1. Vibrations and Waves

3. AMPLITUDE WAVELENGTH CREST TROUGH

4. Vibrations and Waves Vocabulary Transverse wave Longitudinal wave Reflection Standing wave Frequency

5. Vibrations and Waves Quiz 1)How is the motion of the slinky different for transverse and longitudinal waves? 2)How does the amplitude of a single pulse change with time? 3)How does increasing the slinky’s tension affect the speed of a pulse or wave?

6. Vibrations and Waves Vibrations produce waves Vibrations of a slinky produce Vibrations of air produce Vibrations of electrons produce

7. Vibrations and Waves Vibrations produce waves Vibrations of a slinky produce mechanical slinky waves Vibrations of air produce Vibrations of electrons produce

8. Vibrations and Waves Vibrations produce waves Vibrations of a slinky produce mechanical slinky waves Vibrations of air produce sound waves Vibrations of electrons produce

9. Vibrations and Waves Vibrations produce waves Vibrations of a slinky produce mechanical slinky waves Vibrations of air produce sound waves Vibrations of electrons produce electromagnetic waves

10. Vibrations and Waves Vibrations range from simple to complex. Simple harmonic motion (SHM) is the most fundamental type of vibrational motion.

11. Vibrations and Waves Vibrations range from simple to complex. Simple harmonic motion (SHM) is the most fundamental type of vibrational motion. Simple harmonic motion arises whenever an object moves under the influence of a restoring force proportional to its displacement. Examples:

12. Vibrations and Waves Vibrations range from simple to complex. Simple harmonic motion (SHM) is the most fundamental type of vibrational motion. Simple harmonic motion arises whenever an object moves under the influence of a restoring force proportional to its displacement. Examples: Angular motion of a pendulum Linear motion of a mass on a spring

13. Vibrations and Waves The mass on a spring system obeys Hooke’s Law: F = -kx F – restoring force of the spring [N] k – spring constant [N/m] x – displacement from equilibrium [m]

14. Vibrations and Waves The frequency of a vibration is the number of oscillations per second. Frequency f is measured in hertz [Hz] or “cycles per second” Frequency is measured by counting the number of oscillations that occur in some amount of time: Frequency = number of oscillations / time

15. Vibrations and Waves Transverse wave example: electromagnetic radiation, or a “light wave”) Longitudinal wave example: sound wave

16. Vibrations and Waves Waves have a frequency, which is measured in hertz [Hz] or “cycles per second”

17. Vibrations and Waves What is the speed of a wave?

18. Standing Waves on a String: The resonant modes of vibration for a string of length L Vocabulary: node – any point along the string that doesn’t move antinode – points along the string where displacement is maximum fundamental frequency – the lowest resonant frequency of the string n = 1 n = 2 n = 3 n = 4 L Vibrations and Waves

19. Do Now If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?

20. Vibrations and Waves Do Now If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics? f 1 = 440 Hz f 2 = 2 × 440 Hz = 880 HZ f 3 = 3 × 440 Hz = 1320 Hz f 4 = 4 × 440 Hz = 1760 Hz

21. Beets – Common name of Beta vulgaris, a plant with a swollen root which is eaten or used to make sugar

22. Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere

23. 5 Hz Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere

24. 5 Hz 6 Hz Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere

25. 5 Hz 6 Hz 0.01.02.03.0 4.0time [s] Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere

26. 5 Hz 6 Hz 0.01.02.03.0 4.0time [s] composite Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere

27. 5 Hz 6 Hz 0.01.02.03.0 4.0time [s] composite Beat frequency = absolute value of the difference between the two wave frequencies

28. Vibrations and Waves Do Now A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.

29. Vibrations and Waves Do Now A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds. a)Calculate the beat frequency b)What are the possible frequencies being produced by the guitar string?

30. Vibrations and Waves Do Now A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds. a)Calculate the beat frequency 20 beats / 5 seconds b)What are the possible frequencies being produced by the guitar string?

31. Vibrations and Waves Do Now A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds. a)Calculate the beat frequency 20 beats / 5 seconds = 4 beats per second b)What are the possible frequencies being produced by the guitar string?

32. Vibrations and Waves Do Now A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds. a)Calculate the beat frequency 20 beats / 5 seconds = 4 beats per second, or 4 Hz b)What are the possible frequencies being produced by the guitar string?

33. Vibrations and Waves Do Now A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds. a)Calculate the beat frequency 20 beats / 5 seconds = 4 beats per second, or 4 Hz b)What are the possible frequencies being produced by the guitar string? 396 Hz and 404 Hz