{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/42227"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/42227","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Green's function derivations for specific acoustic admittances and impedances","abstract":"Impedance and admittance relationships in acoustics are commonly given in their frequency-domain representations. This is done for many reasons including the simplicity of the mathematics used to compute frequency-domain impedance functions. However, although the frequency-domain representations of acoustical wave propagation typically have very neat closed-form solutions, there is a lack of intuition from the use of such techniques stemming from the added necessity of visualizing both a spatial and a frequency-domain dependence. Time-domain functions complement the frequency-domain constructs by providing new insight and intuition into important problems. The most common geometries under investigation for acoustics are those of a propagating plane wave, an outbound spherical wave, and an outbound cylindrical wave. For all three of these geometries, there exist fully developed frequency-domain techniques to derive the corresponding impedance and admittance functions. However since any frequency-domain function must have a time-domain counterpart, there should exist time-domain representations of these functions as well. Time-domain impedance and admittance functions for acoustical waves can be directly computed without the use of any frequency-domain methods or properties by using Green's functions. The strength of frequency- domain methods can also be realized since in simple geometries time-domain impedance functions can be easily calculated. However it is important to note that even in moderately complex geometries such as an outbound cylindrical wave, computing the time-domain impedance function can be difficult. The end goal of the time-domain analysis of acoustic impedance and admittance functions is an improved physical understanding of acoustic wave propagation. Although frequency-domain constructs are common, they do not provide this intuition. This thesis explores derivations of time-domain functions and provides improved intuition into these solutions.","abstract_html":"Impedance and admittance relationships in acoustics are commonly given in their frequency-domain representations. This is done for many reasons including the simplicity of the mathematics used to compute frequency-domain impedance functions. However, although the frequency-domain representations of acoustical wave propagation typically have very neat closed-form solutions, there is a lack of intuition from the use of such techniques stemming from the added necessity of visualizing both a spatial and a frequency-domain dependence. Time-domain functions complement the frequency-domain constructs by providing new insight and intuition into important problems. The most common geometries under investigation for acoustics are those of a propagating plane wave, an outbound spherical wave, and an outbound cylindrical wave. For all three of these geometries, there exist fully developed frequency-domain techniques to derive the corresponding impedance and admittance functions. However since any frequency-domain function must have a time-domain counterpart, there should exist time-domain representations of these functions as well. Time-domain impedance and admittance functions for acoustical waves can be directly computed without the use of any frequency-domain methods or properties by using Green's functions. The strength of frequency- domain methods can also be realized since in simple geometries time-domain impedance functions can be easily calculated. However it is important to note that even in moderately complex geometries such as an outbound cylindrical wave, computing the time-domain impedance function can be difficult. The end goal of the time-domain analysis of acoustic impedance and admittance functions is an improved physical understanding of acoustic wave propagation. Although frequency-domain constructs are common, they do not provide this intuition. This thesis explores derivations of time-domain functions and provides improved intuition into these solutions.","abstract_has_math":false,"creators":["Kartan, Sundeep"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Allen, Jont B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-02-03T19:28:30Z","date_published":"2013-02-03T19:28:30Z","updated_at":"2026-07-22T22:25:33Z","subjects":["Acoustic wave propagation","Time-domain admittance","time-domain impedance","Green's functions"],"languages":["en"],"rights":["Copyright 2012 Sundeep Kartan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/42227","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Allen, Jont B."]},{"key":"dc:creator","label":"Author","values":["Kartan, Sundeep"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-02-03T19:28:30Z","2012-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Acoustic wave propagation","Time-domain admittance","time-domain impedance","Green's functions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Sundeep Kartan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/42227"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Impedance and admittance relationships in acoustics are commonly given in their frequency-domain representations. This is done for many reasons including the simplicity of the mathematics used to compute frequency-domain impedance functions. However, although the frequency-domain representations of acoustical wave propagation typically have very neat closed-form solutions, there is a lack of intuition from the use of such techniques stemming from the added necessity of visualizing both a spatial and a frequency-domain dependence. Time-domain functions complement the frequency-domain constructs by providing new insight and intuition into important problems. The most common geometries under investigation for acoustics are those of a propagating plane wave, an outbound spherical wave, and an outbound cylindrical wave. For all three of these geometries, there exist fully developed frequency-domain techniques to derive the corresponding impedance and admittance functions. However since any frequency-domain function must have a time-domain counterpart, there should exist time-domain representations of these functions as well. Time-domain impedance and admittance functions for acoustical waves can be directly computed without the use of any frequency-domain methods or properties by using Green's functions. The strength of frequency- domain methods can also be realized since in simple geometries time-domain impedance functions can be easily calculated. However it is important to note that even in moderately complex geometries such as an outbound cylindrical wave, computing the time-domain impedance function can be difficult. The end goal of the time-domain analysis of acoustic impedance and admittance functions is an improved physical understanding of acoustic wave propagation. Although frequency-domain constructs are common, they do not provide this intuition. 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Time-domain functions complement the frequency-domain constructs by providing new insight and intuition into important problems. The most common geometries under investigation for acoustics are those of a propagating plane wave, an outbound spherical wave, and an outbound cylindrical wave. For all three of these geometries, there exist fully developed frequency-domain techniques to derive the corresponding impedance and admittance functions. However since any frequency-domain function must have a time-domain counterpart, there should exist time-domain representations of these functions as well. Time-domain impedance and admittance functions for acoustical waves can be directly computed without the use of any frequency-domain methods or properties by using Green's functions. The strength of frequency- domain methods can also be realized since in simple geometries time-domain impedance functions can be easily calculated. However it is important to note that even in moderately complex geometries such as an outbound cylindrical wave, computing the time-domain impedance function can be difficult. The end goal of the time-domain analysis of acoustic impedance and admittance functions is an improved physical understanding of acoustic wave propagation. Although frequency-domain constructs are common, they do not provide this intuition. This thesis explores derivations of time-domain functions and provides improved intuition into these solutions.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-12-11T16:05:51Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Kartan_Sundeep.pdf: 436362 bytes, checksum: ac1c5485d00ae89be0fd7a2e5e174d62 (MD5)","Made available in DSpace on 2013-02-03T19:28:30Z (GMT). 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