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Physics of SoundsOverview
Properties of vibrating systemsFree and forced
vibrationsResonance and frequency responseSound waves in
airFrequency, wavelength, and velocity of a sound waveSimple and
complex sound wavesPeriodic and aperiodic sound wavesFourier
analysis and sound spectraSound pressure and intensityThe decibel
(dB) scaleThe acoustics of speech productionSpeech spectrograms
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Properties of Vibrating SystemsSome terms displacement:
momentary distance from restpoint Bcycle: one complete
oscillationamplitude: maximum displacement, average
displacementfrequency: number of cycles per second (hertz or
Hz)period: number of seconds per cyclephase: portion of a cycle
through which a waveform has advanced relative to some arbitrary
reference point
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What is the relation between frequency (f) and period (T)?
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How do these differ?
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How do these differ?
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How do these differ?
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Another case of harmonic motion:tuning fork
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Damping
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Free vibrationAs we have so far described them, the mass-spring
system and the tuning fork represent systems in free vibration. An
initial external force is applied, and then the system is allowed
to vibrate freely in the absence of any additional external force.
It will vibrate at its natural or resonance frequency.
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Forced vibrationNow assume that the mass-spring system is
coupled to a continuous sinusoidal driving force (rather than to a
rigid wall).
How will it respond?
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Resonance curve(aka: frequency response or transfer function or
filter function)
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In free vibration, the response amplitude depends only on the
initial amplitude of displacement.
In forced vibration, the response amplitude depends on both the
amplitude and the frequency of the driving force.
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Resonance
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Sound waves
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Sound waves (cont.)
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Frequency, wavelength, and velocity of sound waves
Wavelength: the spatial extent of one cycle of a simple
waveform. (Compare this to period).If we know the frequency (f) and
the wavelength () of a simple waveform, what is its velocity
(c)?
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Simple vs. complex wavesSo far weve considered only sine waves
(aka: sinusoidal waves, harmonic waves, simple waves, and, in the
case of sound, pure tones).However, most waves are not sinusoidal.
If they are not, they are referred to as complex waves.
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Examples of complex waves:sawtooth waves
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Examples of complex waves:square waves
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Examples of complex waves:vowel sounds
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Periodic vs. aperiodic wavesSo far all the waveforms weve
considered (whether simple or complex) have been periodican
interval of the waveform repeats itself endlessly.Many waveforms
are nonrepetitive, i.e., they are aperiodic.
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Some examples of aperiodic waves:
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A sine wave can be described exactly by specifying its
amplitude, frequency, and phase.
How can one describe a complex wave in a similarly exact
way?
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Fourier analysis
Any waveform can be analyzed as the sum of a set of sine waves,
each with a particular amplitude, frequency, and phase.
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How to approximate a square wave
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From time-domain to frequency-domainTimeFrequency
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Periodic vs. aperiodic waves (cont.)Periodic waves consist of a
set of sinusoids (harmonics, partials) spaced only at integer
multiples of some lowest frequency (called the fundamental
frequency, or f0).
Aperiodic waves fail to meet this condition, typically having
continuous spectra.
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Sound pressure and intensitySound pressure (p) = force per
square centimeter(dynes/cm2)Intensity (I) = power per square
centimeter(Watts/cm2)
I = kp2
Smallest audible sound= 2 x 10-4 dynes/cm2= 10-16 Watts/cm2A
problem: Between a just audible sound and a sound at the pain
threshold, sound pressures vary by a ratio of 1:10,000,000, and
intensities vary by a ratio of 1: 100,000,000,000,000! More
convenient to use scales based on logarithms.
Decibels (dBSPL,IL) = 20 log (p1/p0)= 10 log (I1/I0)where p1 is
the sound pressure and I1 is the intensity of the sound of
interest, and p0 and I0 are the sound pressure and intensity of a
just audible sound.
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Decibel scale
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Acoustics of speech production
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Spectrogram