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 =  f v = speed (m/s) = 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 a.Convert the frequency to kiloHertz b.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 10 14 Hz. a.Calculate the speed of light b.Calculate the period

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

8. MaterialSpeed of Sound (m/s) Air (20 o C) 343 Air (0 o C) 331 Water1440 Saltwater1560 Iron/Steel ~5000

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

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 InfrasonicAudibleUltrasonic 20 Hz 20,000 Hz Earthquakes50,000 Hz (dogs) Thunder100,000Hz(bats) Volcanoes Machinery

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

13.  = 10 log I I o I o = 1.0 X 10 -12 W/m 2 = 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/m 2 ?  = 10 log I=10 log (1.0 X 10 -10 W/m 2 ) I o (1.0 X 10 -12 W/m 2 )  = 10 log (100) = 20 dB

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

17. 6.5 = log I I o 6.5 = log I – log I o log I = 6.5 + log I o log I = 6.5 + log (1.0 X 10 -12 W/m 2 ) 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/m 2 )

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, I o = 1.0 X 10 -12 W/m 2 ).

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  1orI 1 r 1 2 = I 2 r 2 2 r 2

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/I o 14 = log I/I o 14 = log I – log I o log I = 14 + log I o = 2 I = 100 W/m 2

22. I 1 r 1 2 = I 2 r 2 2 I 2 = I 1 r 1 2 /r 2 2 I 2 = (100 W/m 2 )(30 m) 2 /(300 m) 2 I 2 = 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 - v s v Source moving away from stationary observer f’ = f 1 + v s v

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

31. 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) = wavelength (meters) f = frequency (cycles/s or Hertz) c = f  (in a vacuum, c = 3.00 X 10 8 m/s)

35. 3. Electromagnetic Spectrum Light Radio Radar MicroIR Visible Light UVX- rays Gamma

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  = c = c/f = (3.0 X 10 8 m/s)/60 s -1 = 5 X 10 6 m What range of the spectrum is this?

38. Waves: Ex 2 Calculate the wavelength of a 93.3 MHz FM radio station f  = c = c/f = (3.0 X 10 8 m/s)/(93.3 X 10 6 s -1 ) = 3.22 m

39. Waves: Ex 3 Calculate the frequency of 500 nm blue light. f  = c f  = c/  f = (3.0 X 10 8 m/s)/500 X 10 -9 m = 6 X 10 14 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 10 3 m)/(3 X 10 8 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 10 8 m/s)(1.33) = 2.26 X 10 8 m/s