Resonance, Revisited

March 4, 2013

Leading Off…• Project report #3 is due!

• Course Project #4 guidelines to hand out.

• Today: Resonance

• Before we get into that: dogs talking!

• And cats, too!

Where were we?• Shorter windows give us:

• Better temporal resolution

• Worse frequency resolution

• = wide-band spectrograms

• Longer windows give us:

• Better frequency resolution

• Worse temporal resolution

• = narrow-band spectrograms

• Higher sampling rates give us...

• A higher limit on frequencies to consider.

“Band”?• Way back when, we discussed low-pass filters:

• This filter passes frequencies below 250 Hz.

• High-pass filters are also possible.

Band-Pass Filters• A band-pass filter combines both high- and low-pass filters.

• It passes a “band” of frequencies around a center frequency.

Band-Pass Filtering

• Basic idea: components of the input spectrum have to conform to the shape of the band-pass filter.

Bandwidth• Bandwidth is the range of frequencies over which a filter will respond at .707 of its maximum output.

bandwidth• Half of the acoustic energy passed through the filter fits within the bandwidth.

• Bandwidth is measured in Hertz.

Different Bandwidths

narrow band wide band

Your Grandma’s Spectrograph

• Originally, spectrographic analyzing filters were constructed to have either wide or narrow bandwidths.

Narrow-Band Advantages• Narrow-band spectrograms give us a good view of the harmonics in a complex wave…

• because of their better frequency resolution.

modal voicing EGG waveform

Narrow-Band Advantages• Narrow-band spectrograms give us a good view of the harmonics in a complex wave…

• because of their better frequency resolution.

tense voicing EGG waveform

Comparison• Remember that modal and tense voice can be distinguished from each other by their respective amount of spectral tilt.

modal voice tense voice

A Real Vowel Spectrum

Why does the “spectral tilt” go up and down

in this example?

The Other Half• Answer: we filter the harmonics by taking advantage of the phenomenon of resonance.

• Resonance effectively creates a series of band-pass filters in our mouths.

+ =

• Wide-band spectrograms help us see properties of the vocal tract filter.

Formants• Rather than filters, though, we may consider the vocal tract to consist of a series of “resonators”…

• with center frequencies,

• and particular bandwidths.

• The characteristic resonant frequencies of a particular articulatory configuration are called formants.

Wide Band Spectrogram• Formants appear as dark horizontal bars in a wide band spectrogram.

• Each formant has both a center frequency and a bandwidth.

formants

F1

F2

F3

Narrow-Band Spectrogram• A “narrow-band spectrogram” clearly shows the harmonics of speech sounds.

• …but the formants are less distinct.

harmonics

A Static Spectrum

Note:

F0 160 Hz

F1

F2

F3 F4

Questions1. How does resonance occur?

• And how does it occur in our vocal tracts?

2. Why do sounds resonate at particular frequencies?

3. How can we change the resonant frequencies of the vocal tract? (spectral changes)

Some Answers• 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.

• In the case of speech:

• The mouth (and sometimes, the nose) resonates in response to the complex waves created by voicing.

Traveling Waves• Resonance occurs because of the reflection of sound waves.

• Normally, a wave will travel through a medium indefinitely

• Such waves are known as traveling waves.

Check out the tsunami!

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

Sound in a Closed Tube

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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?

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.

Tacoma Narrows Movie

Lenticular Clouds• An interesting example of standing waves that we can often see around Calgary is called a lenticular cloud.

• These are formed by air (wind) bouncing in waves over the mountains.

• When the air reaches a certain height, it will condense into clouds. After it drops back down, the condensation will disappear.

• The clouds stay in one place while the wind passes through them! (check out http://www.atoptics.co.uk)

Standing Wave Terminology

node: position of zero pressure change in a standing wave

node

Standing Wave Terminology

anti-node: position of maximum pressure change in a standing wave

anti-nodes