Resonance

1. Resonance October 31, 2012

2. Looking Ahead • I’m almost done with the grading of the second production exercise… • Hopefully you’ll get the results by tomorrow night. • Today: we’ll cover something called resonance • Next week: understanding vowels

3. Ghosts of Lectures Past • Last time we learned: • A complex wave can be built up out of sinewaves. • These component sinewaves are called harmonics. • The frequencies of these harmonics are always integer multiples of the fundamental frequency of the complex wave. • Example: fundamental (F0) = 150 Hz • Harmonic 1: 150 Hz • Harmonic 2: 300 Hz • Harmonic 3: 450 Hz, etc.

4. Some Notes on Music • In western music, each note is at a specific frequency • Notes have letter names: A, B, C, D, E, F, G • Some notes in between are called “flats” and “sharps” 261.6 Hz 440 Hz

5. Harmony • Notes are said to “harmonize” with each other if the greatest common denominator of their frequencies is relatively high. • Example: note A4 = 440 Hz • Harmonizes well with (in order): • A5 = 880 Hz (GCD = 440) • E5 ~ 660 Hz (GCD = 220) (a “fifth”) • C#5 ~ 550 Hz (GCD = 110) (a “third”) • .... • A#4 ~ 466 Hz (GCD = 2) (a “minor second”) • A major chord: A4 - C#5 - E5

6. Where Things Stand, part 2 • Last time, we also learned that: • We can represent the components of complex waves with a spectrum • Frequency of harmonics on the x-axis • Intensity of harmonics on the y-axis

7. Where Things Stand, part 3 • We also got the sense that vowels may be distinguished on the basis of their spectral shapes.

8. Where Things Stand, part 4 • Last but not least, we found out that we can represent spectral change over time with something called a spectrogram. • time on the x-axis • frequency on the y-axis • intensity on the z-axis (represented by shading) • One of the defining characteristics of speech sounds is that they exhibit spectral change over time.

9. Fake Speech • Check out the spectrograms of our synthesized vowels:

10. Ch-ch-ch-ch-changes • Check out the spectrograms of some sinewaves which change in frequency over time:

11. Funky Stuff • Sounds that exhibit spectral change over time sound like speech, even if they’re not speech • Example 1: sinewave speech • Consists of three sinusoids, varying in frequency over time

12. Reality Check • Note that real speech is more fleshed out, spectrally, than sinewave speech.

13. Funky Stuff • Sounds that exhibit spectral change over time sound like speech, even if they’re not speech • Example 2: wah pedal • shapes the spectral output of electrical musical instruments

14. Last but not least • The frequencies of harmonics are dependent on the fundamental frequency of a sound •  We cannot change the frequencies of harmonics independently of each other • To change the spectral shape of a speech sound, we have to change the intensity of different harmonics

15. How is this done? • We can selectively amplify or dampen specific harmonics in a speech sound by taking advantage of a phenomenon known as resonance. • Resonance: • when one physical object is set in motion by the vibrations of another object. • Generally: a resonating object reinforces (sound) waves at particular frequencies • …by vibrating at those frequencies itself • …in response to the pressures exerted on it by the (sound) waves. •  Resonance makes sounds at those frequencies louder.

16. Resonance Examples • Pretty much everything resonates: • tuning forks • bodies of musical instruments (violins, guitars, pianos) • blowing across the mouth of a bottle • pushing someone on a swing • bathroom walls • In the case of speech: • The mouth (and sometimes, the nose) resonates in response to the complex waves created by voicing.

17. More on Resonance • Objects resonate at specific frequencies, depending on: • What they’re made of • Their shape • Their size • Think: pipe organs • Longer, larger tubes resonate at lower frequencies. • Shorter, smaller tubes resonate at higher frequencies.

18. Traveling Waves • How does resonance occur? • Normally, a wave will travel through a medium indefinitely • Such waves are known as traveling waves

19. Reflected Waves • If a wave encounters resistance, however, it will be reflected. • What happens to the wave then depends on what kind of resistance it encounters… • If the wave meets a hard surface, it will get a true “bounce”: • Compressions (areas of high pressure) come back as compressions • Rarefactions (areas of low pressure) come back as rarefactions

20. Sound in a Closed Tube • Java applet: http://surendranath.tripod.com/Applets/Waves/Lwave01/Lwave01Applet.html

21. Wave in a closed tube • With only one pressure pulse from the loudspeaker, the wave will eventually dampen and die out • What happens when: • another pressure pulse is sent through the tube right when the initial pressure pulse gets back to the loudspeaker?

22. Standing Waves • The initial pressure peak will be reinforced • The whole pattern will repeat itself • Alternation between high and low pressure will continue • ...as long as we keep sending in pulses at the right time • This creates what is known as a standing wave. • When this happens, the tube will vibrate in response to the motion of the standing wave inside of it. • = it will resonate.

23. Tacoma Narrows Movie Also check out: http://www.youtube.com/watch?v=j-zczJXSxnw

24. Disaster!

25. A Minor Disaster • The pressure waves of sound can set up standing waves in objects, too. • Check out the Mythbusters video online: • www.youtube.com/watch?v=PMg_nd-O688