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. 1. FREQUENCY (see above) TEMPORAL DIMENSIONS OF WAVES 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) (b) PERIODIC: the pattern of vibration repeats itself 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 PITCH (concrete, physical, (perceptual, subjective) measurable) AMPLITUDE LOUDNESS (concrete, physical, (perceptual, subjective) measurable) 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) Wavelength depends on two factors: a. frequency of vibration -------------- MEASURING WAVELENGTH (λ) high frequency sounds occupy less space per cycle; they have a shorter wavelength than low frequency sounds. b. 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):
λ = c f If Fo is 200 Hz (woman) or 100 Hz (man) c 344m/s λ = = = 1.75 m f 200 Hz c 344m/s λ = = = 3.4 m f 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).