3030 - Sine waves and complex sounds

Periodic vibration

pattern of vibration repeats regularly over time

Aperiodic vibration

No regular pattern of vibration

Properties of a sine wave

1. Starting phase

2. Amplitude

3. Frequency

Starting phase

Point in displacement cycle when object begins to vibrate

Instantaneous phase

Point in displacement cycle at time of measurement

Units: angle (degrees/radian)

Amplitude

height of the wave, related to displacement of particle

Peak amplitude

Peak-to-peak amplitude

Wavelength is the distance between two successive ________ or __________

condensations, rarefactions

0, 180, 360 degrees represents

equilibrium

0-360 degrees is a

complete cycle

90 and 270 represent

maximum displacement

Fourier Analysis

A mathematical procedure by which any signal can be separated into component sine waves at different frequencies. Combining these sine waves will reproduce the original signal.

Complex sound

combination of all puretones

Complex waveform

contains energy at a number of different frequencies, amplitudes, and phase relationships (e.g. speech)

Simple harmonic motion

contains energy at one frequency (e.g. pure tone)

in-phase waves

add together and results in a higher amplitude

out of phase waves

amplitude will not be as high as sounds that are in-phase

completely out of phase waves

if it is a pure tone, the waves will cancel one another out; it would be silent

spectrum

graph with frequency along the x-axis and amplitude along the y-axis

line spectrum

displays frequency content of periodic sounds

continuous spectrum

displays frequency content of aperiodic sounds

Line spectrum of a periodic complex sound

Continuous spectrum of an aperiodic complex sound

Line spectrum of a pure tone

Transient aperiodic sound (waveform and spectrum)

Continuous aperiodic sound (waveform and spectrum)

Perception

tone that reflects different in frequency

A fundamental frequency of 100 Hz has a first harmonic of 200 Hz. What is the fourth harmonic of the fundamental?

400 Hz

Waveform

graphical representation with a time domain

Spectrum

graphical representation with a frequency domain

Amplitude spectrum

amplitude as a function of frequency

phase spectrum

phase as a function of frequency

Line spectrum

graphical representation that indicates a discrete number of sinusoids

Continuous spectrum

graphical representation that contains all frequencies within certain limits

Phase spectrum

nth harmonic (if fundamental frequency is 100 Hz)

n*100 Hz

Octave

is a scale of frequency; DOUBLING of frequency in Hz

How many octaves spans from 100 to 800?

3 octaves

100-200 Hz

200-400 Hz

400-800 Hz

Sawtooth wave

sum of odd and even harmonics

-6 db/octave slope

Square wave

sum of odd harmonics

-6 db/octave slope

Triangular wave

sum of odd harmonics

-12 db/octave slope

Noise

aperiodic complex wave that has instantaneous amplitudes that vary in a RANDOM manner

White noise

noise consisting of all audible frequencies in equal amounts

Broad band noise

aperiodic complex wave that contains all frequencies within certain BROAD limits

Narrow band noise

aperiodic complex wave that contains alll frequencies within NARROW limits

All the frequencies contained within white noise have the same _______ intensity or pressure

average

Amplitude spectrum of white noise characteristics

Continuous and flat

Phase spectrum of noise characteristics

Random