Devil physics The baddest class on campus IB Physics

1. Devil physicsThe baddest class on campusIB Physics

2. Tsokos Lesson 4-6Standing waves

3. IB Assessment Statements AHL Topic 11.1. and SL Option A.2., Standing (Stationary) Waves: 11.1.1. Describe the nature of standing (stationary) waves. 11.1.2. Explain the formation of one-dimensional standing waves. 11.1.3. Discuss the modes of vibration of strings and air in open and closed pipes.

4. IB Assessment Statements AHL Topic 11.1. and SL Option A.2., Standing (Stationary) Waves: 11.1.4. Compare standing waves and travelling waves. 11.1.5. Solve problems involving standing waves.

5. Objectives • By the end of this class you should be able to: • State the differences between a Standing Wave and a Travelling Wave • Describe how a Standing Wave is formed • Draw the various harmonics on strings and tubes and find the wavelength in terms of the string or tube length

6. Objectives • By the end of this class you should be able to: • State the meaning of the terms fundamental and harmonics • State the meaning of the term resonance • Solve problems with standing waves

7. Standing Waves – What It Isn’t

8. Introductory Video 1

9. Introductory Video 2

10. Standing Waves on Strings • “When two waves of the same speed and wavelength and equal, or almost equal, amplitudes travelling in opposite directions meet, a standing wave is formed.” • “This wave is the result of the superposition of the two waves travelling in opposite directions.”

11. Standing Waves on Strings • Difference between standing and traveling waves • No energy or momentum is transferred in a standing wave • Standing wave has points where the displacement is always zero (nodes) • Points of maximum displacement are called antinodes

12. Standing Waves on Strings • A standing wave with a single antinode is known as a fundamental standing wave • When the string is in the stretched position, all of its energy is potential energy • When the string is in its unstretched position, all the energy is kinetic energy

13. Standing Waves on Strings • In this picture, there is one-half of one wavelength depicted • Therefore, the wavelength is:

14. Standing Waves on Strings • This picture also depicts a standing wave, with one entire wavelength between the ends • The string has three nodes and two antinodes • The wavelength is:

15. Standing Waves on Strings • This standing wave has four nodes and three antinodes • The wavelength is:

16. Standing Waves on Strings • A general formula for finding the wavelength of a string with both ends fixed is: • n is called the mode and n = 1 is call the fundamental mode or first harmonic of the string

17. Standing Waves on Strings • There is a frequency associated with the fundamental mode called, coincidentally, the fundamental frequency (f0) • All other harmonics will have frequencies that are integral multiples of f0

18. Standing Waves on Strings • Note that the smallest frequency is associated with the fundamental mode (largest wavelength)

19. Standing Waves on Strings • All points between two consecutive nodes move in the same direction • Particles between adjacent nodes move in the opposite direction

20. Fun With PhET

21. Standing Waves on Strings • String with one end fixed, one end free

22. Standing Waves on Strings • String with one end fixed, one end free

23. Fun With PhET

24. Standing Waves on Strings • String with both ends free

25. Standing Waves on Strings • String with both ends free, general formula

26. Fun With PhET

27. Standing Waves on Strings • No need to memorize formulas • Distance between successive nodes or antinodes is a half wavelength • Distance between a node and adjacent antinode is a quarter wavelength

28. Standing Waves in Tubes • Same as waves on a string • Open end – string free - antinode • Closed end – string fixed - node

29. Standing Waves in Tubes • General Principle: • As the length of the tube gets smaller the wavelength for each harmonic gets smaller • Assuming constant wave speed (like sound), the smaller the wavelength, the higher the frequency • Think of the sound made when filling up a bottle of water

30. Resonance • Resonance occurs whenever a system that is capable of oscillation or vibration is subjected to an external disturbance with a frequency equal to the natural frequency of the system itself • In that case, the amplitude of the oscillations will increase • If the frequencies don’t match, the amplitude is smaller or cyclical

31. Resonance • Examples of resonance • Unbalanced tire • Ceiling fan • Rubbing a finger over the top of a glass • Buildings in earthquakes • Height of the building determines its natural frequency

32. Resonance and Forced Oksilations

33. Σary Review • Can you: • State the differences between a Standing Wave and a Travelling Wave? • Describe how a Standing Wave is formed? • Draw the various harmonics on strings and tubes and find the wavelength in terms of the string or tube length?

34. Σary Review • Can you: • State the meaning of the terms fundamental and harmonics? • State the meaning of the term resonance? • Solve problems with Standing Waves?

35. IB Assessment Statements AHL Topic 11.1. and SL Option A.2., Standing (Stationary) Waves: 11.1.1. Describe the nature of standing (stationary) waves. 11.1.2. Explain the formation of one-dimensional standing waves. 11.1.3. Discuss the modes of vibration of strings and air in open and closed pipes.

36. IB Assessment Statements AHL Topic 11.1. and SL Option A.2., Standing (Stationary) Waves: 11.1.4. Compare standing waves and travelling waves. 11.1.5. Solve problems involving standing waves.

37. Questions?

38. Homework #1-20