Linguistics 401
LECTURE #2
BASIC ACOUSTIC CONCEPTS
(A review)
Unit of wave: CYCLE → one complete wave (=one complete crest and trough)
The number of cycles per second:
FREQUENCY
↓
cycles per second (cps) = Hertz (Hz)
e.g. 100 Hz refers to 100 cycles per second.
The time taken for each cycle is termed a PERIOD.
If the frequency is 20 cps, then the period is 1/20th of a second (= 50 msec)
Algebraically, period and frequency have the relationship:
1
f=
T
where f = frequency
T = the duration of the period
PHYSICAL DIMENSIONS OF WAVES
1.
AMPLITUDE: the increase or decrease of air pressure at a given point during a
sound (= the amount of acoustic energy present!)
The greater the amplitude the higher the crest (and deeper the troughs) of the
waves.
The amplitude indicates the INTENSITY of the sound.
2.
WAVELENGTH: The distance occupied by one cycle.
TEMPORAL DIMENSIONS OF WAVES
1.
FREQUENCY (see above)
2.
SPEED OF PROPAGATION (=velocity of sound)
At normal atmospheric conditions, sound travels through air at about
344 meters per second
or
1130 feet per second
or
758 miles per hour
Velocity of particle movement must not be confused with velocity of sound wave
propagation!
Particles CHANGE velocity; sound wave movement is CONSTANT!
STUDY THE HANDOUT!
Zero velocity and maximum acceleration at B, D, F, H, J, L;
(velocity gradually diminishes as the particle approaches these points).
Maximum velocity at the zero crossing C, E, G, I and K.
3.
PERIOD (see above)
************
WAVEFORMS are common representations of sound signals.
A waveform is an amplitude by time display.
•
it represents particle motion
•
it also represents pressure variation as a function of distance from the
source
The movement of any particle, were it visible, would not look like a waveform by which it is
traditionally represented.
A waveform is an abstract representation of the displacement from rest which the particle
undergoes during a certain time span.
By convention: AMPLITUDE is represented along the ordinate
(y or vertical axis)
TIME is represented along the abscissa
(x or horizontal axis)
STUDY APPENDIX #1
Wave motion can be
(a)
PERIODIC: the pattern of vibration repeats itself
(b)
APERIODIC: the vibration has no repeatable pattern.
Strictly speaking, only waves with an infinite number of repetitions are periodic
(DAMPING!)
↓
causing the vibrations to die away
But, in practice, many speech sound waves have enough repetitions to be regarded as
periodic.
Periodic waves are perceived as ‘musical’ (e.g. vowels); aperiodic waves are perceived
as ‘noise’ (e.g. a fricative sound).
PSYCHOLOGICAL DIMENSIONS OF SOUND
FREQUENCY
→
(concrete, physical,
measurable)
PITCH
(perceptual, subjective)
AMPLITUDE
(concrete, physical,
measurable)
LOUDNESS
(perceptual, subjective)
→
*********
Waves can be divided into:
a.
SIMPLE or SINUSOIDAL WAVES
•
a representation of PURE TONE
•
always periodic
ONE OF THE SIMPLEST KINDS OF VARIATION IN AIR PRESSURE: PURE TONE
Sounds of the same frequency and in phase (see below) may be added: the result will be a
pure tone (= contains only one frequency)
b.
COMPLEX WAVES
•
periodic : if all of its components are periodic
•
aperiodic (see below)
ADDITION OF WAVES:
a.
Adding pure tone of the same frequency: the result will be a pure tone having the
same frequency (phase and amplitude may vary)
PHASE: the difference in the timing of the components is known as a difference in phase.
STUDY THE HANDOUT!
b.
Adding pure tones of different frequencies:
Fourier’s Theorem
↓
ANY COMPLEX PERIODICAL WAVE CAN BE ANALYZED AS THE SUM OF ITS
COMPONENT FREQUENCIES AND AMPLITUDES.
STUDY THE HANDOUT! STUDY APPENDIX #2 AND #3!
Periodic complex variations produce signals in which the component frequencies are integral
multiples of the lowest frequency of pattern repetition:
FUNDAMENTAL FREQUENCY (Fo)
The frequency of the repetition of a complex wave
HARMONICS: whole-number multiples of the fundamental frequency of the waveform.
Why whole-number multiples?
harmonics (=overtones)
LINE SPECTRUM
Another type of display for vibrating patterns is called a LINE SPECTRUM (or
AMPLITUDE SPECTRUM).
horizontal axis : FREQUENCY
vertical axis: AMPLITUDE
STUDY Appendix #1!
APERIODIC COMPLEX SIGNALS:
They consist of more than one frequency, but the frequencies are not harmonically related.
There are two types of aperiodical signals:
a.
TRANSIENT: burst or noise of short duration (e.g. the sound made by dropping a
book).
b.
CONTINUOUS (e.g. hissing noise)
-------------MEASURING WAVELENGTH (λ)
Wavelength depends on two factors:
a.
frequency of vibration
•
•
b.
high frequency sounds occupy less space per cycle;
they have a shorter wavelength than low frequency sounds.
velocity of sound wave propagation in the medium
•
•
sound waves are conducted in solids at a higher velocity than through liquids;
through liquids at a higher velocity than through gases.
WAVELENGTH (λ) EQUALS CONSTANT VELOCITY (c) DIVIDED BY FREQUENCY (f):
c
λ =
f
If Fo is 200 Hz (woman) or 100 Hz (man)
c
λ =
344m/s
=
f
c
λ =
= 1.75 m
200 Hz
344m/s
=
f
= 3.4 m
100 Hz
STANDING WAVES
REFLECTION: whenever waves traveling through a medium reach a boundary surface
(where the properties of the medium suddenly change), the waves undergo reflection.
A reflected wave:
STUDY THE HANDOUT!
NODES: the points at which there is no particle motion (= points of zero influence)
ANTINODES: the points where particles attain maximum displacement.
Because NODES impose a FIXED PATTERN on the wave motions, such waves are called
STANDING WAVES.
FIXED PATTERN: the points of zero influence (= nodes) are always at the same place.
The distance between the nodes is one-half of the wavelength.
STANDING WAVES OCCUR IF THE DISTANCE BETWEEN SOURCE AND
REFLECTOR IS ANY MULTIPLE OF THE DISTANCE BETWEEN NODES.
STANDING WAVE: Multiple reflections of a wave are self-reinforcing resulting in
resonance (see below).
RESONANCE is the phenomenon whereby a body, which has a natural tendency to vibrate at a
certain frequency, will build up vibrations with a comparatively large amplitude when it is set in
motion by another body which is vibrating at a similar frequency.
A RESONATOR is something which is set into vibrating by the action of another vibrator.
A resonator that contains air is an ACOUSTIC RESONATOR.
RESONATORS do not initiate sound energy. A sound is created elsewhere and the resonator
will vibrate in sympathy with it if the sound from the source is at or near the resonant
frequencies of the resonator.
RESONANCE CURVE: an indication of the relative amplitude of vibrations which would be
made by a source in response to different frequencies.
BANDWIDTH: The range of frequencies over which a resonator will respond effectively.
STUDY APPENDIX # 5
The VOCAL TRACT is an acoustic resonator (= air-filled chamber).