The propagation of waves of acoustic frequencies in curved ducts is studied for the first four modes. The analysis makes use of Bessel functions of the order (n + i) to construct curves of wave number in the duct versus imposed wave number. The results apply to ducts of arbitrary width and arbitrary radii of curvature. The characteristics of motion in a bend are compared with propagation of waves in a straight duct, and important differences in the behavior of waves are noted. The propagation of waves of acoustic frequencies in curved ducts is studied for the first four modes. The analysis makes use of Bessel functions of the order to construct curves of wave number in the duct versus imposed wave number. The results apply to ducts of arbitrary width and arbitrary radii of curvature. The characteristics of motion in a bend are compared with propagation of waves in a straight duct, and important differences in the behavior of waves are noted.
{"title":"Frequencies","authors":"D. George, Paul Mallery","doi":"10.4324/9780429056765-7","DOIUrl":"https://doi.org/10.4324/9780429056765-7","url":null,"abstract":"The propagation of waves of acoustic frequencies in curved ducts is studied for the first four modes. The analysis makes use of Bessel functions of the order (n + i) to construct curves of wave number in the duct versus imposed wave number. The results apply to ducts of arbitrary width and arbitrary radii of curvature. The characteristics of motion in a bend are compared with propagation of waves in a straight duct, and important differences in the behavior of waves are noted. The propagation of waves of acoustic frequencies in curved ducts is studied for the first four modes. The analysis makes use of Bessel functions of the order to construct curves of wave number in the duct versus imposed wave number. The results apply to ducts of arbitrary width and arbitrary radii of curvature. The characteristics of motion in a bend are compared with propagation of waves in a straight duct, and important differences in the behavior of waves are noted.","PeriodicalId":356036,"journal":{"name":"IBM SPSS Statistics 26 Step by Step","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129916690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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