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Waves

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characteristics, properties

characteristics, properties

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  • 1. What is a wave?
  • 2. What is a wave? A wave is a disturbance propagated from one place to another with no actual transport of matter
  • 3. Classification of a wave EM waves vs Mechanical waves
  • 4. Mechanical wave Motion requires a medium Electromagnetic wave Motion does not need a medium
  • 5. Electromagnetic wave
  • 6. Transverse wave Displaces particles perpendicular to the motion of the wave
  • 7. Longitudinal wave Cause the particles of a medium to move parallel to the direction of motion of the wave
  • 8. Longitudinal wave Has a crowded area causing a high-pressure region called compression, and the opposite is rarefaction
  • 9. Periodic motion The repetitive motion of a particle about the equilibrium position caused by a restoring force when it is displaced
  • 10. Simple Harmonic Motion (SHM) • within the elastic limit, the distortion in an object is directly proportional to the distorting force • If the restoring force obeys Hooke’s law, then the resulting vibration is called Simple Harmonic Motion (SHM) Hooke’s law
  • 11. Periodic Wave Characteristics Wavelength (λ) The distance from crest to crest (or trough to trough); expressed in meters
  • 12. Periodic Wave Characteristics Amplitude (A) The distance of crest (or trough) from the midpoint of the wave
  • 13. Periodic Wave Characteristics Frequency (f) The number of waves that passed a fixed point per second; measured in hertz (Hz)
  • 14. Periodic Wave Characteristics Period (T) The time it takes a wave to travel a distance equal to a wavelength; measured in second T= 1/f
  • 15. Periodic Wave Characteristics Wave velocity (v) Distance travelled by a wave crest in one period v= λ/T
  • 16. Periodic Wave Characteristics Speed of a transverse wave (v) F= tension μ= mass per unit length v=√ (F/μ)
  • 17. Periodic Wave Characteristics Speed of a longitudinal wave (v) B= bulk modulus of the medium ρ=density of the medium v=√( B/ρ)
  • 18. Periodic Wave Characteristics Speed of a longitudinal wave (v) Ƴ= Young’s modulus of the medium ρ=density of the medium v=√ (Ƴ/ρ)
  • 19. Example The linear mass density of the clothesline is 0.250kg/m. How much tension does Rocky have to apply to produce the observed wave speed of 12.0m/s? F= 36.0N
  • 20. Evaluate Hold an alarm clock at arm’s length from your ear. While it’s still ringing , place the clock on the tabletop, press your ear against the table. Which medium is more efficient in conducting sound?
  • 21. Example A hiker shouts on top of a mountain toward a vertical cliff, 688m away. The echo is heard 4s after. a) What is the speed of sound? b) The wavelength of the sound is 0.75m. What is its frequency? c) What is the period of the wave? v=344.5m/s f=458.67/s T= 2.18x10-3s
  • 22. remember The displacement (y) of a wave is always a function of x and t
  • 23. remember k= wave number k= 2π/λ Note: Wave is moving to the +x
  • 24. Power of a Wave The rate of energy transfer (Pav) ω= angular frequency; A= amplitude ω=2πf 𝑃𝑎𝑣 = 1 2 𝜇𝐹 𝜔2 𝐴2
  • 25. Intensity of a Wave The average power per unit area For fluids in a pipe For a solid rod
  • 26. Example: Work as a group a)In the previous example, if the amplitude of the wave is 0.075m and f=2Hz at what maximum rate does Rocky put energy into the rope? That is, what is his max. instantaneous power? b) What is his ave. power? c) As Rocky tires, the amplitude decreases. What is the average power when the amplitude has dropped to 7.50mm? Pmax=2.83 W Pav=1.415 W Pav= 0.01415W
  • 27. Periodic wave phenomena
  • 28. Displacement y as a function of x and t
  • 29. Wave reflects from a fixed end
  • 30. Wave reflects from a free end
  • 31. Boundary Conditions the conditions at the end of the string, such as a rigid support or the complete absence of transverse force
  • 32. The total displacement at pt. O is zero at all times
  • 33. The total displacement at pt. O is not zero but the slope is always zero.
  • 34. The Principle of Superposition When two waves overlap, the actual displacement of any point on the string at any time is obtained by adding the displacement the point would have if only the first wave were present and the displacement it would have if only the second wave were present.
  • 35. The wave pattern doesn’t appear to be moving in either direction along the string
  • 36. Nodes are points at which the string never moves Antinodes are points at which the amplitude of string motion is greatest
  • 37. Constructive interference Destructive interference Zero displacement Large resultant displacement
  • 38. The wave function for a standing wave Sum of the individual wave function or
  • 39. Adjacent nodes are one half wavelength apart
  • 40. So the length of the string must be: n= 1, 2, 3, ….. For strings fixed at both ends
  • 41. Normal Modes on a String N N A l l =λ/2 λ =2l
  • 42. Normal Modes on a String N N l AA N l =λ
  • 43. Normal Modes on a String N N l A N l =3λ/2 N A A λ =2l / 3
  • 44. Normal Modes on a String A A AA N N N N N l l =2λ λ = l /2
  • 45. Normal Modes on a String For an oscillating system, it is a motion in which all particles of the system move sinusoidally with the same frequency
  • 46. Fundamental frequency The smallest frequency that corresponds to the largest wavelength; n=1
  • 47. SW frequencies The possible standing wave frequencies n= 1, 2, 3, ….. For strings fixed at both ends
  • 48. Harmonic series The series of possible standing wave frequencies (>f1) Note: Musicians call these frequencies overtones f2 is the second harmonic or the first overtone f3 is the third harmonic or the second overtone
  • 49. Standing waves and String Instruments Shows the inverse dependency of frequency on length
  • 50. Example In an effort to get your name in the Guinness Book of World Records, you set out to build a bass viol with strings that have a length of 5.00m between fixed points. One string has a linear mass density of 49.0g/m and a fundamental frequency of 20.0Hz (the lowest frequency that the human ear can hear). Calculate (a) the tension of this string, (b) the frequency and the wavelength on the string of the second harmonic, and (c) the frequency and wavelength on the string of the second overtone.
  • 51. Wave front • It is the locus of all adjacent points on a wave that are in phase • Phases are points on successive wave cycles of a periodic wave that are displaced from their rest position by the same amount in the same direction and are moving in the same direction
  • 52. Interference Superposition of two waves as they come in contact with each other
  • 53. Huygens Principle States that waves spreading out from a point source may be regarded as the overlapping of tiny secondary wavelets and that every point on any wave front may be regarded as a new point source of secondary wavelets
  • 54. Constructive interference Destructive interference Two interacting waves are in-phase Two interacting waves are out-of- phase
  • 55. Diffraction Bending of waves upon interacting with an obstacle

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