Influence of Gas Flow on Sound Attenuation due to a Resonator in a Duct

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  • 共鳴型消音器の音響特性におよぼす気流の影響
  • キョウメイガタ ショウオンキ ノ オンキョウ トクセイ ニ オヨボス キリュウ ノ エイキョウ

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The influence of gas flow on the attenuation of sound in a duct with a muffler has been noticed in these thirty years. This problem, however, has been left unsolved to this day. This paper presents an analysis and physical interpretation of the influence of gas flow on the sound attenuation due to a resonator in a duct. Theoretical values of the sound attenuation with flow were compared with measured values over a range of midstream-flow speeds U_0≦50 m/sec, and been shown in close agreement. The theory of resonators had been analyzed by several authors. As well known, the kinetic energy of the motion can be expressed as Eq. 12 in terms of the mass of the aerial piston m and its velocity ξ. If we assume that gas flow carries away the kinetic energy of the additional mass of the aperture, the energy loss of a resonator in time δt can be expressed as Eq. 20, where U^^^- is the mean flow-velocity near the aperture, ρ is the mean density of air and a is the radius of the aperture. From Eqs. 20-26, we get the equevalent resistance density R_u=(4/3π)Mρc, where M^^^- is the Mach number U^^^-/c. And the attenuation characteristic of sound due to a resonator in a duct with gas flow can be expressed as Eq. 33. Eq. 33 shows that the effect of gas flow is in inverse proportion to the area πa^2 of an aperture, that is, the longer the neck of an aperture becomes, the more the effect of gas flow decreases, provided that the conductivity of an aperture G is kept constant. Theoretical curves are shown in Figs. 7-12 comparing with the measured values. As a practical illustration, the measured values of sound attenuation of an automobile engine installed with simple resonator type mufflers are also presented in Figs. 14-16.

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