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  • 1. Resonance
  • 2. Introduction
    • 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 .
    • At these frequencies, even small periodic driving forces can produce large amplitude oscillations, because the system stores vibrational energy.
  • 3. Cont.,
    • A complex wave can be built up out of sine waves.
    • These component sine waves 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. Cont.,
    • 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. Cont.,
    • We also got the sense that vowels may be distinguished on the basis of their spectral shapes.
  • 8.
    • 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. 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.
  • 16. 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.
  • 17. Traveling Waves
    • How does resonance occur?
    • Normally, a wave will travel through a medium indefinitely
    • Such waves are known as traveling waves
  • 18. 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
  • 19. Sound in a Closed Tube
  • 20. 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?
  • 21. 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 .
  • 22. Resonant Frequencies
    • This is important:
      • a standing wave can only be set up in a tube if pressure pulses are emitted from the loudspeaker at the right frequency .
    • What is the right frequency? That depends on:
      • how fast the sound wave travels through the tube
      • how long the tube is
    • Basically:
      • the longer the tube, the lower the frequency
    • Why?
  • 23. Establishing Resonance
    • A new pressure pulse should be emitted right when:
      • the first pressure peak has traveled all the way down the length of the tube
      • and come back to the loudspeaker.
  • 24. Establishing Resonance
    • The longer the tube, the longer you need to wait for the pressure peak to travel the length of the tube.
      •  longer period between pressure pulses
      •  lower frequency
    F0  F0 
  • 25. The End
    • … .. Thank You …..