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Week3 outline

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Paul Faure

This outline summarizes major points covered in lecture. It is not intended to replace your own lecture notes. Reflection  Law of reflection – applies to both planar and spherical waves  Reverberant waves (echoes) – reflected sound waves  Reverberation time: time for intensity of reflected sound wave to reach -60 dB re: source intensity (i.e. time for energy in reverberant waves to damp down to one millionth of source energy) Reflections and interference  Reflected wave can be considered as a second sound source  Reflected waves can interact (interfere) with incident waves 1. Constructive interference – increase in amplitude of sound energy 2. Destructive interference – decrease in amplitude of sound energy  Phase relationship does not need to be exact for interference to occur  Interference can result in standing wave with nodes (zero amplitude) and anti-nodes (max amplitude) Standing wave fundamental frequency (ƒ ) 0  Fundamental frequency (ƒ ): lowest frequency that creates standing wave pattern 0  Second harmonic frequency – second lowest frequency of vibration (= 2·ƒ ) 0 Reflections and standing waves  Standing waves can occur when two waves of same frequency and amplitude travel in opposite directions (e.g. incident wave and reflected wave)  Reflections can produce standing waves  Resultant wave from the interaction of the incident wave and reflected wave is a standing wave that appears stationary  Distance between two successive nodes or anti-nodes in standing wave is ½·λ  Standing waves occur in fixed geometry (e.g. ear canal)  Confined waveform propagation to a particular geometry leads to reflections and resonance  Know which equation to use for calculating dB change (power, energy, intensity versus pressure) Sound waves reflecting in a tube  Fundamental frequency (ƒ ) i0 the lowest frequency (longest wavelength) that fits in tube  Distance between successive nodes or antinodes = λ/2 = length of tube  Wavelength (λ) of ƒ =02·L (where L = tube length)  Higher frequency standing waves with nodes at both ends are overtones (harmonics) o Integer multiples of ƒ described by: ƒ = c/2·L; ƒ = c/L; ƒ = 3·c/2·L; ƒ = 2·c/L 0 0 2 3 4 Standing wave and resonance  wave traveling along string is similar to geometry of standing wave in a tube  node: point of zero displacement in standing wave (closed end of tube at ƒ ) 0  antinode: point of maximum displacement (open end of tube at ƒ ) 0  standing wave in tube can occur when tube closed at both ends (nodes at both ends), closed at one end and open at the other, or open at both ends (antinodes at both ends)  tube close at one end and open at other is similar to anatomy of ear canal  tube length (L) determines ƒ ;0if you know tube geometry one can determine ƒ 0  ƒ = c/2·L tube closed /open at both ends 0  ƒ 0 c/4·L tube closed at one end and open at other end o for ear canal standing wave, harmonics can occur only at odd integer multiples because those frequencies satisfy geometry (node at one end and antinode at the other end)  Distance between two successive nodes or antinodes is L = λ/2 (half a wavelength).  Higher frequency standing waves with nodes at both ends are known as overtones or harmonics.  Harmonics occur at integer multiples of the fundamental frequency (ƒ ). R0member that ƒ depends0on the geometry of the tube (open ends, open and closed ends, closed ends).  For example, ƒ = 2ƒ = 2(c / (2L) ) = c / L in a tube with both ends open. 2 0 Psych 3A03 24 September 2012 Week 3 Dr. Paul A. Faure  Important Case: When one end is closed and the other is open, you must have a node at the closed and an anti-node at the open end. Therefore, only odd integer multiples of ƒ i0 possible. Diffraction  Bending of waves around objects (or after passing through slit), both 2D & 3D wave spreading  Interaction of object size and wavelength (λ)  Diffraction most efficient when acoustic wavelength (λ) >> object size  Small objects do not cast sound shadow, largest amount of diffraction Absorption  Impedance change at boundary between two media (e.g. air/object interface)  Impedance mismatch determines amount of sound energy penetration (=absorption)  When impedance difference is infinite, all incident sound energy will reflect; when not infinite, some energy will penetrate and be transmitted to new medium  Absorption inversely proportional to reflection Absorption coefficient (a)  Quantifies sound energy that penetrates or is absorbed by medium/obstacle  Equation: a = Ia i , where:  Ia= intensity of sound absorbed by mediu
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