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  1. 1. Resonance
  2. 2. Introduction <ul><li>Resonance  is the tendency of a system to oscillate with larger amplitude at some frequencies than at others. These are known as the system's  resonant frequencies . </li></ul><ul><li>At these frequencies, even small periodic driving forces can produce large amplitude oscillations, because the system stores vibrational energy. </li></ul>
  3. 3. Cont., <ul><li>A complex wave can be built up out of sine waves. </li></ul><ul><li>These component sine waves are called harmonics. </li></ul><ul><li>The frequencies of these harmonics are always integer multiples of the fundamental frequency of the complex wave. </li></ul><ul><li>Example: fundamental (F0) = 150 Hz </li></ul><ul><ul><li>Harmonic 1: 150 Hz </li></ul></ul><ul><ul><li>Harmonic 2: 300 Hz </li></ul></ul><ul><ul><li>Harmonic 3: 450 Hz, etc. </li></ul></ul>
  4. 4. Some Notes on Music <ul><li>In western music, each note is at a specific frequency </li></ul><ul><li>Notes have letter names: A, B, C, D, E, F, G </li></ul><ul><ul><li>Some notes in between are called “flats” and “sharps” </li></ul></ul>261.6 Hz 440 Hz
  5. 5. Harmony <ul><li>Notes are said to “harmonize” with each other if the greatest common denominator of their frequencies is relatively high. </li></ul><ul><li>Example: note A4 = 440 Hz </li></ul><ul><li>Harmonizes well with (in order): </li></ul><ul><li>A5 = 880 Hz (GCD = 440) </li></ul><ul><li>E5 ~ 660 Hz (GCD = 220) (a “fifth”) </li></ul><ul><li>C#5 ~ 550 Hz (GCD = 110) (a “third”) </li></ul><ul><li>.... </li></ul><ul><li>A#4 ~ 466 Hz (GCD = 2) (a “minor second”) </li></ul><ul><li>A major chord : A4 - C#5 - E5 </li></ul>
  6. 6. Cont., <ul><li>Last time, we also learned that: </li></ul><ul><li>We can represent the components of complex waves with a spectrum </li></ul><ul><ul><li>Frequency of harmonics on the x-axis </li></ul></ul><ul><ul><li>Intensity of harmonics on the y-axis </li></ul></ul>
  7. 7. Cont., <ul><li>We also got the sense that vowels may be distinguished on the basis of their spectral shapes. </li></ul>
  8. 8. <ul><li>Last but not least, we found out that we can represent spectral change over time with something called a spectrogram. </li></ul><ul><ul><li>time on the x-axis </li></ul></ul><ul><ul><li>frequency on the y-axis </li></ul></ul><ul><ul><li>intensity on the z-axis (represented by shading) </li></ul></ul><ul><li>One of the defining characteristics of speech sounds is that they exhibit spectral change over time. </li></ul>Cont.,
  9. 9. Fake Speech <ul><li>Check out the spectrograms of our synthesized vowels: </li></ul>
  10. 10. Ch-ch-ch-ch-changes <ul><li>Check out the spectrograms of some sinewaves which change in frequency over time: </li></ul>
  11. 11. Funky Stuff <ul><li>Sounds that exhibit spectral change over time sound like speech, even if they’re not speech </li></ul><ul><li>Example 1: sinewave speech </li></ul><ul><li>Consists of three sinusoids, varying in frequency over time </li></ul>
  12. 12. Reality Check <ul><li>Note that real speech is more fleshed out, spectrally, than sinewave speech. </li></ul>
  13. 13. Funky Stuff <ul><li>Sounds that exhibit spectral change over time sound like speech, even if they’re not speech </li></ul><ul><li>Example 2: wah pedal </li></ul><ul><li>shapes the spectral output of electrical musical instruments </li></ul>
  14. 14. Last but not least <ul><li>The frequencies of harmonics are dependent on the fundamental frequency of a sound </li></ul><ul><li> We cannot change the frequencies of harmonics independently of each other </li></ul><ul><li>To change the spectral shape of a speech sound, we have to change the intensity of different harmonics </li></ul>
  15. 15. Resonance Examples <ul><li>Pretty much everything resonates: </li></ul><ul><ul><li>tuning forks </li></ul></ul><ul><ul><li>bodies of musical instruments (violins, guitars, pianos) </li></ul></ul><ul><ul><li>blowing across the mouth of a bottle </li></ul></ul><ul><ul><li>pushing someone on a swing </li></ul></ul><ul><ul><li>bathroom walls </li></ul></ul><ul><li>In the case of speech: </li></ul><ul><ul><li>The mouth (and sometimes, the nose) resonates in response to the complex waves created by voicing. </li></ul></ul>
  16. 16. More on Resonance <ul><li>Objects resonate at specific frequencies, depending on: </li></ul><ul><ul><li>What they’re made of </li></ul></ul><ul><ul><li>Their shape </li></ul></ul><ul><ul><li>Their size </li></ul></ul><ul><li>Think: pipe organs </li></ul><ul><ul><li>Longer, larger tubes resonate at lower frequencies. </li></ul></ul><ul><ul><li>Shorter, smaller tubes resonate at higher frequencies. </li></ul></ul>
  17. 17. Traveling Waves <ul><li>How does resonance occur? </li></ul><ul><li>Normally, a wave will travel through a medium indefinitely </li></ul><ul><li>Such waves are known as traveling waves </li></ul>
  18. 18. Reflected Waves <ul><li>If a wave encounters resistance, however, it will be reflected. </li></ul><ul><li>What happens to the wave then depends on what kind of resistance it encounters… </li></ul><ul><li>If the wave meets a hard surface, it will get a true “bounce”: </li></ul><ul><ul><li>Compressions (areas of high pressure) come back as compressions </li></ul></ul><ul><ul><li>Rarefactions (areas of low pressure) come back as rarefactions </li></ul></ul>
  19. 19. Sound in a Closed Tube
  20. 20. Wave in a closed tube <ul><li>With only one pressure pulse from the loudspeaker, the wave will eventually dampen and die out </li></ul><ul><li>What happens when: </li></ul><ul><ul><li>another pressure pulse is sent through the tube right when the initial pressure pulse gets back to the loudspeaker? </li></ul></ul>
  21. 21. Standing Waves <ul><li>The initial pressure peak will be reinforced </li></ul><ul><li>The whole pattern will repeat itself </li></ul><ul><li>Alternation between high and low pressure will continue </li></ul><ul><ul><li> long as we keep sending in pulses at the right time </li></ul></ul><ul><li>This creates what is known as a standing wave. </li></ul><ul><li>When this happens, the tube will vibrate in response to the motion of the standing wave inside of it. </li></ul><ul><ul><li>= it will resonate . </li></ul></ul>
  22. 22. Resonant Frequencies <ul><li>This is important: </li></ul><ul><ul><li>a standing wave can only be set up in a tube if pressure pulses are emitted from the loudspeaker at the right frequency . </li></ul></ul><ul><li>What is the right frequency? That depends on: </li></ul><ul><ul><li>how fast the sound wave travels through the tube </li></ul></ul><ul><ul><li>how long the tube is </li></ul></ul><ul><li>Basically: </li></ul><ul><ul><li>the longer the tube, the lower the frequency </li></ul></ul><ul><li>Why? </li></ul>
  23. 23. Establishing Resonance <ul><li>A new pressure pulse should be emitted right when: </li></ul><ul><ul><li>the first pressure peak has traveled all the way down the length of the tube </li></ul></ul><ul><ul><li>and come back to the loudspeaker. </li></ul></ul>
  24. 24. Establishing Resonance <ul><li>The longer the tube, the longer you need to wait for the pressure peak to travel the length of the tube. </li></ul><ul><ul><li> longer period between pressure pulses </li></ul></ul><ul><ul><li> lower frequency </li></ul></ul>F0  F0 
  25. 25. The End <ul><li>… .. Thank You ….. </li></ul>