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13.3 Harmonics

13.3 Harmonics. pp. 494 - 503 Mr. Richter. Agenda. Check 13.1 Homework Finish Notes from 13.2 Forced Vibrations and Resonance Notes: Harmonics Harmonics and Timbre Beat Frequencies. Objectives: We Will Be Able To…. Relate harmonic frequencies to the fundamental frequency of vibration.

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13.3 Harmonics

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  1. 13.3 Harmonics pp. 494 - 503 Mr. Richter

  2. Agenda • Check 13.1 Homework • Finish Notes from 13.2 • Forced Vibrations and Resonance • Notes: • Harmonics • Harmonics and Timbre • Beat Frequencies

  3. Objectives: We Will Be Able To… • Relate harmonic frequencies to the fundamental frequency of vibration. • Relate harmonics and timbre. • Relate the frequency difference between two waves to the beat frequency.

  4. Warm-Up:

  5. Harmonics

  6. Harmonics • As we saw in Chapter 12: • Every vibrating object can produce a variety of standing waves. • The simplest standing wave occurs at the fundamental frequency: the lowest frequency of vibration of a standing wave.

  7. Harmonics • As we saw in the standing wave lab: all harmonics are integral multiples of the fundamental frequency.

  8. Harmonics: Example • What are the first 5 harmonics of an instrument whose fundamental frequency is 200 Hz? • f1 = 200 Hz (fundamental frequency = first harmonic) • f2 = 400 Hz • f3 = 600 Hz • f4 = 800 Hz • f5 = 1000 Hz

  9. Harmonics and Timbre

  10. Harmonics and Timbre • When two sources of sound produce a sound at the same frequency can you tell them apart? • Of course you can! How come? • The “sound quality” of a note is called timbre. Timbre is the richness or fullness of a sound. • The timbre of a note depends on the harmonics that are produced by the sound source.

  11. Harmonics and Timbre • The tuning fork an uncomplicated tone. • The viola has a more complex tone, and thus a fuller sound.

  12. Harmonics and Frequency: Fun Facts • The fundamental frequency determines the pitch. This frequency dominates the sound wave. Other harmonics contribute to each wave. • The frequency of the second harmonic is exactly one octave above the first note. • If harmonics of multiple notes are aligned, overtones can be heard.

  13. Beat Frequency

  14. Beat Frequency • When two waves of slightly different frequencies interfere, the interference pattern creates loudness and then softness repetitively. (I’m sorry for what’s about to happen)

  15. Calculate the Beat Frequency • The alternating loudness and softness occurs periodically, and produces what is called a beat frequency. • The beat frequency (numerically) is the absolute value of the difference between the two given frequencies. • For example: If I play a note at 440 Hz and a note at 443 Hz, the beat frequency is… • 3 Hz!

  16. Wrap-Up: Did we meet our objectives? • Relate harmonic frequencies to the fundamental frequency of vibration. • Relate harmonics and timbre. • Relate the frequency difference between two waves to the beat frequency.

  17. Homework • p. 503 #1, 2, 3, 5

  18. Cool Standing Wave Video! • This is called a Ruben’s Tube.

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