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Waves and Sound

This article explores the concepts of periodic motion, wave classification, and wave properties, including amplitude, wavelength, phase, frequency, and speed. It also discusses wave graphs, wavefronts, and wave phenomena such as superposition, resonance, Doppler effect, diffraction, reflection, and refraction.

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Waves and Sound

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  1. Waves and Sound

  2. Remember Periodic Motion? • Motion which repeats in a regular cycle • Pendulum, vibrating spring, vibrating guitar string

  3. Simple Harmonic Motion • Motion around a point of equilibrium • Force proportional to displacement of object from equilibrium

  4. What is a wave? • Wave=disturbance that carries energy through matter or space • Note that the actual matter does not travel far but the energy can- the energy in this wave could have traveled from Alaska!

  5. Classification of Waves Waves Are: Mechanical or Non-Mechanical One (or More) Pulses or Periodic Longitudinal or Transverse or Combined

  6. Mechanical Waves Require A Medium For Transmission Medium = Mass / Atoms / Material Transmitted Via Vibration Of Particles In The Medium Around A “Rest” Position Examples Sound Water Wave

  7. Non-Mechanical Waves No Medium Is Required For Transmission Can Be Transmitted Through Empty Space Examples: Visible Light Infrared Or Ultraviolet Light Radio/TV Waves Microwaves Any Electromagnetic Radiation

  8. Pulse vs. Periodic Pulse A Single Vibratory Disturbance Periodic Wave A Series Of Regular Disturbances Regular: Identical & Evenly Timed

  9. Transverse waves • Disturbance is perpendicular to the motion of the wave • http://www.youtube.com/watch?v=cPKGa2DsIs0

  10. Longitudinal Waves • Disturbance is parallel to motion of wave • Ex- sound waves • Fluids usually only transmit longitudinal waves

  11. Surface Waves/Elliptical Waves • Underwater, waves are longitudinal but at the surface they have elements of both longitudinal and transverse • Motion of a particle on the surface is an ellipse

  12. Torsional Waves • Twist around a central axis • Like Tacoma Narrows Bridge

  13. Wave properties • Equilibrium • Crest • Trough • Amplitude • Phase • Wavelength

  14. Amplitude • Maximum displacement of a particle in a wave from the equilibrium • Examples: brightness of a light, loudness of a sound

  15. Wavelength • Distance between 2 corresponding locations • Usually measured from crest to crest or trough to trough • Symbol is 

  16. Amplitude and Wavelength • These waves have the same wavelength but different amplitudes • These waves have the same amplitude but different wavelengths

  17. Phase Points On A Periodic Wave Are In Phase If They Have: Same Displacement From Rest Position AND Same Direction Of Motion C and F are “In Phase”

  18. Phase • Points that are “in phase” act the same- they are a whole multiple of a wave apart • Since wavelength is one complete cycle, we usually refer to it as 360 • So in phase= n360 • Points that are “out of phase” are not a whole multiple of 360 apart- they can be any # of degrees apart • We usually look at 90, 180, and 270 apart

  19. Phase Problems- • Using A as a reference, which point(s) are: • 360 in phase • 90out of phase • 180 out of phase • 270out of phase

  20. Frequency • Number of vibrations per second • Symbol is f • Unit is Hz (1/s)

  21. Period • Time to complete one cycle • Symbol is T • Unit is s • T=1/f

  22. Speed • Speed of a wave= wavelength x frequency • v= f • Examples- we see the baseball hit the bat before we hear it b/c light wave travels faster than sound wave

  23. Comparing Wave Speeds Light: 3.00 x 108 m/s Sound: 3.31 x 102 m/s We See The Lightning Flash Before We Hear The Thunder. We See The Bat Hit The Ball Before The Crack Is Heard

  24. Speed of a Wave on a String • For faster waves: tighter string (more tension) or lighter string (less mass per length) • Mass/length is known as the linear mass density

  25. Speed of wave problems • A ball of string is purchased at a local hardware store. According to the manufacturer, the package contains 100 yards (91.5 meters) of string and has a mass of 12 oz (341 grams) • What is the string's linear mass density? • If the string's tensile strength is 90 N, what is the maximum speed a pulse could travel along the string?

  26. solutions • Mass/length= 3.73 x 10-3 kg/meter • Speed=155.3 m/sec

  27. Wave Graphs- same shape but different info • Vibration graph- shows behavior at one spot • Waveform graph shows wave behavior in many spots at one time

  28. Problems A periodic wave goes through twenty complete cycles of its motion in 4.0 seconds What is the frequency of the wave? What is its period? Determine the frequency of a wave whose period is 5.0 seconds

  29. Wavefront The Locus Of Adjacent Points Which Are In Phase Such As The Crest Of A Water Wave

  30. Spherical Wavefront

  31. Spherical Wavefront

  32. Periodic Wave Phenomena Superposition/Interference Resonance Doppler Effect Diffraction Reflection Refraction

  33. Waves at An Interface • Interface • A Boundary With A Different Medium • Part Of The Wave Is Reflected • Part Is Transmitted Through The Second Medium • Part Is Absorbed (Turns Into Heat) • Speed can change

  34. Reflection At a rigid boundary, when wave hits with an upward force, the boundary medium will react with a downward force so reflected wave is INVERTED • If boundary is nonrigid (it can move) wave will reflect in same orientation

  35. Refraction • When a wave enters a new medium velocity can change causing wave to bend

  36. Doppler Effect A Variation In Observed Frequency When There Is Relative Motion Between A Source And An Observer Approaching: Higher Frequency Observed Receding Lower Frequency Observed • Sound • Pitch Changes • Light • Color Changes

  37. Doppler Effect Examples Siren Passing

  38. Doppler Effect

  39. Calculations involving Doppler Effect • Let fs be the source frequency and fd be the detected frequency • If source moving towards you, frequency will increase so choose + or - accordingly • fd=(v+vd)/(v+vs) *fs • Thus, if moving away, frequency will be lower • If moving towards, frequency will be higher

  40. Example: Doppler • A car is traveling 20 m/s away from a stationary observer. If the car’s horn emits a frequency of 600Hz, what frequency will the observer hear? • Use v=340m/s for the speed of sound

  41. Solution • Since car is traveling away from observer, frequency will be lower • fd=(340+0)/(340+20) * 600Hz= 567Hz

  42. Breaking the sound barrier • Speed of sound varies in different mediums • When something travels faster than the local speed of sound it “breaks the sound barrier”

  43. Breaking the sound barrier Regions of constructive interference=SHOCK WAVES

  44. Superposition of waves • When 2 waves meet, the displacement in the medium is the sum of the individual displacements • They then continue, unchanged by their meeting

  45. Constructive Interference Maximum Constructive Interference Occurs When The Phase Difference Is 0° “In Phase”

  46. Destructive Interference • Maximum Destructive Interference Occurs When The Phase Difference Is 180 “Out of Phase”

  47. Interference Patterns Symmetrical Patterns Produced By Sources In Phase In The Same Medium

  48. Interference Can Produce Colors

  49. Interference Patterns

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