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.  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?  f 1 = 200 Hz (fundamental frequency = first harmonic)  f 2 = 400 Hz  f 3 = 600 Hz  f 4 = 800 Hz  f 5 = 1000 Hz

9. Harmonics and Timbre

10.  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.  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.Ruben’s Tube