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Properties of Waves and Simple Harmonic Motion

Explore the properties of waves and simple harmonic motion, including the transmission of sound waves and the behavior of pendulums and springs.

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Properties of Waves and Simple Harmonic Motion

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  1. SIMPLE HARMONIC MOTION PROPERTIES OF WAVES WAVE INTERFERENCE SOUND WAVES WAVES

  2. Telephone TEST - 50 points Write your set of 5 words for transmission . Write words you heard in 1 minute . Take turns . Repeat for a different phone . Describe the clarity of transmission of data Using : • String Phone • Shorter String Phone • Fishing line Phone • Shorter Fishing line Phone • Wire Phone • Shorter Wire Phone LABORATORY REPORT – 50 POINTS Purpose : Determine the best medium( string. Fishing line, wire) to transmit sound waves .Why ? What is the effect of the length of the medium to sound wave transmission . Materials : Data Table Conclusion :

  3. Pendulum Motion Packet Groups of 4 • Force Analysis Of Pendulum • Sinusoidal Nature of a Pendulum • Energy analysis • Period of A Pendulum Read your topic – 20 minutes Take Notes Share your information – 5minutes /each person . Write and number all the information about pendulum regarding all subtopic on paper . Score it.

  4. Pendulum Experiment

  5. Spring Motion Packet Groups of 4 • Force Analysis Of Spring • Sinusoidal Nature of a Spring • Energy analysis • Period of A Spring Read your topic – 20 minutes Take Notes Share your information – 5minutes /each person . Write and number all the information about pendulum regarding all subtopic on paper . Score it.

  6. SIMPLE HARMONIC MOTION • Motion that is repeating or periodic. • Two types • Spring • Hooke’s Law states that the restoring force is proportional to the displacement • F = -kx • Units: Newtons • Negative: direction of the Force is opposite the displacement.

  7. SIMPLE HARMONIC MOTION

  8. SIMPLE HARMONIC MOTION

  9. SIMPLE HARMONIC MOTION • Stretch or compression provides three types of energy. • Max displacement • EPE = ½ k x 2 • V = 0 • A increase to max • Equilibrium position • Min x • Max KE • Max velocity • a = 0

  10. SIMPLE HARMONIC MOTION • Horizontal springs: • EPE elastic • KE • Vertical springs: • PE gravitational • EPE elastic • KE • Conservation of energy applies • Friction or damping force

  11. SIMPLE HARMONIC MOTION • Period of a spring • T = 2 √ m/k • Units: sec/cycle or sec/revolution or sec • f = 1 / T • Units: cycle/sec or revolution/sec or Hertz or s-1

  12. SIMPLE HARMONIC MOTION • Simple pendulum • For small angles • Restoring force is proportional to x. • Work done is ZERO • Max PE at the highest point • Max KE at the lowest point • Period of a pendulum • T = 2 √ l/g • Units: sec/cycle or sec/revolution or sec

  13. SIMPLE HARMONIC MOTION

  14. SIMPLE HARMONIC MOTION

  15. SIMPLE HARMONIC MOTION

  16. PROPERTIES OF WAVES • Follows a simple harmonic motion • Needs a source • Medium = matter • Matter does NOT travel only energy • Mechanical waves need a medium to travel • EM does not need a medium to travel • Pulse: single wave

  17. PROPERTIES OF WAVES • Two types of waves • Transverse waves • Disturbance is perpendicular to the propagation • EM

  18. PROPERTIES OF WAVES • Longitudinal or compressional waves • Disturbance is parallel to the propagation • Sound waves

  19. PROPERTIES OF WAVES • Parts of the wave • Wavelength (): length of a wave measured between two consecutive identical points • Frequency (f) • Period (T) • Amplitude (A): max height of the wave

  20. PROPERTIES OF WAVES • Crest: highest point of transverse wave • Trough: lowest point of transverse wave

  21. PROPERTIES OF WAVES

  22. PROPERTIES OF WAVES • Compression: high density portion of compressional wave • Rarefaction: low density portion of compressional wave

  23. PROPERTIES OF WAVES

  24. 1) repeating motion through equilibrium position…F is proportional to x 2) varies 3) no, a changes…zero at equilibrium position and greatest at max displacement 4) No for angles less than 15 degrees 5) GPE…GPE to KE to GPE 6) frictional forces are neglected 7) tangent component; pulls the bob toward the equilibrium position 8) 130 N/m 9) 580 N/m 10) 2 x 11) 4 A 12) Inversely related 13) Square root of 2; independent of mass 14) same; independent of mass 15) no; g changes so T changes 16) Make shorter 17) Increase; g decreases 18) Same; independent of a HWK pg 396

  25. 19) 9.7 m 20) a) 2.000 s b) 9.812 m/s/s c) 9.798 m/s/s 21) a) 0.57 s b) 1.8 Hz 22) Movement of disturbance 23) transverse: disturbance is perpendicular to propagation longitudinal: disturbance is parallel to propagation 24) a) vertically, perpendicular to wave motion b) transverse 25) Longitudinal 26) One wavelength 27) 1/3 s; 3 Hz 28) sound, water, spring…light waves do not need medium; mechanical waves do 29) Up and down; no horizontal movement 30) Half as long; stays the same 31) Sound waves are vibration of particles…no particle no propagation 32) neither; constant in given medium HWK

  26. Pg 371 3) 2700 N/m 4) 81 N Section Review C 0.52 N F and a decreases; v increases momentum Pg 379 3) 3.6 m 4) a) 3.749 s; 0.2667 Hz b) 3.754 s; 0.2664 Hz c) 3.758 s, 0.2661 Hz HWK

  27. Pg 381 3) 39.7 N/m 4) 0.869 s 5) a) 1.7 s; 0.59 Hz b) 0.14 s; 7.1 Hz c) 1.6 s; 0.62 Hz Section Review 3.0 Hz; 0.33 s 3.2 s; 0.31 Hz 25 N/m; 1.1 s Larger mass…greater period HWK

  28. Wave Equation • Speed = frequency x wavelength c = f  v = f  • c = speed of light = 3.0 x 10 8 m/s

  29. WAVE INTERFERENCE • Energy travels…NOT matter • Superposition Principle: two or more waves will combine algebraically • Waves pass through without altering their shapes and size.

  30. WAVE INTERFERENCE • Constructive: resulting wave is larger in amplitude • In phase

  31. WAVE INTERFERENCE • Destructive: resulting wave is smaller in amplitude • Out of phase

  32. WAVE INTERFERENCE

  33. WAVE INTERFERENCE

  34. WAVE INTERFERENCE

  35. WAVE BEHAVIOR • Determining behavior when wave reaches a boundary (interface between two medium) • Incident pulse: incoming wave • Reflected pulse: a wave bouncing off a boundary • Transmitted pulse: wave continuing through to next medium • Upright • Inverted

  36. WAVE BEHAVIOR • Reflection: wave hits a boundary and returns • Newton’s third law • Speed and wavelength are the same • Amplitude is smaller

  37. WAVE BEHAVIOR

  38. WAVE BEHAVIOR • Transmitted: slower than reflected and smaller wavelength • Reflected: speed and wavelength are same as incident

  39. WAVE BEHAVIOR • Transmitted: faster and larger wavelength • Reflected: same speed and wavelength as incident

  40. WAVE BEHAVIOR • Refraction: change in direction of waves traveling from one medium to another • Speed and wavelength changes

  41. WAVE BEHAVIOR Diffraction: change in direction of waves as the wave passes through opening or around a barrier.

  42. SOUND WAVES • Compressional or longitudinal wave • High pressure and low pressure region • Speed depends on medium vsolid > vliquid> vgas • Speed depends on temperature Direct relationship 343 m/s at room temperature

  43. SOUND WAVES

  44. SOUND WAVES

  45. SOUND WAVES • Range of sound 20 to 20000 Hz • Infrasonic, audible, ultrasonic • Measured in decibels • Loudness is not intensity but related to amplitude of the wave • Energy of the wave is proportional to A2 • Intensity is power / area

  46. STANDING WAVES • Standing waves: reflected and incident wave interact to appear to be standing • Antinodes: largest amplitude • Nodes: zero amplitude

  47. STANDING WAVES

  48. STANDING WAVES • L = /2 • L = 2 / 2 =  • L = 3 / 2 • L = 4 / 2 = 2

  49. STANDING WAVES • Increases by increments of  /2 • Longest wavelength: L = n /2 where n = 1, 2, 3, 4…… • Fundamental frequency: lowest frequency v = f  f = v /  = nv / 2L • Harmonics: multiples of the fundamental frequency

  50. OPEN PIPES • L = /2 • L = 2 / 2 =  • L = 3 / 2 • L = 4 / 2 = 2

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