vowel acoustics march 10, 2014 some announcements today and wednesday: more resonance + the...
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Vowel Acoustics
March 10, 2014
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Some Announcements• Today and Wednesday: more resonance + the acoustics of vowels
• On Friday: identifying vowels from spectrograms.
• Also: I have an acoustics homework for you!
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Back at the Ranch• Last time, we learned about resonance:
• when one physical object is set in motion by the vibrations of another object.
• In speech, the vocal tract resonates in response to…
• the periodic vibrations of the vocal folds.
• We can envision a resonating sound wave as a standing wave…
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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
• We can also check out a spontaneous resonance video from closer to home!
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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?
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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.
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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
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Making the Leap• First: let’s check out the pop bottle demo
• To relate resonance to speech, we need to add two elements to the theory:
1. It is possible for sound waves of more than one frequency to resonate in a tube at the same time.
2. The vocal tract is a tube that is open at one end (the mouth)…
• so it behaves a little differently from a closed tube.
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Higher Resonances• It is actually possible to set up more than one standing wave in a tube at the same time.
First Resonance
Second Resonance
• In a closed tube, the second resonance frequency will be exactly twice as high as the first.
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First ResonanceTime 1: initial impulse is sent down the tubeTime 2: initial impulse bounces at end of tubeTime 3: impulse returns to other end and is reinforced by a new impulse
• Resonant period = Time 3 - Time 1
Time 4: reinforced impulse travels back to far end
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Second ResonanceTime 1: initial impulse is sent down the tube
Time 2: initial impulse bounces at end of tube + second impulse is sent down tube
Time 3: initial impulse returns and is reinforced; second impulse bounces
Time 4: initial impulse re-bounces; second impulse returns and is reinforcedResonant period = Time 2 - Time 1
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Different Patterns• This is all fine and dandy, but speech doesn’t really involve closed tubes.
• Think of the vocal tract as a tube with:
• one open end
• a sound pulse source at the closed end
(the vibrating glottis)
• The vocal tract will vibrate in response to the sound pulses…
• at the particular frequencies that will set up standing waves down its length.
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Just So You Know• A weird fact about nature:
• When a sound pressure peak hits the open end of a tube, it doesn’t get reflected back.
• Instead, there is an “anti-reflection”.
• The pressure disperses into the open air, and...
• A sound rarefaction gets sucked back into the tube.
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Open Tubes, part 1
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Open Tubes, part 2
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Open Tube Resonances• Standing waves in an open tube will look like this:
1st Resonance Frequency: F1
tube length
2nd Resonance Frequency:
F2 = 3 * F1
3rd Resonance Frequency:
F3 = 5 * F1
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An Evenly Spaced Spectrogram
• Go to Praat and check out:
• My neutral vowel
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My “Open Tube” Vowel
formants
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Spectral Analysis: Vowels• Remember: Fourier’s theorem breaks down any complex sound wave (e.g., speech) into its component sinewaves.
• For each component sinewave (harmonic), this analysis shows us:
• its frequency
• its amplitude (intensity)
• In vowels:
• resonating harmonics have higher intensity
• other harmonics will be damped (have lower intensity)
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A Vowel Spectrum
Note:
F0 160 Hz
F1
F2
F3 F4
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Different Vowels,Different Formants
• The formant frequencies of resemble the resonant frequencies of a tube that is open at one end.
• For the average man (like Peter Ladefoged or me):
• F1 = 500 Hz
• F2 = 1500 Hz
• F3 = 2500 Hz
• However, we can change the shape of the vocal tract to get different resonant frequencies.
• Vowels may be defined in terms of their characteristic resonant frequencies (formants).