Energy relations in sound propagation in porous materials with rigid skeleton |
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Authors: | F Kolmer J Tichý |
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Institution: | (1) Image and Reproduction Technique, Research Institute of Sound, Prague;(2) Dept. of Physics, Electrotechnical Faculty, Czech Technical University, Prague |
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Abstract: | The paper deals with the determination of the frequency dependence of the acoustic resistance, of the structure factor, the porosity factor and the constant giving whether the process in the propagation of sound in porous materials with a rigid skeleton is isothermal, adiabatic or polytropic. The latter dependence enables a conclusion to be reached on the energy relations during sound propagation in porous materials.The derivation of the wave resistance and of the constant of wave propagation in a porous material with a rigid skeleton is given and a method described for calculating the constants characterizing the material on the basis of measurements of the wave resistance and the acoustic impedance of the material. The calculation was carried out for felt and it was found that the acoustic resistance and structure factor depends on the frequency and that the process at low frequencies approaches the isothermal and at high frequency the adiabatic. It is shown that the structure factor is not equal to unity even in order of magnitude, as is often assumed in the literature. It is shown that for a complete knowledge of the acoustic resistance necessary for the calculations it is not enough to determine it by the static method.
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![shchcy](/content/g4761685913vk2wk/xxlarge1097.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) . ![Rcy](/content/g4761685913vk2wk/xxlarge1056.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) 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![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![ucy](/content/g4761685913vk2wk/xxlarge1091.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) 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![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![tscy](/content/g4761685913vk2wk/xxlarge1094.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![zcy](/content/g4761685913vk2wk/xxlarge1079.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![bcy](/content/g4761685913vk2wk/xxlarge1073.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![zcy](/content/g4761685913vk2wk/xxlarge1079.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![zcy](/content/g4761685913vk2wk/xxlarge1079.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![mcy](/content/g4761685913vk2wk/xxlarge1084.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![mcy](/content/g4761685913vk2wk/xxlarge1084.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![bcy](/content/g4761685913vk2wk/xxlarge1073.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) ![ycy](/content/g4761685913vk2wk/xxlarge1099.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) — ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![bcy](/content/g4761685913vk2wk/xxlarge1073.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![mcy](/content/g4761685913vk2wk/xxlarge1084.gif) . ![Dcy](/content/g4761685913vk2wk/xxlarge1044.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![zcy](/content/g4761685913vk2wk/xxlarge1079.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) , ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![ucy](/content/g4761685913vk2wk/xxlarge1091.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ucy](/content/g4761685913vk2wk/xxlarge1091.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![ycy](/content/g4761685913vk2wk/xxlarge1099.gif) ![fcy](/content/g4761685913vk2wk/xxlarge1092.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![yacy](/content/g4761685913vk2wk/xxlarge1103.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![yacy](/content/g4761685913vk2wk/xxlarge1103.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![ycy](/content/g4761685913vk2wk/xxlarge1099.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![tscy](/content/g4761685913vk2wk/xxlarge1094.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![zhcy](/content/g4761685913vk2wk/xxlarge1078.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![yacy](/content/g4761685913vk2wk/xxlarge1103.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) , ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![ecy](/content/g4761685913vk2wk/xxlarge1101.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ucy](/content/g4761685913vk2wk/xxlarge1091.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![gcy](/content/g4761685913vk2wk/xxlarge1075.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) . ![Pcy](/content/g4761685913vk2wk/xxlarge1055.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![zcy](/content/g4761685913vk2wk/xxlarge1079.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) , ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![gcy](/content/g4761685913vk2wk/xxlarge1075.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![ucy](/content/g4761685913vk2wk/xxlarge1091.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![gcy](/content/g4761685913vk2wk/xxlarge1075.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![pcy](/content/g4761685913vk2wk/xxlarge1087.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![vcy](/content/g4761685913vk2wk/xxlarge1074.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) , ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![bcy](/content/g4761685913vk2wk/xxlarge1073.gif) ![khcy](/content/g4761685913vk2wk/xxlarge1093.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![mcy](/content/g4761685913vk2wk/xxlarge1084.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![gcy](/content/g4761685913vk2wk/xxlarge1075.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![lcy](/content/g4761685913vk2wk/xxlarge1083.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) , ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![gcy](/content/g4761685913vk2wk/xxlarge1075.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![zcy](/content/g4761685913vk2wk/xxlarge1079.gif) ![mcy](/content/g4761685913vk2wk/xxlarge1084.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![rcy](/content/g4761685913vk2wk/xxlarge1088.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![ncy](/content/g4761685913vk2wk/xxlarge1085.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![acy](/content/g4761685913vk2wk/xxlarge1072.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![chcy](/content/g4761685913vk2wk/xxlarge1095.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![scy](/content/g4761685913vk2wk/xxlarge1089.gif) ![kcy](/content/g4761685913vk2wk/xxlarge1082.gif) ![icy](/content/g4761685913vk2wk/xxlarge1080.gif) ![mcy](/content/g4761685913vk2wk/xxlarge1084.gif) ![iecy](/content/g4761685913vk2wk/xxlarge1077.gif) ![tcy](/content/g4761685913vk2wk/xxlarge1090.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) ![dcy](/content/g4761685913vk2wk/xxlarge1076.gif) ![ocy](/content/g4761685913vk2wk/xxlarge1086.gif) .
The work was carried on through the cooperation of the Research Institute of Sound, Image and Reproduction Technique and the department of physics at the Electrotechnical Faculty of the Czech Technical University in Prague. The authors would like to thank Prof. J. B. Slavík, head of the department of physics, and M. Jahoda, director of the Research Institute of Sound, Image and Reproduction Technique, for the attention they paid to this work. |
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