Crash course in acoustics - Columbia UniversityCrash course in acoustics 2 Outline •What is sound...
Transcript of Crash course in acoustics - Columbia UniversityCrash course in acoustics 2 Outline •What is sound...
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Crash course in
acoustics
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Outline
• What is sound and how does it travel?
• Physical characteristics of simple sound waves
– Amplitude, period, frequency
• Complex periodic and aperiodic waves
• Source-filter theory
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Take home message
• Two types of visual representation of speech: – Waveforms (time by amplitude displays)
– Spectrograms (time by frequency displays)
• Characteristics of waveforms
– simple, complex, periodicity, frequency…
• Speech sounds
– The source • vocal folds: produces a range of frequencies (harmonics)
• Other sources, e.g. noise
– Articulators filter this source
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What is speech acoustically?
• Acoustically, speech sounds are similar to other sounds.
• What is sound? – Movement of particles which causes pressure
fluctuation in the surrounding air.
• What happens to the air pressure? – Compression: Pressure increases so the air particles are
close together
– Rarefaction: Pressure decreases so the air particles are further apart
• Air pressure changes cause our eardrum and bones of the middle ear to vibrate.
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How does sound travel?
• In order to even reach our ears, sound must travel from its source.
• Pressure fluctuations caused by the source propagate through elastic media:
– there is room for molecules to move back and forth.
• In other words, sound moves in waves
– A sound wave is a traveling pressure fluctuation
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Propagation of a sound wave
From http://home.att.net/~cat4a/wave-II.htm
See also http://entertainment.howstuffworks.com/sci-fi10.htm
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The waveform as pressure
changes • Graphic representation showing changes
in air pressure:
atmospheric pressure
compression
rarefaction
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The simplest sound
• The simplest type of sound is a pure tone (e.g. the sound of a tuning fork)
– Generated by simple harmonic motion (think pendulum)
Waveform of a pure tone = a sine wave
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What does this graph
represent?
• We can interpret this graph as showing the movement of one air particle from its rest position
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What is a periodic wave?
• This type of wave is called periodic because the motion of the particle is repeated at regular intervals
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Frequency of a periodic wave
• Cycle: The completed movement of a wave • Period (T): The time it takes for each cycle in a
wave to be completed • Frequency: The number of cycles completed
in one second • Hertz (or cycles per second): Frequency is
measured in Hz and is perceived as pitch • Humans can hear sounds whose frequency
ranges from 20-20,000 Hz, though speech sounds essentially utilize the lowest half of this range
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Frequency in more detail • Frequency: the number of times a cycle is
repeated within a time interval (in speech, the standard unit of time is 1 second)
Frequency = 1/T (period)
• If one cycle of vocal fold vibration is completed every 1/100 of a second, then T= 0.01 and frequency is 1/0.01 = 100 cycles per second = 100 Hz (Hertz)
• Conversely, if the frequency of a sound is 200 Hz, then there are 200 cycles of the sound wave per second, and the period is 1/200 = 0.005 s = 5 ms (milliseconds)
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Amplitude of a periodic wave
• The amplitude of the wave is related to the extent of particle displacement
• Roughly speaking, the greater the displacement (amplitude), the louder the sound
• NB: Amplitude and frequency are independent of one another
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The independence of
frequency and amplitude
From Ladefoged, 1996
Two sine waves with the same frequency but different amplitude
Two sine waves with the same amplitude but different frequency
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Question
• What are the frequencies of these two sine waves? (Hint: Calculate how many cycles must be completed in one second.)
0 .01 .02
Time in seconds
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Beyond tuning forks
• If only speech were that simple. But in fact:
• Speech sounds are not pure tones
• Rather, they are made up of tones of several frequencies, and can be distinguished into two categories
– (complex) periodic sounds
– aperiodic sounds
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Complex periodic sounds
• Complex periodic sounds are made up of two or more sine waves.
• Complex waves still have a repeating pattern.
• The component sine wave with the lowest frequency is called the fundamental frequency (F0).
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A complex periodic wave
Source: http://www.umanitoba.ca/faculties/arts/linguistics/russell/138/sec4/acoust1.htm
+
=
300 Hz
500 Hz
0 .01 .02
0 .01 .02
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Fundamental Frequency • The waveform of a complex periodic sound has
a complex shape that is repeated with the same periodicity as its lowest frequency component.
What is the
fundamental frequency?
100 Hz
0 .01 .02
300 Hz
0 .01 .02
0 .01 .02
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Waves of different frequencies
(and amplitudes)
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Further aspects of complex
waves • The waveform of a complex periodic wave is
derived by adding up the amplitude of the component waves at every point in time.
• When the complex wave is known but the components aren’t, the wave can be broken down using a method called Fourier analysis.
• Vowels (and to an extent other vowel-like speech sounds, i.e. approximants) are complex periodic waves
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Aperiodic waves
• Aperiodic waves have components at several frequencies, not only at frequencies that are whole number multiples of the fundamental.
• The result is an irregular non-repetitive waveform
• An example is radio static or white noise, which include components of equal amplitude at all audible frequencies
• In speech, fricatives are aperiodic.
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Examples of aperiodic
waves
White noise
From Denes & Pinson, 1973
ʃ
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Visual waveforms of
speech • One way speech can be examined is in the time domain.
• This is plotted as a time by amplitude waveform.
• No frequency information is contained in a waveform.
p eɪ p ə
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Limitations of waveforms
• By examining waveforms we may not be able to tell exactly which sound is shown: e.g. we can tell the sound is a stop, but we may not be able to tell whether it is a [p] or a [t]
• The difficulties are similarly great for vowels
• Frequency information is needed, in addition to time and amplitude
• Spectrograms are a representation that provides us with time, frequency and amplitude information
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Harmonics (overtones) • What is the difference between the tuning fork
and the vocal folds in how they vibrate?
• The fork corresponds to (more or less) a simple sine wave whereas the vocal folds correspond to a complex wave.
• Components of complex waves are called harmonics.
• Harmonics are not arbitrary sine waves: – Rather, waves with frequencies that are whole number multiples
of the fundamental frequency (F0, the lowest frequency component)
• The amplitude of each component wave is not necessarily the same.
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Spectrum
• Spectrum is a plot of frequency against amplitude at a particular point in time
Freq. in kHz
A
m
p
Source input (vocal
folds)
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Source-Filter Theory
• In the speech wave, not all harmonics have equal amplitude.
• This is because the human vocal tract acts as a filter: – Frequency-selective
– Amplifies some frequencies (called formants), damps others;
• Phonation (vocal fold vibration) is the sound source that is shaped by the vocal tract
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The vocal tract filter • Different sounds
have different vocal tract configurations.
• For example, consider the difference between [u], [ʊɑ], and [ɑ].
The sound source from the vocal folds always contains the same frequencies, but
different vocal tract shapes will amplify some frequencies and damp others.
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Freq. in kHz
A
m
p
Source input
(vocal folds) Resonator filter
(vocal tract) Output
(vowel)
Frequency response for
[ɑ]: amplified frequencies
(formants) at 800Hz,
1300Hz, 2500Hz (approx)
Spectrum
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Spectrogram
X-axis is time; Y-axis is frequency; darkness is intensity
Time
F r e q u e n c y
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Try to find the individual phonemes of “In English” in the waveform:
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Summary
• Two types of visual representation of speech: – Waveforms (time by amplitude displays)
– Spectrograms (time by frequency displays)
• Characteristics of waveforms
– simple, complex, periodicity, frequency…
• Speech sounds
– Articulators filter the source
– Spectrum, harmonics