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# SPAA 260 Week 5-6 SPAA 260

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This 8 page Class Notes was uploaded by Molly O'Keefe on Monday February 22, 2016. The Class Notes belongs to SPAA 260 at Ball State University taught by Dr. Shaffer in Spring 2016. Since its upload, it has received 22 views. For similar materials see SPAA 260 in Linguistics and Speech Pathology at Ball State University.

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Date Created: 02/22/16

Force 02/10/2016 ▯ Force is a push or pull ▯ Force/Area = Pressure ▯ Displacing gas molecules have force ▯ Sound is a pressure wave ▯ Pressure changes over time ▯ Wavelength Distance traveled in one cycle of the wave Given symbol: λ λ=c/f where c = speed of sound, f = frequency ▯ Speed of Sound The velocity of wave travel c=λf Where c = speed of sound, λ = wavelength, and f = frequency ▯ Speed of sound in air 340 meters/second o Assumes air temperature if 15 degrees C o Assumes air pressure of 1atm (atmospheric pressure at sea level) ▯ Factors affecting speed of sound Other factors that affect speech of sound include o Density (ρ) and stiffness (K) of the medium through which sound travel o And the air tempersure K c ρ o ▯ Density and Stiffness Effects In most cases, more dense media (steel) transmit sound faster than less dense media (air) this does not seem to fit with the equation Dense media are generally stiffer than less dense media The higher speed of sound is not due to the higher density but to the greater stiffness of dense materials ▯ Speed of Sound One important property of the speed of sound is that is does not depend on the sound frequency Regardless of frequency, waves will arrive at the listener at the same time ▯ Temperature Effects It has an effect on the speed of sound As temperature increases, density of air decreases and stiffness decreases Speech of sound in air can be determined easily given the temperature c [m/s] (331.45(0.6T)) o air o T is temperature in degreesC o 331.45 m/s is the speed of sound in air, at a pressure of 1 atm and a temperature of 0 degrees C (standard pressure and temperature) ▯ Sonic Boom When the speed of sound is exceeded an audible and sometimes visible pressure wave is created called a shock wave ▯ Wavelength The frequency range of hearing for mammals is determined partly by the side of their head Hearing tends to be less sensitive for frequencies of sound with wavelengths below the width of the species head o Solving for frequency from wavelength/ Human skull width is approx. 17cm Let’s calculate the frequency that corresponds to a wavelength of 17cm (convert to meters first) c=λf ^ Will need to rearrange equation f=c/λ f=? c=340 λ=17cm which is .17meters f=340/.17 f=2000Hz ▯ Solving to find the width of the elephant (blue line) head c=λf To find λ… o λ=c/f o 340ms/1000s=λ o .340m=λ o 34cm=λ o to convert to inches….. o 34cm/2.54cm=λ o 26.77 inches=λ ▯ Cues for localizing sound Interaural time difference Interaural intensity difference Interaural spectral difference ▯ Interaural time difference The wider your head the longer it takes sound to get to the other side But ITD is also a type of phase detection that can be ambiguous at high frequencies Time it takes for sound to hit your ears ▯ Interaural intensity difference Your head blocks the sound making it less intense on the opposite side - "head shadow" ▯ Interaural spectral differences Different frequencies are attenuated to different intensities depending on the location of the sound and how much the head shadows each frequency Head more effectively blocks high frequencies than low frequencies, creating better spectral differences cues at high frequencies As head size decreases from large to small, the frequencies blocked become higher The smaller the head, the higher frequency the hearing range must be to take advantage of spectral difference cues ▯ Functional head size-the time it take for sound to travel from one side to the opposite ▯ Human range of hearing- Humans hear in the frequency range of 20-20,000Hz o Infrasound-sounds below the range of human hearing o Ultrasound-sounds above the range of human hearing ▯ Sometimes animals head size does not match their range of hearing due to the anatomical specializations of the out, middle, and inner ear ▯ Mass and stiffness affect the frequency of vibration Objects with more mass (and less stiffness) tend to vibrate better at lower frequencies Objects with less mass (and more stiffness) tend to vibrate better at higher frequencies ▯ Wavelengths of human hearing Calculate wavelengths of the lowest and highest frequencies that humans hear Wavelengths 20 & 20,000 c/f=lambda 340/20=17 340/20,000=0.017 ▯ Wavelength from period Period of a sound is 1 ms. Calculate the wavelength of the sound. o f=1/.001= 1,000s o 340/1,000=0.34m ▯ Complex vibrations can be aperiodic The vibration is random with no repeating cycle This type of vibration is called noise This vibration has a clearly repeating pattern, a clear cycle o This is periodic ▯ Periodicity: An acoustic property of having recurrent periods, cycles ▯ Adding sine waves Complex periodic sounds arise from object vibrating in multiple modes All the frequencies add together o They would sum together to produce this complex sound ▯ What are harmonics? If a complex wave is periodic, then the individual sine wave frequencies are referred to as harmonics Harmonics are whole number multiples of the lowest frequency (aka the fundamental frequency) ▯ Fundamental period of a complex wave The fundamental period (T ) is the duration of one cycle of a o complex wave Here T = 0.5 s o The fundamental frequency (f ) is tho inverse of T . o o f =o1/T o Here, f o 2 Hz. In this example the fundamental frequency is fo= 4 Hz The harmonic components of the complex wave are 4 Hz, 8 Hz, 16 Hz ▯ Harmonic Numbering The fundamental frequency f and theofirst harmonic f are the same1 The second harmonic, f is 2 2 f o The third harmonic, f is 3 x f 3 o Etcetera…. ▯ When harmonics add the phase can make a big difference in the shape (and sound) of the complex wave ▯ Frourier A French mathematician who first developed the mathematical proofs that a complex periodic wave is a sum of sine wave components Fourier’s Theore: Any complex periodic wave can be broken down into a series of sinusoidal waves that are harmonics of the fundamental frequency, each having specific amplitude and phase characteristics ▯ Famous complex waves are known by their harmonics ▯ Fourier’s Analysis Mathematical algorithm that analyzes the frequencies, amplitudes and phases of any sound o Aka spectral analysis The computer process is called Fast Fourier Transform ▯ Time domain vs Frequency domain A time waveform displays vibration in the time domain, showing the displacement or pressure of a vibration across time A spectrum is used to show the frequency domain of the vibration o Two types of spectra o Amplitude spectrum: Shows amplitudes of each frequency in the complex wave o Phase Spectrum: Shows phase of each frequency The y axis for the time waveform is magnitude of displacement or pressure The y axis for the spectrum is the amplitude of the sinusoidal components A complex periodic vibration with three harmonics has a spectrum with three vertical lines ▯ Plotting a spectrum ▯ Calculate the frequencies of each harmonic 1. 2 cycles 2. 4 cycles 3. 8 cycles ▯ Converting to frequency 1. 20 Hz 2. 40 Hz 3. 80 Hz ▯ ▯ ▯

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