Harmonics and OvertonesWaveforms / Wave Interaction

Phase Concepts / Comb FilteringBeat Frequencies / Noise

AUD202Audio and Acoustics Theory

Last Week >

Frequency and Dynamic Ranges of Hearing

Frequency / Wavelength / Period / Speed

Upcoming Assessments

Week 8 - NIHL Report

Week 11 - Sound Observations Report

Week 13 - Exam

Units of Measurement

= velocity of sound (in metres per second)

f

v = wavelength (in metres)

= frequency in Hertz (Hertz is cycles per second)

= period of one cycle (in seconds)

HARMONICS & OVERTONES

Harmonics are integer multiples of the

fundamental frequency.

Harmonics

For example, if the fundamental frequency is 200Hz, the harmonics would be:

200Hz400Hz 600Hz 800Hz

1000Hz

Fundamental frequency2nd harmonic3rd harmonic4th harmonic5th harmonic

An overtone is any frequency higher than the fundamental frequency of a sound..

SIMPLE WAVEFORMS

Fundamental frequency only, no harmonics

Sine Wave

Odd and even harmonics at inverse amplitudes

Sawtooth Wave

Odd harmonics at inverse amplitudes

Square Wave

Odd harmonics at inverse squared amplitudes

Triangle Wave

Making a sawtooth from a sine wave

A sawtooth wave's sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency

Simple Harmonic Motion

Constant frequency without regard to amplitude

Simple Harmonic Motion

PHASE

Phase Concepts

The word ‘Phase’ is used to describe a specific location in a cycle of a periodic (repeating) wave

“In phase”, “out of phase” and “completely out of phase” are terms used to describe relative positions of a wave cycle

Phase Concepts

Phase Angles

Wave Interaction

Two sine waves with the same amplitude and frequency can add

either destructively or constructively depending on their relative phase

Two sine waves travelling in oppositedirections can create a standing wave

Beat Frequencies

Beat Frequencies

When two sound waves of different (but close) frequencies are played together, the alternating constructive and destructive interference causes

an oscillation of the resulting waveform

frequency 1 – frequency 2 = Beat frequency 

502 Hz - 500 Hz = 2 beats per second

COMB FILTERING

Comb filtering is caused by a wave combining with a delayed version

of itself

Comb Filtering

A wave delayed by 180 degrees (half a

wavelength) results in the fundamental frequency of cancellation.

Frequencies delayed by 1.5x, 2.5x, 3.5x the wavelength will cancel, while whole number multiples (1, 2, 3 etc) will reinforce.

Comb Filtering

A wave delayed by half a wavelength results in the fundamental frequency of cancellation.

Single signal, no comb filter issues

1ms delayed version of the signal added

Comb Filtering

Common causes of comb filtering:

1.Two microphones at different distances from the same source.

2.Reflective nearby surface causing a reflected sound to arrive at the microphone slightly after the direct sound.

3.Two identical sounds in a DAW with a 1 to 10ms delay

WHITE NOISE & PINK NOISE

Noise

White noise: Equal energy per frequency

Pink noise: Equal energy per octave

Pink noise is simply White noise with a ‘pinking filter’ added (-3dB/octave roll off)

Speed Writing Exercise

List anything that might cause NIHL

List occupations where NIHL might be a problem

List ways to avoid NIHL

Next Week >

Sound EnvelopesInstrument Acoustics