CDS 389 - Exam 3 - Complex Waves and Resonance+ Filtering

Without resonance, we would only be able to vary

Amplitude (intensity), Frequency (pitch), Duration

Periodic Waves

Periodic waves have a repeatable pattern to them

Text definition: A periodic wave repeats itself atregular intervals over time

Aperiodic Waves

have an absence of periodicity

What does a periodic wave sounds like

melodic like a pure tone, a tuningfork, or a vowel

What does an aperodic wave sound like

like noise, such as, thump on a table, constant, or wind noise

A complex wave can be characterized as

any sound wave that is not sinusoidal

a complex wave is theresult of

adding together two or moresimple sinusoidal waves.

Waves in a complex wave can differ in

Amplitude, Frequency, Phase

Two identical waves that are 180 degrees out of phase will have what kind of output?

will cancel one another outand we hear nothing

what happens when they're notidentical waves or when they're not 180degrees out of phase?

They combine to form complex waves

Fourier Theorem

The degree of complexity of a complex sound wave depends on the specific dimensional values (amplitude, frequency, and phase) of th sinusoidal components.

Types of periodic waves

Sinusoidal, Complex

A sinusoidal wave is a wave that results

from simple harmonic motion and that comes from a mathematical relation that contains a sine function

A Complex Periodic Wave

is a periodicwave that is not sinusoidal

According to Fourier, any complex periodicwave consists of

some number of simplesinusoids that are summed

The sinusoidal components cannot beselected randomly if

if the resultant wave isto be periodic

Rather than being randomly selected, theymust satisfy a simple mathematicrelationship called a

harmonic relation

Harmonic Relation means

the frequencies of all of the sinusoids that compose the series must be integer (whole number) multiples of the lowest frequency component in the series.

Harmonic Series

When a harmonic relationexists among frequency components, theseries of frequencies

All of the sinusoids in the harmonic seriesare called

harmonics

We number the harmonics consecutively from

lowest to highest

the lowest harmonic

fundamental frequency, first harmonic (f sub 0)

sawtooth waves

spectrogram of the wave looks like a sawblade.

Consists of an infinite number of sinusoid components, Is periodic, Is complex, Resembles the waveform produced by vocal fold vibration, Are comprised of all of the odd and even whole number multiples of the fundamental frequency

complex wave similiarities

harmonics = partials = overtones

If a complex wave is periodic

the sinusoida lcomponents must be integer multiples of the fundamental frequency

In a complex wave that is not a sawtooth wave, the components cannot be ____________, but must be ____________ ______________

random, integer multiples

A sound wave is created as a result of a

vibrating object

The vibrating object is

the source of the disturbance which moves through the medium

Examples of sound sources

Vocal folds, String of an instrument (and soundboard), Vibrating tines of a tuning fork, Vibrating diaphragm of a speaker

Any object which vibrates

will create a sound

The frequency or frequencies at which an object tends to vibrate with when disturbed is known as the

natural frequency of the object

If the amplitude of the vibrations are largeenough and if natural frequency is withinthe human frequency range, then thevibrating object will

produce sound waves which are audible

The quality or timbre of the sound producedby a vibrating object is dependent upon

the natural frequencies of the sound waves produced by the objects

Some objects tend to vibrate at a single frequency and they are often said to produce a

pure tone

Examples of pure tone producers

flute, tuning fork, more

Other objects vibrate and produce more complex waves with a set of frequencies which have a whole number mathematical relationship between them; these are said to produce

a rich sound

a person or thing putsenergy into the instrument by

direct contact with it

This input of energy disturbs the particles and forces the object into

vibrational motion at its natural frequency

The tendency of one object to force another adjoining or interconnected object into vibrational motion is referred to as a

forced vibration

an increase in the amplitude

increase in loudness of sound

standing wave pattern

a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source

Because the observed wave pattern ischaracterized by points which appear to bestanding still, the pattern is often called

a standing wave pattern

As we add more and more of the odd integer harmonics, the waveform becomes

more square

summed all of the whole integers (both odd and even) and the resultant wave is a

triangular wave

When we change the starting phase of eachof the components

the resultant wave also changes.

waveforms and spectrums

function of amplitude, over time

amplitude spectrum

instantaneous magnitudes (amplitude as a function oftime), the amplitude spectrum show amplitude as a function of frequency

Notice that the sawtooth wave shows energy at all of the ___ and ___ harmonics

even, odd

The square wave, however, shows energy only at the ___ harmonics

odd

The dotted line that connects the tops of each of the peaks of frequency energy is called an

envelope (sometimes shown with the lines which represent the spectral energy and sometimes just the envelope alone is shown)

Notice that the energy decreases at a steady rate at

consecutively higher harmonics

The rate of decrease is ______ for an amplitude spectrum

6 dB per octave

octave

a doubling or halving of frequency

The amplitude spectra shown earlier are called

line spectra (only energy present where there is a vertical line, there is NO ENERGY present between the lines)

If we had an aperiodic complex waveform, the resultant spectrum would be a

continuous spectrum

Aperiodic complex waves have energy at

all frequencies (would be a solid block of lines)

With continuous spectra, we're showing that energy is present at __________ ____________ between specified boundaries

all frequencies

The boundaries are called the ______ frequency limit and the _______ frequency limit

upper, lower

The phase spectrum defines the starting phase as a

function of frequency

Signal-to-Noise-Ratio (SNR)

the signal (typically the individual speaking to us) and it's relationship to any background noise (other speakers, or any competing sounds that are NOT the signal we want to hear)

We calculate the SNR by

subtracting the dBSPL of the noise source(s) from the dB SPL of the signal of interest.

A negative SNR

makes hearing difficult

allsystems have a natural resonantfrequency (f sub c)

also called the characteristic frequency or simply the natural frequency

Tuning fork natural frequency is determined by

mass and frequency

Over time, the amplitude of the vibration will

diminish

The intensity is determined by the _______ with which the fork is struck

force

Helmholtz resonators

any resonating cavity that is closed on one end and open on the other (open bottle, ear canal, vocal tract, trumpet)

filter curves

show the amplitude of vibration as a function of frequency for a vibrating system

the characteristic frequency (or center frequency) of a vibrating system is the point on the curve where

the greatest displacement (amplitude) occurs

As we move away from the characteristic frequency,

the system responds less and less well (there is decreased amplitude of vibration).

as we move up or down fromthe natural frequency (characteristic frequency) the system vibrates with less and less amplitude.

frequency-selective system

inner ear is also a frequency selective system with overlapping filters called

auditory filters

The entire cochlea is lined with "haircells" which are

nerve endings

The cochlea is arranged tonotopically with ____ frequencies at the basal end of the cochlea and ____ frequencies at the apical end of the cochlea

high, low

These nerve endings each have a characteristic frequency to which they respond best

The result is an auditory filtering effect

___________ tuned filters will always"ring" longer (like a tuning fork )than a ___________ tuned system

narrowly, broadly

Broadly tuned systems are always associated with _________ resistance than narrowly tuned systems are

higher

If we have a sound that has equal inputs across a given frequency spectrum and apply a filter to the system,

only the sounds that fit within the filter will pass through

band pass filter

it means that it stops everything above and below it's upper and lower limits and shapes the frequency response

Parameters of Filters

1. Filters have a natural frequency (or center frequency) denoted by the peak of the curve

2. They also have an upper cutoff frequency (f sub u) above which no sound will pass

3. They have a lower cutoff frequency(f sub L) below which no sound will pass

4. Bandpass filters have a bandwidth (Δf)

5. They have an attenuation rate,which is also called the rejection rate

When we look at the filter, it appears that everything above the center frequency is

attenuated by some amount

the 3 dB-downpoint (or the half-power point)

A convention has been developed to determine the frequency at which filtering is said to commence. The upper cutoff frequency (That means that it's the point where the power is 3 dB less (half as much) as the power output at the peak (f sub c))

Bandwidth

Δf = f sub u - f sub L

only frequencies within the passband will be

allowed to pass through the filter

Attenuation Rate (in dB/Octave)

a.k.a Attenuation rate, Filter slope, Roll-off rate, Rejection rate

The attenuation rate

is described in decibels per octave

Low pass filters

IT allows frequencies below a certain point to pass through while blocking all frequencies above that point.Just like a bandpass filter which acts like the "ultimate doorman" a low pass filter acts like the ultimate doorman by keeping all of the high frequencies out.

Low pass filters have two defining parameters

F sub u, Attenuation rate

high pass filters

only allows frequencies above a certain point to pass through. It's like a low pass filter in reverse

band-reject filter

"notch filters" with hearing aids to stop feedback problems

When dealing with hearing aids, they were called a high cut (low pass) and a low cut (high pass)

used those two parameters to shape the frequency response to the person's hearing loss