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# Resonance

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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.
Cont.,
• 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:
• 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 …..