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 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 What is the relation between frequency f and period T How do these differ How do these differ How do these differ Another case of harmonic motion tuning fork Damping Free vibration As 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 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 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 Resonance Sound waves Sound waves cont 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 Simple vs complex waves 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 square waves Examples of complex waves vowel sounds Periodic vs aperiodic waves 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 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 Fourier analysis 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 From time domain to frequency domain Time Frequency 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 Sound pressure and intensity 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 Acoustics of speech production Spectrogram
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