L 5 Review of Standing Waves on a String

1. L 5Review of Standing Waves on a String

2. <ct.10.1.4> Below is a picture of a standing wave on a 30 meter long string. What is the wavelength of the running waves that the standing wave is made from? 30 m • 30 m • 60 m • 10 m • 20 m • Impossible to tell

3. Ct 10.1.5 Could you observe standing waves made from running waves with a wavelength of 2/3 m on a string of length 1 m? (If so, what mode would that be? ) • Yes, n = 1 • Yes, n = 2 • Yes, n = 3 • Yes, n = 4 • No

4. <ct.10.1.6> A string vibrates with a fundamental frequency of 220 Hz. Besides 220 Hz, which of the following are "resonant frequencies" you might also observe? i) 110 Hz ii) 330 Hz iii) 440 Hz A: i only B: ii only C: iii only D: i and ii E: all three

5. <ct.10.1.8b> If the tension is increased by a factor of 9 what happens to the speed of waves on a string? • Goes up by a factor of 3 • Goes up by a factor of 4.5 • Goes up by a factor of 9 • Goes up by a factor of 81 • None of these / I don’t know What happens to the frequency of the fundamental?

6. <ct.10.1.8b> If you want to lower the pitch of a string by two octaves, what must be done to its tension? • Raise it by a factor of 4 • Lower it by a factor of 4 • Lower it by a factor of 2 • Lower it by a factor of 16 • None of these

7. ct.10.1.10a A string on an instrument plays an A (440 Hz) when plucked. If you lightly touch the string ½ way from one end, and then pluck, you are mostly likely to hear… A: Still 440 Hz B: 220 Hz C: 880 Hz D: Something entirely different

8. Ct 10.1.4b ii i Which of the two points on the string oscillates with the LARGER (higher) frequency? Left point (i) Right point (ii) They both have the same frequency

9. <ct.10.1.3> Below is a picture of a standing wave on a 30 meter long string. What is the wavelength of running waves that the standing wave is made from? • 30 m • 60 m • 15 m • Impossible to tell 30 m

10. Sound Waves Frequency, Harmonics, Tone Quality (spectral content),Pitch

11. The “Sonic” SpectrumInfrasound: < 20 HzSound:20 Hz – 20,000 Hz (20kHz)Ultrasound: > 20 kHz (~1013 Hz maximum)

14. Sound- a Pressure WavePhET Simulation “Wave Interference” (Sound, Particles)

16. Components of Sound1) Longitudinal (along direction of propagation) vibrations, e.g. speaker cone.2) Material medium capable of transmission of these vibrations, e.g. air.3) Detector of the sound wave e.g.ear.

17. Longitudinal wave representation

18. Longitudinal wave propagation

19. Pressure wave amplitudeabout 10-5 atmosphereDisplacement wave amplitudeabout 10-7m

20. We define 1 N/m2 to be 1 Pascal (Pa)

22. In air at atmospheric pressure and at 20 degrees Celsius, the speed of sound, v, is 344 m/sv is temperature dependent, V = 331 m/s +0.6 T,where T is the temperature in degrees Celsius above freezing, i.e. above 0 degrees Celsius

23. What happens when an object exceeds the speed of sound?

26. Standing Sound Waves

27. L Cylindrical tube Open at both ends (a flute, more or less) Easy to get overpressure in middle (Ends are just open atmosphere…)

28. http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.htmlhttp://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html

31. L overpressure

32. open tube overpressure L n=2, the 2nd mode of the tube

33. L Displacement (not pressure) graphs. open tube displacement

34. Displacement is longitudinal (despite the graph going “up”) • Pressure nodes <=> displacement antinodes (and vice versa)

36. “Open” TubeFrequencies and Wavelengthsf = v / λN = 1 λ = 2Lo f = v/2Lo = foN = 2 λ = Lof = v/Lo = 2foN = 3 λ = 2Lo/3 f = 3v/2Lo = 3foN = 4 λ = 2Lo/4 f = 4v/2Lo = 4foN = 5 λ = 2Lo/5 f = 5v/2Lo = 5foN = 6 λ = 2Lo/6 f = 6v/2Lo = 6fo

37. Pressure waves “fit” in the open tube n (/2) = L Since f  = v, fn= n (v/2L) Samemodes as a string! Note that in the case of the string, the “v” is the speed of the wave moving down the string. Here v is the speed of the wave motion through the medium, i.e. the speed of SOUND.

38. CT 12.1. 1 How will the normal mode frequencies of an open tube compare with those of a string (with the same fundamental frequency)? • All different frequencies (except fundamental) • All the same frequencies • Some of the overtones will be the same and some different

39. CT 12.1.1c The air in an open pipe is in the n=2 mode (shown above). A small speck of dust is located 1/2 of the way down the pipe. What does the dust do ? Wiggles up and down (towards /away from wall of tube) B) Wiggles back and forth (left/right, along the tube…) C) Sit still at center of the pipe D) Something else

40. Standing pressure wavehttp:/ www.physics.smu.edu/~olness/www/03fall1320/applet/pipe-waves.html

41. CT 12.1.1b What is “v” in the formula f  = v for a pipe whose both ends are open to the air? • The speed of sound in air, 344 m/s • Speed of vibrations of the pipe wall • Related to speed of sound, but depends of pipe diameter

42. CT 12.1.1d The speed of sound in helium gas is considerably higher than 344 m/s. If I fill a tube with helium, what will happen to the fundamental tone produced by that tube? • Goes up in pitch • Goes down in pitch • Stays about the same

43. real tubes - end effect overpressure L Outer node is a bit outside tube (about 0.3 * diameter)

44. Tube closed at one end, open at the other

45. L Closed tubes(closed on one end) overpressure Closed end: pressure antinode open end: pressure node

46. L Closed tubes(closed on one end) overpressure Closed end: antinode open end:node

48. L CT 12.1.3 What is the wavelength of the fundamental (shown above) in a closed tube? =L B) =2L C) =4L D) =L/2 E) =L/4

49. L Draw the next higher mode (zero at right end, antinode at left, one extra node in middle) overpressure Closed end: antinode open end:node

50. L Draw the next higher mode (zero at right end, antinode at left, one extra node in middle) overpressure Closed end: antinode open end:node