycle of motion. T = 1/f Frequency- The number of cycles of motion per second. f = 1/T in units of Hertz. Amplitude- the maximum distance that an oscillating object moves from equilibrium position. Cycle- refers to the complete to and fro motion from some initial point back to that same point.

9. Examples of SHM

10. Period of Simple Harmonic Motion The time for one cycle through of the motion is called the Period (T).

11. Hooke’s Law: the Spring Constant. Hooke’s Law is the application of Newton’s second law F = ma to springs. Formula: F = - kx where k is the spring constant and x is the distance the displacement. The negative sign is the “restoring” convention

12. Hooke’s Law of Springs Examples

13. Hooke’s Law Problem

14. The Potential Energy of a Spring System: Just as when you pull back a rubber band to pop someone; the elastic effect of the rubber stores energy. Springs likewise convert kinetic motion to Potential Energy: Elastic PE. Formula: PE (elastic) = ½ kx 2 =U It can convert the energy back to kinetic with the release of the spring and the restoring force takes effect.

15. Pendulum: The Big Energy Exchanger.

16. The Trigonometry Analysis of the Pendulum

17. Pendulum Formulas The Frequency The Period Time period of a spring:

18. Pendulum Length Formula

19. Frequencies and Functions When we look at different frequencies you are looking at different functions that you already know. EM waves are transverse waves.

20. Frequencies you Know AM Radio - KHz (1,000 Hz) FM Radio - MHz ( 1,000,000 Hz) Microwave Oven – 2.5 GHz TV - 45 MHz to 10 GHz X-rays – 30-30,000 PHz (10 15 Hz) Visible Light – 380 – 780 nm (10 -9 m) Sound waves- 20 Hz – 20,000 Hz

21. QUALITIES AND MEASURES OF A WAVE: FREQUENCY is the number of complete vibrations per second measured at a fixed location per unit of time. It has the units of hertz (Hz). One vibration per second is = 1 Hz.

22. QUALITIES AND MEASURES OF A WAVE: PERIOD is the shortest time interval in which the motion repeats itself. This is equal to the inverse of the frequency: T= 1/f

23. QUALITIES AND MEASURES OF A WAVE: WAVELENGTH is the shortest distance between points where the wave pattern repeats itself. The units are meters and the symbol is the (lambda)

24. QUALITIES AND MEASURES OF A WAVE: D. AMPLITUDE is the maximum displacement from the resting position of equilibrium of the medium. The larger the amplitude, the larger the amount of work needed for the displacement and the larger the amount of energy transferred. The high points are called crests and the low points are troughs.

25. Speed of a WAVE The speed of any wave is calculated with the equation: speed = frequency x wavelength. v = f λ Units: vel = m/s freq = Hz wavelength = meters

26. What determines Speed of a Wave? The speed of a mechanical wave is independent of amplitude or the frequency of the wave. It depends upon the nature of the medium it is transferred through, specifically the density or tension of the material. The denser the material, the faster the wave.

28. TYPES OF WAVES: a. MECHANICAL WAVES – the 2 kinds that move through matter – 1. TRANSVERSE WAVES move the matter particles perpendicular to the direction of the motion of the wave. This type is shown in, lateral spring displacements and secondary earthquake waves.

29. TYPES OF WAVES: 2. LONGITUDINAL WAVES move the matter particles parallel to the direction of the motion of the wave. This type is seen in compressional spring displacements and primary earthquake waves that move faster than secondary waves.

30. LONGITUDINAL WAVES

31. TYPES OF WAVES: 3. SURFACE WAVES are a mixture of transverse and longitudinal waves. This is the type found in water. 4. IMPULSE WAVE is a single disturbance that travels through a medium 5. TRAVELING WAVE is a continuous wave produced by a source that is vibrating with simple harmonic motion.

32. SURFACE WAVE Surface waves are a combination of longitudinal and transverse waves.

33. TYPES OF WAVES: B. ELECTROMAGNETIC WAVES do not require matter to move through. – Examples are electromagnetic waves such as light, x-rays, microwaves, and radiation.

34. Properties of a Wave

35. 2. QUALITIES AND MEASURES OF A WAVE: F. VELOCITY - is the speed of the wave and is found with the equation: VELOCITY (v) = lambda ( ) x frequency (f). The speed of a mechanical wave is independent of amplitude or the frequency of the wave. It depends upon the nature of the medium it is transferred through, specifically the density or tension of the material. The denser the material, the faster the wave.

36. 3. WAVES AT A BOUNDARY: An INCIDENT WAVE is any wave that encounters a boundary during its travels. –. When a wave hits a solid boundary, it bounces back and turns into a REFLECTED WAVE and returns the original direction. However, the wave is inverted from its original direction.

37. Wave inversion

38. INTERFERENCE OF WAVES: A. Principle of SUPERPOSITION says that when two independent waves passing through a medium meet; the result is the ALGEBRAIC SUM of the DISPLACEMENTS caused by the individual waves.

39. INTERFERENCE OF WAVES: B. INTERFERENCE is the result of the superpositioning of two independent waves acting on each other.

40. Interference

41. CONSTRUCTIVE INTERFERENCE a. CONSTRUCTIVE INTERFERENCE - is when the waves displace the medium in the same direction at the same time. They simply reinforce each other and add to the amplitude. The amount of reinforcement is found by the algebraic sum of the two wave amplitudes.

42. DESTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE - is when the waves displace the medium in different directions at the same time. If the amplitudes of the two pulses are equal but opposite, the displacement produces a net ZERO DISPLACEMENT. If the amplitudes are unequal, the destructive interference will not be complete and there will be some net but reduced wave amplitude

43. INTERFERENCE DIAGRAM Constructive Destructive

44. 5. STANDING WAVES STANDING WAVES : A standing wave is a wave pattern that results when two waves of the same frequency, wavelength and amplitude travel in opposite directions and interfere. The wave appears stationary. The period of this wave is equal to the time it takes for the wave to travel to a fixed point and back. That means the nodes and antinodes stay in the same position. This shows the property of RESONANCE where the wave is reinforced in synch.

45. STANDING WAVES a. A NODE is a position in a wave where the medium displacement is zero and is not moving. This is the result of maximum destructive interference. b. An ANTINODE is the position where the displacement is at its maximum. This is the result of maximum constructive interference

46. Standing Wave

47. Bow Waves When a boat exceeds the speed with which the ripple waves in front travel, the boat overtakes the waves. The overtaken waves form a bow wave — a single wave made up of all the ripple waves that would have propagated ahead of the boat but could not move fast enough to do so.

48. Shock Waves Almost the same thing happens when the jet breaks the sound barrier. When the jet exceeds the speed of sound — the sound waves can’t get out of the way of the jet. So, they scrunch together and form a kind of "bow wave" that is called a shock wave — a sonic boom. The only difference is that the boat wave forms a 2-dimensional "V" on the water surface and the shock wave forms a 3-dimensional cone. Sound barrier link

49. Reflection, Refraction, Diffraction Reflection is where a wave hits a barrier and is bounced back ( reflected like echo’s or spring reflections off fixed objects). Refraction is the bending of a wave due to entering a different density medium. Like light bending through glasses and contacts. Diffraction is the spreading out of a wave when it hits a barrier and goes around it. Like light and water around a barrier.

50. LAW OF REFLECTION The Incoming Light Ray Angle is Equal to the Outgoing Ray angle. Angle of incident wave to normal is equal to the angle of reflection at a solid boundary.

51. INDEX OF REFRACTION A measure of the density of a medium that can slow the velocity of a wave. Formula for light: n = c/v where n = index of refraction, c = speed of light, v is velocity of light in the medium.

52. Diffraction Examples

53. The Doppler Effect The Doppler effect refers to the change in pitch of a sound due to the motion of either the source or the listener. If they are approaching each other, the pitch is higher. If they are moving apart, the pitch is lower. This is also the basis of a modern radar system that shows weather movement well. The formula would be: f ‘ = f((v +/-v o ) / (v -+ v s ))

54. The Doppler Effect

55. ENERGY IN SHM Energy of an object in simple harmonic motion is the mechanical energy ( PE + KE) E = ½ mv 2 + ½ kx 2 Recall that the period of a SHM is T = 2   L/g (pendulum) OR 2   m/k ( spring )

56. Sound Waves