Physics of sounds
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Physics of Sounds. Overview Properties of vibrating systems Free and forced vibrations Resonance and frequency response Sound waves in air Frequency, wavelength, and velocity of a sound wave Simple and complex sound waves Periodic and aperiodic sound waves

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Physics of sounds

Physics of Sounds

Overview

Properties of vibrating systems

Free and forced vibrations

Resonance and frequency response

Sound waves in air

Frequency, wavelength, and velocity of a sound wave

Simple and complex sound waves

Periodic and aperiodic sound waves

Fourier analysis and sound spectra

Sound pressure and intensity

The decibel (dB) scale

The acoustics of speech production

Speech spectrograms


Properties of vibrating systems
Properties of Vibrating Systems

Some terms

  • displacement: momentary distance from restpoint B

  • cycle: one complete oscillation

  • amplitude: maximum displacement, “average” displacement

  • frequency: number of cycles per second (hertz or Hz)

  • period: number of seconds per cycle

  • phase: portion of a cycle through which a waveform has advanced relative to some arbitrary reference point


Physics of sounds

What is the relation between

frequency (f) and period (T)?







Free vibration
Free vibration

  • As we have so far described them, the mass-spring system and the tuning fork representsystems 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.


Forced vibration
Forced vibration

  • Now assume that the mass-spring system is coupled to a continuous sinusoidal driving force (rather than to a rigid wall).

    How will it respond?


Resonance curve aka frequency response or transfer function or filter function
Resonance curve(aka: frequency response or transfer function or filter function)


Physics of sounds


Resonance
Resonance the initial amplitude of displacement.


Sound waves
Sound waves the initial amplitude of displacement.


Sound waves cont
Sound waves (cont.) the initial amplitude of displacement.


Frequency wavelength and velocity of sound waves
Frequency, wavelength, and the initial amplitude of displacement.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 (λ) of a simple waveform, what is its velocity (c)?


Simple vs complex waves
Simple vs. complex waves the initial amplitude of displacement.

  • So far we’ve 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.


Examples of complex waves sawtooth waves
Examples of complex waves: the initial amplitude of displacement.sawtooth waves


Examples of complex waves square waves
Examples of complex waves: the initial amplitude of displacement.square waves


Examples of complex waves vowel sounds
Examples of complex waves: the initial amplitude of displacement.vowel sounds


Periodic vs aperiodic waves
Periodic vs. aperiodic waves the initial amplitude of displacement.

  • So far all the waveforms we’ve considered (whether simple or complex) have been periodic—an interval of the waveform repeats itself endlessly.

  • Many waveforms are nonrepetitive, i.e., they are aperiodic.


Some examples of aperiodic waves
Some examples of aperiodic waves: the initial amplitude of displacement.


Physics of sounds


Fourier analysis
Fourier analysis amplitude, frequency, and phase.

  • Any waveform can be analyzed as the sum of a set of sine waves, each with a particular amplitude, frequency, and phase.


How to approximate a square wave
How to approximate a square wave amplitude, frequency, and phase.


From time domain to frequency domain
From time-domain amplitude, frequency, and phase.to frequency-domain

Frequency

Time


Periodic vs aperiodic waves cont
Periodic vs. aperiodic waves (cont.) amplitude, frequency, and phase.

  • 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.


Sound pressure and intensity
Sound pressure and intensity amplitude, frequency, and phase.

  • Sound 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/cm2

  • A 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.


Decibel scale
Decibel scale amplitude, frequency, and phase.


Acoustics of speech production
Acoustics of speech production amplitude, frequency, and phase.


Spectrogram
Spectrogram amplitude, frequency, and phase.