Introduction to acoustic phonetics
Dr. Christian DiCanio
cdicanio@buffalo.edu
University at Buffalo
10/8/15
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Pressure & Waves
Waves
Sound waves are fluctuations in pressure that travel through a
medium, e.g. air, water.
These fluctuations cause air molecules to compress together and
spread apart (rarefy).
Assuming that the sound wave is periodic, the regions of compression
will be evenly spaced.
Small displacements in the air spread outward and when they come in
contact with one’s eardrum, they cause it to move.
Demo:
http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html
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Pressure & Waves
Longitudinal waves involve a displacement of the medium parallel to
the propagation of the wave. Sound waves in air are longitudinal
waves.
Transverse waves involve a displacement of the medium perpendicular
to the propagation of the wave. The ripples on a pond are a good
example.
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Pressure & Waves
Waveforms
Detecting and graphing these changes in air pressure over time gives
us a waveform, or plot of the wave:
The sound waveform represents displacements from normal
atmospheric pressure (the horizontal line)
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Pressure & Waves
Musical instruments (and vocal cords) produce periodic waves, with
regular, self-reinforcing repetitions. Perceived as having a note.
Periodic sound waves have periods at even intervals and are perceived
as tones (given that they fall within one’s range of hearing).
Aperiodic (random, non-repetitive) sound waves are perceived as
noise. Doors slamming, wind blowing, and rain falling are each
examples of aperiodic sounds.
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Frequency
In a periodic wave, the same cycle (pressure displacement pattern)
repeats.
The frequency is the number of cycles per second, measured in hertz
(Hz.)
The period is the time required for one complete cycle.
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Frequency
Frequency is the inverse of the period duration.
The frequency F is the number of cycles per second (Hz), and the
period T is the time it takes to complete one cycle, often measured in
milliseconds (ms.).
Hence F T = 1, F =
1
T,
and T =
1
F
Example: if T = .01 seconds, then F =
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1
.01 s
= 100 Hz
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Frequency
The frequency F , wavelength λ, and speed C of a wave are related by
the formula F λ = C. C is a constant representing the speed at which
vibrations may travel in different medias.
The speed of sound C in the air is about 350 meters/second, but can
fluctuate depending on the temperature. If it is colder, sound moves
more slowly. If it is warmer, sound moves faster.
Example:
Suppose the wavelength λ is one meter
That means in one second we would measure 350 cycles
In this case F = C/λ = 350/1 = 350 Hz
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Frequency
The speed of sound depends on the density of the medium
Air
Water
Rock
Density (g/cm3 ) 0.001
1
2-3
Speed (m/s)
350
1500 2000-5000
Which sound has a shorter wavelength, 1 kHz in the air or 3 kHz in
the water?
Air: λ = C/F = 350/1000 = 0.35m
Water: λ = C/F = 1500/3000 = 0.5m
Answer: 1 kHz in the air has a shorter wavelength
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Frequency
Frequency range of human hearing is about 25 - 16,000 Hz
Examples of wavelengths at various frequencies:
Sound
Lowest C on piano
Middle C on piano
Violin A string
Four octaves above middle C
F0 of human males
F0 of human females
Highest audible tone
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Freq. F
32.7 Hz
262 Hz
440 Hz
4,186 Hz
70 - 250 Hz.
120 - 350 Hz.
20,000 Hz
Acoustics
Wavelength λ
10.51 m
1.29 m
0.76 m
8.25 cm
5 - 1.4 m
2.9 - 1 m
1.7 cm
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Frequency
Frequency bandwidth of various media
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Frequency
Frequency and Pitch
Frequency is a physical measure. Pitch is psychoacoustic. Frequency
is the basis of perceived pitch.
Pitch is what we hear, not what is produced.
Reflects the interval between successive harmonics in a periodic wave.
Each musical octave has twice the frequency of the octave below it.
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Amplitude & Intensity
The amplitude of a wave is the degree by which the peak is displaced.
The difference in displacement reflects how much individual molecules
in the medium are compressed when a wave travels through the
medium.
Measured in micro-Pascals (µPa), but for sound the deciBel scale is
used, which reflects the perceived loudness or intensity of a sound.
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Amplitude & Intensity
Sound
Hearing threshold
Whisper
Quiet office
Conversation
City bus
Subway platform
Rock concert
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Pressure (µPa)
20
200
2,000
20,000
200,000
2,000,000
20,000,000
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Amplitude & Intensity
The decibel scale expresses the difference between two intensities I1
and I2 as 10 log II12 dB
2
= 20 dB
For example, a whisper is 10 log 200
202
Example
Sound
Hearing threshold
Whisper
Quiet office
Conversation
City bus
Subway platform
Rock concert
Jet engine
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Pressure
µP a
20
200
2,000
20,000
200,000
2 × 106
2 × 107
2 × 108
Acoustics
Intensity
µP a2
400
40,000
4 × 106
4 × 108
4 × 1010
4 × 1012
4 × 1014
4 × 1016
Decibels
dB
0
20
40
60
80
100
120
140
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Amplitude & Intensity
Intensity at a distance r is inversely proportional to r2
Thus, doubling the distance reduces intensity by a factor of 4
In decibels, difference is 10 log
1
4
= −6.0 dB
However, in real life, reverberation (off of walls, floors, etc.) often
prevents the intensity from decreasing this much
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Simple and Complex Waves
Simple and Complex Waves
Sinusoidal wave: a periodic wave with one frequency component, also
known as a sine wave.
Sine waves are simple waves.
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Simple and Complex Waves
Real-word sound waves (animal calls or human speech) appear to be
and are, in fact, much more complex than sinusoidal waves.
There is a regular pattern in this wave, but it is far more complex than
a sine wave. The extra fluctuations in the wave signify that the air
pressure is fluctuating in a much more complex fashion.
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Simple and Complex Waves
From simple to complex
When two or more simple waves are combined, they create a more
complex wave.
Similarly, complex waves can be decomposed into simple (sinusoidal)
component waves.
The complex wave is the sum of the component waves.
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Simple and Complex Waves
How do waves combine together?
When the peaks (pressure maxima) and valleys (pressure minima) of
two waves coincide, we say the waves are in phase.
The two pressure maxima/minima combine when both waves are
produced to create a peak of greater amplitude (constructive
interference).
Positive pressure values and identical negative values cancel each other
out (destructive interference).
Waves of different phases but identical frequencies will still create
another sine wave.
http://www.acs.psu.edu/drussell/Demos/superposition/–
superposition.html; Praat
example
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Simple and Complex Waves
Complex waves have a number of different frequency components, all
or some of which may be periodic.
Each of these components may be represented as a single frequency
value on a sound spectrum, which plots frequency on the x-axis and
amplitude on the y-axis.
A spectrum differs from a waveform, which does not indicate specific
frequency components.
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Simple and Complex Waves
Sound Spectrum (left) and Sound Waveform (right) showing the same
waves.
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Fundamental Frequency and Harmonics
Fundamental Frequency & Harmonics
A periodic wave has a fundamental frequency, F0 , which is the
frequency at which the entire wave repeats itself, its greatest common
divisor.
However, waves may have one or more harmonic frequencies, which
are whole number multiples of F0 .
The fundamental frequency of a periodic harmonic wave determines
the perceived pitch.
In this example, we have an F0 of 100 Hz, and two harmonics:
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Fundamental Frequency and Harmonics
A plucked string vibrates at several frequencies at the same time.
This produces a series of harmonics, called “overtones” in musical
theory.
Harmonic frequencies change the quality or timbre of the sound, but
not the pitch.
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Fundamental Frequency and Harmonics
Harmonics in a complex wave
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Fundamental Frequency and Harmonics
Middle C (262 Hz) on flute:
A-sharp (116.5 Hz) on bass clarinet:
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Fundamental Frequency and Harmonics
In reality, perceived pitch is determined by the spacing of harmonics as
much as by the F0 .
If we remove the 100 Hz. component from the wave below, the F0
and perceived pitch do not change (but timbre does).
On telephones, recall that the bandwidth is cut off at the lower end of
250 Hz.
But most human voices use a pitch range of 80 - 250 Hz!
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Spectrograms
Spectrograms
A spectrogram displays
Time along the x-axis
Component frequencies along the y-axis
Relative intensity (amplitude) using darkness (the z-axis).
More complex than a waveform or a spectrum because three
dimensions are conveyed.
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