An acoustic space-time and the Lorentz transformation in aeroacoustics

被引：24

作者：

Gregory, Alastair L. ^{[1
,3
]}

Sinayoko, Samuel ^{[2
]}

Agarwal, Anurag ^{[1
]}

Lasenby, Joan ^{[1
]}

机构：

[1] Univ Cambridge, Dept Engn, Cambridge CB2 1PZ, England

[2] Univ Southampton, Inst Sound & Vibrat Res, Southampton SO17 1BJ, Hants, England

[3] Univ Cambridge, Magdalene Coll, Cambridge CB3 0AG, England

来源：

INTERNATIONAL JOURNAL OF AEROACOUSTICS | 2015年 / 14卷 / 07期

关键词：

MATHEMATICAL LANGUAGE; SOUND RADIATION; MODEL; PROPELLER;

D O I：

10.1260/1475-472X.14.7.977

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics, We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation of the space-time transformation, and are able to give neat and lucid derivations of the free-field Green's function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow.

引用

页码：977 / 1003

页数：27

共 50 条

[1] LORENTZ TRANSFORMATION IN INDETERMINISTIC SPACE-TIME
CHEON, IT
LETTERE AL NUOVO CIMENTO, 1982, 34 (02): : 47 - 51
[2] A GENERALIZATION OF SPECIAL LORENTZ TRANSFORMATION IN DESITTER SPACE-TIME
TAKENO, H
PROGRESS OF THEORETICAL PHYSICS, 1953, 10 (04): : 431 - 441
[3] N-dimensional space-time unit spheres and Lorentz transformation
Wuming Li
Fan Yang
Advances in Applied Clifford Algebras, 2003, 13 (1) : 57 - 64
[4] Discrete Space-Time and Lorentz Symmetry
B. G. Sidharth
International Journal of Theoretical Physics, 2004, 43 : 1857 - 1861
[5] LORENTZ TRANSFORMATIONS AS SPACE-TIME REFLECTIONS
KRAUSE, J
JOURNAL OF MATHEMATICAL PHYSICS, 1977, 18 (05) : 889 - 893
[6] Discrete Space-time and Lorentz Transformations
Jensen, Gerd
Pommerenke, Christian
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2016, 59 (01): : 123 - 135
[7] Discrete space-time and Lorentz symmetry
Sidharth, BG
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2004, 43 (09) : 1857 - 1861
[8] Fields of Lorentz transformations on space-time
Gottlieb, DH
TOPOLOGY AND ITS APPLICATIONS, 2001, 116 (01) : 103 - 122
[9] ON ROTATIONS AND LORENTZ TRANSFORMATIONS IN A GALOIS SPACE-TIME
BELTRAME.EG
BLASI, A
ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1969, 46 (04): : 390 - &
[10] GENERALIZED LORENTZ GROUP OF SPACE-TIME TRANSFORMATIONS
Yarman, Tolga
Altintas, Azmi A.
Kholmetskii, Alexander L.
Arik, Metin
Marchal, Christian B.
Yarman, Ozan
Ozaydin, Fatih
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2020, 10 (04): : 987 - 1008

← 1 2 3 4 5 →