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Home , Waveform

Simple and complex Simple motion • Back and forth oscillation between two positions or states. • Physical systems behave in exactly this way • tuning forks • pendula • springs • Time function of motion is a mathematically a sinusoid Tuning Forks

PERIOD PERIOD =10 MS FREQ =100 Hz Springs Pendula I The here is 1 cycle per second per second (Hz) I that slow would not cause a sensation of

Frequency and • Frequency: How many times per second the ear drum vibrates in and out, and is measured in Hz. • Amplitude: The extent to which the ear goes in and out, i.e. how far in and how far out, is the amplitude or Visualizingenergy of sound:vibration. Waveform

Eardrum

B A C

Cycle C

A (from rest) Distance PERIOD

Louis Goldstein (USC Linguistics) Ling 285: Lecture 3: Intro to September 1, 2015 4 / 21

Tuesday, January 21, 14 Period and amplitude in SHM • Period and amplitude are unrelated in SHM • Period • determined by the physical properties of the vibrating system: • length of pendulum bob • stiffness of spring • size, stiffness of tuning fork tine • Amplitude • depends on initial conditions: how the object was set into motion • how far from equilibrium position it it displaced • how hard it is pushed Complex • Very few of the in the world exhibit SHM. These are pure tones . • How do we characterize other patterns? (1) (f0)

1/period of repetition of complex pattern

(2) Fourier Analysis

Any pattern of vibration can be analyzed as the sum of SHMs each with its characteristic amplitude and frequency. Fundamental Frequency

f0 is perceived as pitch of the voice Each period corresponds to one vibration go the vocal folds Fourier Analysis • Any pattern of vibration can be analyzed as the sum of SHMs each with its characteristic amplitude and frequency. • For a periodic sound (with an observable fundamental frequency), simple harmonic () components always occur at integer multiples of the fundamental frequency, and are referred to as . • 2nd harmonic frequency = 2f0 3rd harmonic frequency = 3f0 …. • of harmonics may differ • Different vowels spoken on the same pitch (f0) • Spectrum shows relative amplitude of harmonics English Vowels file:///Users/artphon/Dropbox/Active/Classes/Ling 580 Web/Ges...

English Vowels

Click on vowels to listen. superimpose vowels Graphs show filter functions. Vertical grid lines are 1000 Hz apart. Vowels: different patterns of amplitude of harmonics "heed" "who'd"

"hid" "hood"

English Vowels English Vowels file:///Users/artphon/Dropbox/Active/Classes/Ling 580file:///Users/artphon/Dropbox/Active/Classes/Ling Web/Ges... 580 Web/Ges...

"hayed" "hoed" English Vowels English Vowels

Click on vowels to listen. superimposeClick vowels on vowels to listen. superimpose vowels Graphs show filter functions. GraphsVertical harmonic showgrid linesfilter arefunctions. 1000 amplitudes: Hz Vertical apart. grid lines are 1000 Hz apart. f0 are all the same "head" formants: high amplitude harmonics

AMPLITUDE 0 5000 0 5000 0 5000 "heed" "had" "heed" "who'd" "who'd" FREQUENCY (HZ) "hod" Return to Linguistics 120 Home Page

1 of 2 9/2/14 6:39 PM "hid" "hid" "hood" "hood"

"hayed" "hayed" "hoed" "hoed"

"head" "head"

"had" "had" "hod" "hod"

Return to Linguistics 120 Home Page Return to Linguistics 120 Home Page

1 of 2 1 of 2 9/2/14 6:39 PM 9/2/14 6:39 PM