1. 15.1 Properties and Detection of Sound Interference of sound waves

2. 15.1 Properties and Detection of Sound At which of the labeled point(s) would constructive interference occur?

3. 15.1 Properties and Detection of Sound How many of the six labeled points represent anti-nodes?

4. Noise reduction headphones utilize destructive interference 15.1 Properties and Detection of Sound

5. Beats The periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another 15.1 Properties and Detection of Sound

6. Beats The periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another 15.1 Properties and Detection of Sound

7. 15.1 The Physics of Music

8. 15.2 The Physics of Music

9. Beats Beat Frequency - the rate at which the volume is heard to be oscillating from high to low volume Equal to the difference in frequency of the two notes which interfere to produce the beats Two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected 15.1 Properties and Detection of Sound

10. 15.2 The Physics of Music all objects have a natural frequency or set of frequencies at which they vibrate when struck, plucked, strummed or somehow disturbed when an object vibrating at its natural frequency experiences resonance, a standing wave is produced

11. 15.2 The Physics of Music If a sound wave within the audible range of human hearing is produced, a loud sound is heard. Resonance occurs when two interconnected objects share the same vibrational frequency. When one of the objects is vibrating, it forces the second object into vibrational motion.

12. 15.2 The Physics of Music Standing wave patterns in a given object will appear at specific frequencies - harmonics

13. 15.2 The Physics of Music This standing wave pattern, is the fundamental frequency, or the 1 st harmonic (one antinode, two nodes) This is only half of a wavelength

14. 15.2 The Physics of Music one full wavelength one and a half wavelengths The guitar string will resonate at various frequencies, but because the ends are fixed there will be nodes at the ends

15. 15.2 The Physics of Music Each harmonic results in an additional node and antinode added, and an additional half wavelength to the string We can create equations relating the wavelength of the standing wave pattern to the length of the string

16. 15.2 The Physics of Music Each harmonic results in an additional node and antinode added, and an additional half wavelength to the string We can create equations relating the wavelength of the standing wave pattern to the length of the string

17. 15.2 The Physics of Music Remember that the properties of a medium determine the speed of a wave For a guitar string, the speed of the wave is determined by: 1. The tension in the string 2. The linear density of the string These two factors and the string length will determine the frequency of the fundamental and the other harmonics

18. 15.2 The Physics of Music A guitar string with a length of 80.0 cm is plucked. The speed of a wave in the string is 400 m/sec. Calculate the frequency of the first, second, and third harmonics. For a fixed string, each harmonic is an integer multiple of the fundamental frequency

19. 15.2 The Physics of Music A closed-pipe resonator is a resonating tube with one end closed to the open air A clarinet is an example of a closed-pipe resonator

20. 15.2 The Physics of Music An open-pipe resonator is a resonating tube with both ends open to the open air A flute is an example of a open-pipe resonator

21. 15.2 The Physics of Music In air columns, open ends will be displacement antinodes and closed ends will be displacement nodes The wavelength for the fundamental frequency is two times the pipe length

22. 15.2 The Physics of Music The wavelength for the 2 nd harmonic is equal to the pipe length The wavelength for the 3 rd harmonic is equal to 2/3 the pipe length

23. 15.2 The Physics of Music In air columns, closed ends will be displacement nodes and open ends will be displacement antinodes The wavelength for the fundamental frequency is four times the pipe length ¼ wavelength

24. 15.2 The Physics of Music The wavelength for the 3 rd harmonic is equal to 4/3 the pipe length The wavelength for the 5th harmonic is equal to 4/5 the pipe length There are no even numbered harmonics for a closed-pipe resonator

25. 15.2 The Physics of Music A tuning fork will produce a simple, pure sound A clarinet, however, will produce a sound of many frequencies

26. 15.2 The Physics of Music Both waves have the same frequency, but they will sound very different The difference in sound between these two waves is called timbre constructive interference of multiple frequencies (the fundamental and several harmonics)

27. 15.2 The Physics of Music

28. consonance – when a combination of pitches has a pleasant sound dissonance – when a combination of pitches has an unpleasant sound Different cultures have different definitions for consonance and dissonance

29. 15.2 The Physics of Music Noise involves several frequencies and involves random changes in frequency and amplitude