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Chapter 17

Chapter 17. The Principle of Linear Superposition and Interference Phenomena. What Do You Think?. What is linear superposition? What is the difference between constructive and destructive interference? What is diffraction? What is a sound wave?. Objectives.

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Chapter 17

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  1. Chapter 17 The Principle of Linear Superposition and Interference Phenomena

  2. What Do You Think? • What is linear superposition? • What is the difference between constructive and destructive interference? • What is diffraction? • What is a sound wave?

  3. Objectives • The principle of linear superposition • Constructive and destructive interference • Diffraction • Beats • Transverse standing waves • Longitudinal standing waves

  4. Constructive and Destructive Interference

  5. Constructive and Destructive Interference For two wave sources vibrating in phase, a difference in path lengths that is zero or an integer number (1,2,3,...) of wavelengths leads to For two wave sources vibrating out of phase, a difference in path lengths that is a half-integer number ( ½,1 ½, 2 ½,...) of wavelengths leads to

  6. Constructive and Destructive Interference

  7. Constructive and Destructive Interference Example The figure shows two in phase loudspeakers, A and B that are separated by 3.20 m. A listener is stationed at point C, which is 2.40 m in front of speaker B. Both speakers are playing 214 Hz and the speed of sound is 343 m/s. Does the listener hear a loud sound or no sound? (p. 498)

  8. Constructive and Destructive Interference To decide whether two sources of sound produce constructive or destructive interference at a point, determine the difference in path lengths between each source and that point and compare it to the wavelength of sound.

  9. Constructive and Destructive Interference distance from AC: distance from BC: difference: compare with the wavelength

  10. Diffraction

  11. Diffraction single slit – first minimum circular opening – first minimum

  12. Diffraction Example A 1500 Hz sound and a 8500 Hz sound each emerge from a loudspeaker through a circular opening whose diameter is 0.30 m. Assuming that the speed of sound in air is 343 m/s, find the diffraction angle  for each sound. (p. 501)

  13. Beats

  14. Beats

  15. Transverse Standing Waves In reflecting from a wall, the forward traveling wave becomes a backward traveling wave

  16. Transverse Standing Waves At certain frequencies (resonant frequencies), a standing wave pattern occurs. Standing waves occur because two sets of waves of equal amplitudes and wavelengths pass through each other in opposite directions and combine with the principle of linear superposition.

  17. Transverse Standing Waves L n=1 =2L n=2 =L =2/3L n=3

  18. Transverse Standing Waves Example The heaviest string on an electric guitar has linear density of m/L = 5.28 X 10-3 kg/m and is stretched with a tension of F= 226 N. Thsi string produces a musical noteE at the fundamental frequency of 164.8 Hz. (a) Find the length L of the string between its two fixed ends. (p. 507)

  19. Transverse Standing Waves Unknown Variables v = L= Known Variables m/L = 5.28 X 10-3 kg/m F = 226 N f = 164.8 Hz Formulae

  20. Transverse Standing Waves Example The heaviest string on an electric guitar has linear density of m/L = 5.28 X 10-3 kg/m and is stretched with a tension of F= 226 N. Thsi string produces a musical noteE at the fundamental frequency of 164.8 Hz. (b) A guitar player wants the string to vibrate at a fundamental frequency of 2 X 164.8 Hz = 329.6 Hz. To accomplish this, he presses the string against the proper fret and then plucks the string. Find the distance L between the fret and the bridge of the guitar. (p. 507)

  21. Transverse Standing Waves Example Known Variables m/L = 5.28 X 10-3 kg/m F = 226 N f = 329.6 Hz v= 207 m/s Unknown Variables L= Formulae

  22. Longitudinal Standing Waves

  23. Longitudinal Standing Waves Tube open at both ends

  24. Longitudinal Standing Waves Tube open at only one end

  25. What Do You Think? • What is linear superposition? • What is the difference between constructive and destructive interference? • What is diffraction? • What is a sound wave?

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