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Travelling Waves

Travelling Waves. Chapter 20. Waves. Mechanical Waves Require a medium Sound, water, strings Electromagnetic Waves Can travel through a vacuum Radio to gamma Matter Waves Electrons and atoms. Transverse and Longitudinal. Transverse Up and down Displacement is perpendicular to medium

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Travelling Waves

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  1. Travelling Waves Chapter 20

  2. Waves • Mechanical Waves • Require a medium • Sound, water, strings • Electromagnetic Waves • Can travel through a vacuum • Radio to gamma • Matter Waves • Electrons and atoms

  3. Transverse and Longitudinal • Transverse • Up and down • Displacement is perpendicular to medium • Strings, water, electromagnetic • Longitudinal • pulses • Displacement • Sound

  4. Formula T = 1/f v = l f v = speed (m/s) l = wavelength (m) f = frequency (cycles/s or Hz)

  5. Example 1 A sound waves travels at 343 m/s and has a frequency of 17,000 Hz • Convert the frequency to kiloHertz • Calculate the wavelength

  6. Example 2 A photon has a wavelength of 5.50 X 10-7 m and a frequency of 5.45 X 1014 Hz. • Calculate the speed of light • Calculate the period

  7. Speed of Sound • Varies with the medium • v = \/ B/r • Solids and liquids • Less compressible • Higher Bulk modulus • Move faster than in air

  8. Material Speed of Sound (m/s) Air (20oC) 343 Air (0oC) 331 Water 1440 Saltwater 1560 Iron/Steel ~5000

  9. Speed of Sound: Temperature • Speed increases with temperature (oC) • v ≈ (331 + 0.60T) m/s • What is the speed of sound at 20oC? • What is the speed of sound at 2oC?

  10. Speed of Sound: Example 1 How many seconds will it take the sound of a lightening strike to travel 1 mile (1.6 km) if the speed of sound is 340 m/s? v = d/t t = d/v t = 1600 m/(340 m/s) ≈ 5 seconds (count five seconds for each mile)

  11. Pitch • Pitch – frequency (not loudness) • Audible range 20 Hz – 20,000 Hz Infrasonic Audible Ultrasonic 20 Hz 20,000 Hz Earthquakes 50,000 Hz (dogs) Thunder 100,000Hz(bats) Volcanoes Machinery

  12. Intensity • Intensity = Loudness • Louder = More pressure • Decibel (dB) – named for Alexander Graham Bell • Logarithmic scale • Intensity level =b

  13. b = 10 log I Io Io = 1.0 X 10-12 W/m2 = lowest audible intensity

  14. Example • Rustle of leaves = 10 dB • Whisper = 20 dB • Whisper is 10 times as intense Example • Police Siren = 100 dB • Rock Concert = 120 dB

  15. Decibels: Example 1 How many decibels is a sound whose intensity is 1.0 X 10-10 W/m2? b = 10 log I = 10 log (1.0 X 10-10 W/m2) Io (1.0 X 10-12 W/m2) b = 10 log (100) = 20 dB

  16. Decibels: Example 2 What is the intensity of a conversation at 65 dB • = 10 log I Io • = log I • Io 65 = log I 10 Io

  17. 6.5 = log I Io 6.5 = log I – log Io log I = 6.5 + log Io log I = 6.5 + log (1.0 X 10-12 W/m2) log I = 6.5 – 12 = -5.5 I = 10-5.5 = 3.16 X 10-6

  18. Decibels: Example 3 What is the intensity of a car radio played at 106 dB? (Ans: 1.15 X 10-11 W/m2)

  19. Decibels: Example 4 A blender produces an intensity level of 83dB. Calculate the decibels if a second blender is turned on (doubles the intensity, Io = 1.0 X 10-12 W/m2).

  20. Intensity and Distance • Intensity = Power/area • Inverse-squared radius • Intensity decreases proportionally as you move away from a sound (area of a ripple increases as you move out) I a1 or I1r12 = I2r22 r2

  21. Distance: Example 1 The intensity level of a jet engine at 30 m is 140 dB. What is the intensity level at 300 m? 140 dB = 10 log I/Io 14 = log I/Io 14 = log I – log Io log I = 14 + log Io = 2 I = 100 W/m2

  22. I = 100 W/m2 I1r12 = I2r22 I2 = I1r12/r22 I2 = (100 W/m2)(30 m)2/(300 m)2 I2 = 120 dB

  23. Distance: Example 2 If a particular English teacher talks at 80 dB when she is 10 m away, how far would you have to walk to reduce the sound to 40 dB? (Hint: Find the raw intensity of each dB first). ANS: 1000 m

  24. Doppler Effect • Frequency of sound changes with movement • Moving towards you = frequency increases (higher pitch) • Moving away = frequency decreases (lower frequency)

  25. Moving Source Source moving towards stationary observer f’ = f 1 - vs v Source moving away from stationary observer f’ = f 1 + vs v

  26. Moving Observer Observer moving towards stationary source f’ = 1 + vo f v Observer moving away from stationary source f’ = 1 - vo f v

  27. Doppler Effect and the Universe • Universe is expanding • Evidence (Hubble’s Law) • Only a few nearby galaxies are blueshifted • Most are red-shifted • Universe will probably expand forever

  28. Doppler: Example 1 A police siren has a frequency of 1600 Hz. What is the frequency as it moves toward you at 25.0 m/s? f’ = f 1 - vs v f’ = 1600 Hz = 1600 Hz = 1726 Hz [1 – (25/343)] 0.927

  29. What will be the frequency as it moves away from you? f’ = f 1 + vs v f’ = 1600 Hz = 1600 Hz = 1491 Hz [1 + (25/343)] 1.07

  30. Doppler: Example 2 A child runs towards a stationary ice cream truck. The child runs at 3.50 m/s and the truck’s music is about 5000 Hz. What frequency will the child hear? f’ = 1 + vo f v

  31. f’ = 1 + vo f v f’ = [1+(3.50/343)]5000 Hz f’ = (1.01)(5000 Hz) = 5051 Hz

  32. Electromagnetic (EM) Waves • Can travel through space • Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays • All on the electromagnetic spectrum • James Clerk Maxwell

  33. EM Wave • Sinusoidal • E and B are perpendicular to one another • E and B are in phase • Accelerating electric charges produce electromagnetic waves

  34. Wave Properties • First man-made EM waves detected by Hertz (8 years of Maxwell’s death) l = wavelength (meters) f = frequency (cycles/s or Hertz) c = f l (in a vacuum, c = 3.00 X 108 m/s)

  35. Light 3. Electromagnetic Spectrum

  36. Visible light • 4 X 10-7 m to 7X 10-7 m (400 to 700 nm) • Electrons • Radio – running electrons up and down an antenna • Electrons moving within atoms and molecules • X-rays - Electrons are rapidly decellerated by striking metal • Gamma Rays – Nuclear decay

  37. Waves: Ex 1 Calculate the wavelength of a 60 Hz EM wave f l = c • = c/f • = (3.0 X 108 m/s)/60 s-1 = 5 X 106 m What range of the spectrum is this?

  38. Waves: Ex 2 Calculate the wavelength of a 93.3 MHz FM radio station f l = c • = c/f • = (3.0 X 108 m/s)/(93.3 X 106 s-1) = 3.22 m

  39. Waves: Ex 3 Calculate the frequency of 500 nm blue light. f l = c f= c/ l f = (3.0 X 108 m/s)/500 X 10-9 m = 6 X 1014 Hz

  40. Waves: Ex 4 When you speak to a telephone to someone 4000 km away, how long does it take the sound to travel? v = d/t t = d/v T = (4000 X 103 m)/(3 X 108 m/s) = 1.3 X10-2 s Speed is less because of wires

  41. Index of Refraction • Light slows when passing through a substance • Must be absorbed and re-emitted • Eyes slow light by ~30% • Bose-Einstein condensate (50 nanokelvins) v = 38 mph

  42. n = c v v = speed in material n = index of refraction

  43. Refraction: Ex 1 Calculate the speed of light in water n = c v v = c/n v = (3.00 X 108 m/s)(1.33) = 2.26 X 108 m/s

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