CHAPTER 4

COMPLEX STIMULI

Types of Sounds

• So far we’ve talked a lot about sine waves

= periodic

= energy at one frequency

• But, not all sounds are like that

Periodic/Aperiodic Sounds

• Periodic -- Repeating regular pattern with a constant period

• Aperiodic-- no consistent pattern repeated.

Simple/Complex Sounds

• Simple -- Having energy at only one frequency

• have a sinusoidal waveform

• Complex -- Having energy at more than one frequency

• may be periodic or aperiodic

A Complex Sound

Looking at a Waveform

• You may not be able to tell much about frequencies present in the sound

• Another way of displaying sound energy is more valuable:

AMPLITUDE SPECTRUM--display of amplitude (y-axis) as a function of frequency (x-axis)

Waveform and Spectra

Harmonic Series

• When energy is present at multiples of some frequency

• Lowest frequency = FUNDAMENTAL FREQ

• Multiples of fundamental = HARMONICS

Transients

• Brief acoustic signals or “clicks”

Envelope--The Outline of the Waveform

One Interesting Envelope

• Amplitude Modulated (AM) Tone

• Tone whose energy is varied is called CARRIER

• You can also talk about the FREQUENCY OF MODULATION--How many times a second does amplitude cycle up and down and back again.

AM Tone: Waveform & Spectrum

Spectrum of an AM tone:

• Has Energy at 3 frequencies:

1. at the frequency of the CARRIER

2. at Carrier freq PLUS Modulation freq.

3. at Carrier freq MINUS Modulation freq.

Square Wave

• Similar to transient spectrum

• Fundamental frequency at reciprocal of period

• Can also be a modulator

• All harmonics are at a 90 degrees phase angle

Square Wave

Frequency Modulation (FM)

• Waveform shape changes like a spring

• Looking at TIME domain

Not Everything is so Regular

• Aperiodic sounds vary randomly

• = NOISE

• Waveforms may look wild

• EXAMPLE:

• White Gaussian Noise = equal energy at all frequencies

Gaussian Noise Waveform

Amp. Spectra: White & Pink Noise

Levels of a Band of Noise

• Overall Level = SPL (Total Power)

• Spectrum Level = Ls level at one frequency

• Bandwidth Level = Lbw freq width (in dB)

Lbw = 10 log (bandwidth (in Hz)/ 1 Hz)

• SPL = Ls + Lbw

Overall Level Equals Spectrum Level Plus Bandwidth Level

Lbw

Ls

SPL

Example of Deriving Ls

• Given SPL = 80 dB

• and Bandwidth = 1000 Hz

• Lbw = 10 log (1000Hz / 1Hz) = 30 dB

• SPL = Ls + Lbw

• 80 dB = Ls + 30 dB

• 50 dB = Ls

Combining Sound Sources

• Adding additional (identical) sources produces summing of intensities

• e.g., adding a second speaker playing the same signal

• If one produced 60 dB IL, what would two produce?

Working out the example:

• one produces 60 dB IL

• 60 = 10 log (Im/10-16 W/cm2)

• 6 = log (Im/10-16 W/cm2)

• 106 = Im/ 10-16 W/cm2

• 10 6 + (-16) = Im

• 10 -10 = Im

• 2 x 10 -10 = Intensity of two sources

• New IL = 10 log (2 x 10 -10 /10-16 W/cm2)

Working it out (cont’d)

• New IL = 10 log (2 x 10 -10 - (-16) )

• = 10 log (2 x 10 6)

• = 10 (6.3010)

• = 63 dB IL

How About a SHORT CUT?

• New IL = IL of OLD # + 10 log (new #/old #)

• = 60 + 10 log (2/1)

• = 60 + 3

• = 63 dB IL