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Paul Faure

September 25 , 2013 Psych 3A03: Audition Resonators Wavelength of Standing Wave - Distance between two successive nodes or antinodes is L = λ/2 - Higher frequency standing waves with nodes at both ends also exist. These are the overtones or harmonics, and occur at integer multiples of the funfamental frequency  Fundamental: L = λ/2  2 harmonic: L = λ rd  3 harmonic: L = 3λ/2  4 harmonic: L = 2λ E.g. Fundamental Frequency and Harmonic - How many cycles you can fit in to satisrd the geometry - Ex.: fundamental frequency fits 1.5 3 harmonics into half a wavelength Wavelength of Standing Waves - Fundamental frequency: the lowest frequency (longest λ) equal to the distance between two successive nodes Standing Waves in a Tube - Tube dimensions and sound wavelength determine position of standing wave nodes and antinodes - Nodes always located at closed end of tube - Antibodes always located at open end of tube - For an open tube and a tube closed at both ends, the distance between successive nodes and antinodes occurs at integer multiples of the fundamental frequency 0 - F = c/2L - Nodes (no vibration) at closed end; - Antinodes (maximum vibration) at open end Ear Canal: A Tube Open at One End - For a tube open at one end and closed at the other end, the fundamental standing wave pattern occurs at a frequency equal to 4x the length of the tube - ¼ of the wavelength, so fundamental frequency is 4 times the length of that 0ube - f = c/4L Diffraction - Diffraction is the bending of waves around objects or scattering of waves after passing through a slit or gap - It is due to any wave’s ability to spread in circles or spheres in 2D or 3D space - Interaction of the size of the obstacle (size of the slit) relative to the size of the wave  More diffraction when the slit is smaller  As the opening gets much larger the sound just passes through and does not get bent as much  Not due to a change of speed (that is refraction!) - Low frequency sounds are much larger wavelengths then the obstacles they are encountering - High frequencies do not diffract around as easily - Very small objects cast no shadow, they do not register with the wave - Sound shadow: bending and reflection (zone of pressure decrement behind to object) - Relative to the wavelength of the sound - Ex.: locating sound is space due to the sound shadow that your head casts with passing waves the amount of diffraction that occurs depends on the size of the obstacle relative to the wavelength of sound that impinges upon the obstacle - Diffraction is most efficient when sound λ us much larger than the size of the obstacle Absorption - When sound waves encounter an obstacle or boundary they experience an impedance change - Impedance mismatch between two boundaries determines the degree of sound penetration - When impendence mismatch is infinite (theoretical construct), there is no penetration and the intensity of the reflected wave equals the intensity of the incident wave – all wave will be reflected - When impendence mismatch is not infinite, some energy will penetrate and be transmitted in the new medium, thus the reflected wave intensity will not equal the intensity of the incident wave - The amount of sound energy penetration defines the degree of sound absorption by the medium - Absorption coefficient: describes the magnitude of sound absorption - Absorption quantification is very simple and intuitive - The magnitude of absorption, expressed as the absorption coefficient (a), is the proportion of sound energy in an incident wave that penetrates a medium - Absorption coefficient (a) is the ratio of sound energy absorbed to sound energy emitted in incident wave - a = a /i, where:  I = sound energy (intensity) absorbed by medium a  i = sound energy of incident wave - Absorption is inversely proportional to reflection - Some of this energy is absorbed or held and not transformed to the next medium due to the compliance of the other medium Refraction - Sound energy that encounters an obstacle will be absorbed and transmitted in the new medium - If two media differ in the Z c then the velocity of sound propagation (c) will also differ - A change in sound velocity results in a change of direction of propagation, and a bending of the sound wave will occur - Refraction is the bending of sound waves (a change in the direction of sound- wave propagation) due to a change in speed of propagation at a boundary interface Refraction: Sound Waves Change Direction - If the speed of sound in medium 1 < medium 2, t
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