Chapter 4: Complex Vibration and Waveform Analysis

Question 1

components
frequency components
(partials in music)

Answer 1

an individual element of a complex system ( e.g., a sinusoidal component of a complex waveform or a component of an electric circuit)

the sinusoidal vibrations that make up a complex vibration.

Question 2

Fourier Theorem

Answer 2

any complex vibration is the sum of various sinusoidal motions of varying amplitude, frequency, and phase.

a theorem stating that any complex oscillatory (vibratory) motion is the sum of various sinusoidal motions of varying amplitude, frequency, and phase.

Question 3

fundamental period

Answer 3

(To) the duration of one cycle.

the amount of time it takes to complete one cycle of complex periodic vibration

Question 4

fundamental frequency

Answer 4

the lowest frequency of a vibrating system; the reciprocal of the fundamental period of a complex periodic wave.

(fo or f1) fo = 1/To

Question 5

complex vibration

Answer 5

the sum of two or more simple vibrations.

Question 6

aperiodic vibration

Answer 6

a vibration without a repeating pattern in time.

Question 7

periodic vibration

Answer 7

vibratory motion in which an object returns to the same point in space periodically (at equal periods of time) during the motion.

Question 8

waveform synthesis

Answer 8

the process of combining several individual sinusoidal motions into a complex waveform.

adding sine waves to form complex waveforms.

Question 9

harmonics

Answer 9

frequency components of a complex waveform that are whole-number multiples of its fundamental frequency.

(f2 is the first harmonic for this class)

Question 10

missing fundamental

Answer 10

when the greatest common factor of a group of harmonically related frequency components of a waveform is not present in the waveform, this waveform has a missing fundamental.

Question 11

periodicity

Answer 11

the concept that a periodic wave keeps repeating itself for an infinite amount of time.

Question 12

noise

Answer 12

a stochastic (random) sequence of events resulting from the combination of a very large (infinite) number of unrelated components.

Question 13

transient

Answer 13

a brief single event that ceases to exist after a very short time (door slam)

Question 14

complex inharmonic vibration

Answer 14

the sum of a finite number of components that does not repeat its pattern within a time period of observation.

Question 15

waveform analysis

(spectrum analysis)?

Answer 15

taking a complex waveform and breaking it down into individual components

Question 16

time domain

Answer 16

representation of a phenomenon as a function of time

Question 17

spectrum

Answer 17

a graphical representation of a complex waveform showing the waveform energy (amplitudes) of the individual components (y axis) arranged in order of frequency (x axis).

Question 18

spectrum components

Answer 18

individual components, displayed as lines perpendicular to the x axis, are called spectrum components (spectrum components, frequency components) Thus, the spectrum provides a graphical representation of the Fourier series of a complex vibratory motion.

Question 19

frequency domain

Answer 19

representation of a phenomenon as a function of frequency.

Question 20

line spectrum (discrete spectrum)

Answer 20

a spectrum that consists of one or more separate vertical lines.

Question 21

continuous spectrum

Answer 21

a spectrum in which the energy is spread across a rang of frequencies rather that at discrete sinusoidal components.

Question 22

white noise

Answer 22

a noise that consists of an infinite number of sinusoidal components having the same amplitude, but random phase, that spread evenly across a wide frequency range; a noise that has a spectrum density that is independent of frequency.

Question 23

amplitude spectrum

Answer 23

the distribution of the amplitudes of the sinusoidal components of a vector quantity as a function of frequency.

Question 24

power spectrum

Answer 24

a distribution of energy (power) as a function of frequency.

Question 25

phase spectrum | (did he say to skip this?)

Answer 25

a spectrum display that indicate the initial ( t=0) phase angle of all the spectral components as a function of frequency

Question 26

nodes

Answer 26

a point or line in space or along a vibrating element at which the magnitude displacement is zero for the mode of vibration. where the string is attach to guitar.

Question 27

antinodes

Answer 27

the place on vibrating system or in a sound field where the changes in a specific quality greatest

Question 28

mode

Answer 28

the specific vibration pattern of a vibrating system associated with each resonance frequency of the system

Question 29

octave

Answer 29

a relative unit of frequency in which one octave represents a doubling in frequency.

Question 30

rod

Answer 30

a rigid, one dimensional structure made of a material such as metal or wood, which has a small cross section in comparison to its length and is round.

Question 31

bar

Answer 31

a rigid, one dimensional structure made of a material such as metal or wood, which has a small cross section in comparison to its length and is square or rectangular.

Question 32

transverse vibrations

Answer 32

when vibration is along a rod or bars length

Question 33

torsional vibrations

Answer 33

when vibration is along a rod or bars axis.

Question 34

plate

Answer 34

a two-dimensional physical object in which the thickness of the object is much smaller than the length and width and it can vibrate without any structured support.

Question 35

radical mode

Answer 35

mode of vibration that runs across a plate or membrane.

Question 36

circular mode of vibration

Answer 36

mode of vibration that runs in a circular manner in a plate or membrane.

Question 37

chladni figures (patterns)

Answer 37

figures that illustrate the distribution of the various nodes of vibration of a plate.

Question 38

impedance

Answer 38

the opposition to the flow of energy through a system

Question 39

mechanical impedance

Answer 39

impedance of a mechanical system; depends on the mass, stiffness, and friction coefficient of the system.

Question 40

resistance(R)

Answer 40

the opposition of a system to movement; resistance is the result of internal and external friction.

Question 41

reactance (X)

Answer 41

the opposition of a system to change in its state by the system's ability to store energy and prevent its transfer to or from another system

Question 42

mass reactance (Xm)

Answer 42

the ability of a mass to store energy and prevent its transmission through a system.

Question 43

stiffness reactance (Xs)

Answer 43

the ability of the stiffness of a system to store energy and oppose its passage through a system.

Question 44

compliance (C)

Answer 44

the inverse of stiffness (K) that is C=1/K

Question 45

admittance (Y)

Answer 45

the ease with which a system can vibrate due to an applied force; the inverse of impedance

Question 46

conductance (G)

Answer 46

the ease with which energy travels through a frictional element in a system; the inverse of resistance.

Question 47

susceptance (B)

Answer 47

the ease with which energy travels through a mass or spring (stiffness) element in a system; the inverse (reciprocal) of reactance (X)

Question 48

mass susceptance (Bm)

Answer 48

the ease with which energy flows through a mass.

Question 49

stiffness susceptance (Bs)

Answer 49

the ease at which energy travels through a spring element.

Question 50

source and load (pg87)

Answer 50

to transfer the greatest possible amount of energy from one system to another, the impedance of both objects -the source and the load (receiver of energy)- should be equal.

Question 51

impedance matching

Answer 51

the practice of making the impedance of a load equal the impedance of a source of power in order to transfer as much energy as possible from the source to the load.

Question 52

membrane

Answer 52

a thin sheet-like material that is stretched and fixed along its edges to create stiffness. (ear drum)

Question 53

overtone

Answer 53

a harmonic other than the fundamental frequency

Question 54

cycle

Answer 54

one full repetition of a periodic motion

Question 55

elasticity

Answer 55

the property of matter that allows matter to recover its form (size and shape) after it has been distorted (expanded or compressed).