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Sound Transmission- Propagation, Absorption, and Attenuation.docx

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Paul Faure

September 17 , 2013 Psych 3A03: Audition Sound Transmission: Propagation, Absorption, and Attenuation Vibration damping - The duration of the continued oscillations or vibrations is directly proportional to the magnitude of input force and inversely proportional to amount of damping - Low damping: vibrations continue for long time (e.g. tuning fork) - High damping: vibrations continue for only a brief time The Damping Factor - In any damped system, the ratio of amplitudes (A /A ) for1two2consecutive cycles of a vibration is constant - xt(t) = X0e - Any function with a constant ratio can be expressed logarithmically, e.g. natural log (ln) or e - Magnitude of damping is described by the damping factor - d f ln(A /1 ) 2 Damping factor of zero indicates that there is no attenuation - Types of Damped Systems 1. Unda,ped (lolssless) system: theoretical concept; no energy transfer (i.e. there is no friction present); d =0 f 2. Underdamped system: vibrations continue for long time; slow steady energy loss from system (e.g. tuning fork) 3. Overdamped system: does not vibrate or oscillate; so much friction that energy is slowly drained from system 4. Critically damped system: does not oscillate; energy decays to zero as quickly as possible without overshooting (e.g. car shock absorbers) Underdamped Vibrations - Vibrations continue to oscillate for some time Overdamped Vibrations - Quickly returns to zero Critically Damped Vibrations - Slowly return to zero There is No Perpetual Motion - When energy is imparted into a system with a low damping (i.e. the system is underdamped), it will vibrate freely at its natural or resonant frequency (resonate for the longest period of time as it is the frequency the object is naturally tuned to) - An object’s resonant frequency is described by √ ⁄ , where  S = stiffness of object  M = mass of object - Vibrations do not continue forever Resonant Frequency (f ) rf a System - Sine wave generator in which we can change the frequency (the period of the vibration) is attached by a probe in order to measure the frequency output - Can also measure amplitude input and amplitude output - Driving frequency: frequency of the input - Constant amplitude of vibration - Objects vibrating freely do so at their natural or resonant frequency - Energy transfer is most efficient when the input (driving) force frequency is close to an object’s resonance frequency of vibration - In other words, when the driving frequency approaches an object’s resonant frequency the object will vibrate or resonate at maximum amplitude - We can also measure the amplitude out by adjusting the input amplitude to maintain the same output amplitude (A input output= 1) – complementary to the first experiment Acoustic Impedance (Z) - Impedance (Z) is the total opposition to motion - Units of impedance: Ohms (Ω) - The impedance of a system ahs 2 components: 1. Resistance (R) (energy dissipating component) 2. Reactance (X) (energy storing component) - The acoustical impedance of a system is the complex sum of the resistance ® and the reactance (X) components of a system  √ , where  R = resistance  X = mass reactance
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