![Page 1: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/1.jpg)
Acoustic diffraction by Acoustic diffraction by an Oscillating stripan Oscillating strip
![Page 2: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/2.jpg)
This problem isbasically solved by a technique
calledWiener Hopf
technique
![Page 3: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/3.jpg)
Scheme of Presentation Scheme of Presentation This presentation includes: This presentation includes:
1.1. Introduction of Introduction of OriginatorsOriginators of this Technique of this Technique
2.2. A general tour of A general tour of Wiener Hopf techniqueWiener Hopf technique
4.4. Applications of Wiener-Hopf techniqueApplications of Wiener-Hopf technique
5.5. Acoustic diffraction by an Oscillating stripAcoustic diffraction by an Oscillating strip
a)a) GeometryGeometry
b)b) Formation of the ProblemFormation of the Problem
c)c) Solution of the problemSolution of the problem
d)d) Graphical / Numerical ComputationGraphical / Numerical Computation
![Page 4: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/4.jpg)
Introduction of
Originators of this
Technique
![Page 5: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/5.jpg)
![Page 6: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/6.jpg)
![Page 7: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/7.jpg)
A general tour ofWiener Hopf
technique
![Page 8: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/8.jpg)
![Page 9: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/9.jpg)
![Page 10: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/10.jpg)
![Page 11: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/11.jpg)
Application ofApplication of Wiener-Hopf technique Wiener-Hopf technique
![Page 12: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/12.jpg)
![Page 13: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/13.jpg)
Acoustic diffraction by Acoustic diffraction by an Oscillating stripan Oscillating strip
![Page 14: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/14.jpg)
![Page 15: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/15.jpg)
What is an acoustic Plane What is an acoustic Plane Wave?Wave?
![Page 16: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/16.jpg)
A wave coming from a source A wave coming from a source located at an infinite distance with located at an infinite distance with
constant frequency and amplitude. constant frequency and amplitude.
![Page 17: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/17.jpg)
How it looks like?How it looks like?
![Page 18: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/18.jpg)
![Page 19: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/19.jpg)
GeometryGeometry
![Page 20: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/20.jpg)
Strip GeometryStrip Geometry
![Page 21: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/21.jpg)
![Page 22: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/22.jpg)
Formulation Formulation of the of the
ProblemProblem
![Page 23: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/23.jpg)
We consider the scattering of plane acoustic We consider the scattering of plane acoustic wave from an oscillating strip occupying the wave from an oscillating strip occupying the space at and is oscillating space at and is oscillating in a direction perpendicular to the screen in a direction perpendicular to the screen with velocity , where is a with velocity , where is a periodic function of time whose periodic function of time whose generalized Fourier seriesgeneralized Fourier series is given by is given by
l x 0 y 0
u0 f1t f1tt
f1t n n Cnein 0t.
![Page 24: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/24.jpg)
Here, the Fourier coefficients are given Here, the Fourier coefficients are given
byby
Cn
Cn 1T0
f1te in 0tdt,
with non zero fundamental frequency
0 2T0
0.
![Page 25: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/25.jpg)
Assume the continuity of the velocity across the boundary as given in P. A Cannel paper
ty u0 ft, l x 0,
where the total velocity potential satisfies the wave equation
t
2
x2 2
y2 t 1
c2
2 t t2
.
For convenience, we write
t i,
y 0, x 0,
![Page 26: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/26.jpg)
iwhere φ is the diffracted field and is the incident field given by
i exp ik 1x cos 0 y sin 0 i 1 t, 0 0 ,
Where is the frequency and is the speed of the sound.
k 1 1c , 1 c
![Page 27: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/27.jpg)
We need to solve the following boundaryWe need to solve the following boundary
value problem:value problem:
2
x2 2
y2 1
c2
2 t2
,
y x, 0, t ik 1 sin 0e ik1x cos 0 i 1t u0 f1t l x 0,
x, 0 , t x, 0 , t,y x, 0 , t
y x, 0 , t,, x l, x 0, y 0.
![Page 28: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/28.jpg)
Scheme of SolutionScheme of Solution
1.1. Fourier temporal transformFourier temporal transform of the of the ProblemProblem is taken to is taken to convert it from convert it from time domaintime domain to to frequency domainfrequency domain
2.2. Then Then Fourier Integral transformFourier Integral transform is taken to switch the is taken to switch the problem to problem to Complex domainComplex domain from from Spatial domainSpatial domain
3.3. Problem is now solved using Wiener-Hopf technique in Problem is now solved using Wiener-Hopf technique in Complex domainComplex domain
4.4. Inverse Fourier transform Inverse Fourier transform is taken bring back the problem is taken bring back the problem in in Spatial domainSpatial domain
5.5. Then Then Inverse Temporal transformInverse Temporal transform is taken to bring it back is taken to bring it back to to time domaintime domain
![Page 29: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/29.jpg)
Solution of the ProblemSolution of the Problem
![Page 30: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/30.jpg)
x,y,
x,y, tei tdt,
x,y, t 12
x,y, e i td .
Define the temporal Fourier transform pair as
![Page 31: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/31.jpg)
We need to solve the following boundaryWe need to solve the following boundary
value problem:value problem:
2
x2 2
y2 1
c2
2 t2
,
y x, 0, t ik 1 sin 0e ik1x cos 0 i 1t u0 f1t l x 0,
x, 0 , t x, 0 , t,y x, 0 , t
y x, 0 , t,, x l, x 0, y 0.
![Page 32: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/32.jpg)
Taking the temporal Fourier transform, the above take the form as follows:
2
x2 2
y2 k 2 x,y, 0,
y x, 0, 2 ik 1 sin 0e ik1x cos 0 1 u0 f , l x 0,
x, 0 , x, 0 , ,y x, 0 ,
y x, 0 , , x l, x 0, y 0,
where
k c k 1 ik 2 with k 2 0 and
f 2 Cn n 0.
![Page 33: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/33.jpg)
,y,
x,y, ei xdx,
x,y, 12
,y, e i xd ,
Define Spatial Fourier transform over the variable as follows:x
with
,y, ,y, 1 ,y, e i l ,y, ,
,y, 0
x,y, ei xdx,
![Page 34: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/34.jpg)
1 ,y, l
0
x,y, ei xdx,
,y,
0
x,y, ei xdx.
1 , 0, 2 k1 sin 0 1
k1 cos 01 exp i k 1 cos 0l
u 0f i 1 exp i l
, l x 0,
Transforming above equations into -plane,
x, 0 , x, 0 , ,y x, 0 ,
y x, 0 , , x l, x 0, y 0,
where 2 2 k 2 with Re 0 in the strip Imk Im Imk.
d 2
dy2 2 ,y, 0,
![Page 35: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/35.jpg)
,y, A , e y , if y 0,
A , e y, if y 0,
The Solution of after using the continuity of Ψ′ across y=0 is given by
d 2
dy2 2 ,y, 0,
,y, ,y, 1 ,y, e i l ,y, ,Now using above and following equation,
we have
A , 0 , 1 , 0 , e i l , 0 , ,
and
A , 0 , 1 , 0 , e i l , 0 , .
![Page 36: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/36.jpg)
Adding and subtracting above two equations Adding and subtracting above two equations we have we have First Wiener HopfFirst Wiener Hopf equation: equation:
2S e i l 2 , 0, 2J1 , 0, 0,
2S , 0 , , 0 , ,
2J1 , 0, 1 , 0 , 1 , 0 , ,
2 , 0, 2 , 0 , , 0 , , 0 , ,
where
![Page 37: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/37.jpg)
andandA J2 , 0, ,
whereJ2 , 0, 1
2 1 , 0 , 1 , 0 , ,
,y, A , e y , if y 0,
A , e y, if y 0,
Now, solving again
,y, ,y, 1 ,y, e i l ,y, ,and
x, 0 , x, 0 , ,y x, 0 ,
y x, 0 , , x l, x 0, y 0,
and
![Page 38: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/38.jpg)
A , 0, 1
, 0, e i l , 0, .
Using the continuity of across y 0
We arrive at the Second Wiener Hopf equation
e i l , 0, J2 , 0,
, 0, 2 k 1 sin 0 1G u 0f
i 1 exp i l,where
G 1 exp i k1 cos 0l k1 cos 0
.
equations mentioned above in red boxes
and after solving
We get
![Page 39: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/39.jpg)
Solution of above W.E equation, as laid down in B. Noble’s book, we Solution of above W.E equation, as laid down in B. Noble’s book, we arrive at the following value of the arrive at the following value of the
A 1 A exp i k 1 cos 0l k 1 cos 0 k 1 cos 0
A R2 exp i l
exp i lA kT C2
iu0 f exp i l
0
exp i lT Tk k iu0 f k1
2kT2k 1
k 1
0
exp i lT Tk k iu0 f
k1 2kT2k
A
k 1 cos 0 k 1 cos 0
A eilk1 cos 0R1 iu0 f
0
T Tk k iu0 f
k1 2kT2k
1 k
1 0
T Tk k iu0 f
k1 2kT2k
AT kC1. 5.44
A
![Page 40: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/40.jpg)
![Page 41: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/41.jpg)
x,y, 12
,y, e i xd 12
A , e |y | i xd .
The function x,y, can be obtained by taking the inverse Fourier transform
Now, x,y, can be broken up as follows:
x,y, sepx,y, intx,y, ,
sepx,y, 12
1
A exp i k1 cos 0l k1 cos 0 k1 cos 0
A k1 cos 0 k1 cos 0
where
iu 0f exp i l 0
iu 0f 0
e |y | i xd ,
![Page 42: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/42.jpg)
intx,y, 12
1 A R2 exp i l A kT C2 exp i l
T Tk k iu 0f exp i l
k1 2kT2k
1 k
1 0
T Tk k iu 0f exp i l
k1 2kT2k
A eilk1 cos 0R1 T Tk k iu 0f
k1 2kT2k
1 k
1 0
T Tk k iu 0f
k1 2kT2k
AT kC1 e |y | i xd .
Here sepx,y, consists of two parts each representing the diffracted field produced by the edges at x 0
and x l, respectively, as though the other edge were absent while intx,y, gives the interaction of
one edge upon the other.
![Page 43: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/43.jpg)
Far Field Approximation Far Field Approximation
The far field approximation can found asymptotically. We arrive at the following results
![Page 44: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/44.jpg)
![Page 45: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/45.jpg)
![Page 46: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/46.jpg)
![Page 47: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/47.jpg)
Graphical Graphical DiscussionDiscussion
![Page 48: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/48.jpg)
Case 1Case 1We consider the case where the We consider the case where the
angle of incidence to the oscillating angle of incidence to the oscillating strip (strip (with constant frequencywith constant frequency) is) is
different say 30different say 30oo, 45, 45oo and 90 and 90oo
![Page 49: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/49.jpg)
![Page 50: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/50.jpg)
![Page 51: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/51.jpg)
![Page 52: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/52.jpg)
![Page 53: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/53.jpg)
Amplitude of the separated field for different values of angle of incidence
![Page 54: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/54.jpg)
Case 2Case 2We consider the case where the We consider the case where the frequency of the incidence ray is frequency of the incidence ray is
different and the strip is oscillating different and the strip is oscillating with constant frequency. with constant frequency.
![Page 55: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/55.jpg)
![Page 56: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/56.jpg)
![Page 57: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/57.jpg)
![Page 58: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/58.jpg)
![Page 59: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/59.jpg)
Amplitude of the separated field for different values of wave frequency
![Page 60: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/60.jpg)
Case 3Case 3We consider the case where the We consider the case where the frequency of the incidence ray is frequency of the incidence ray is
constant and the strip is oscillating constant and the strip is oscillating with different frequencies. with different frequencies.
![Page 61: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/61.jpg)
![Page 62: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/62.jpg)
![Page 63: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/63.jpg)
![Page 64: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/64.jpg)
![Page 65: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/65.jpg)
Amplitude of the separated field for different values of strip frequency
![Page 66: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/66.jpg)
Respected Gentlemen Respected Gentlemen I take pride to introduce aI take pride to introduce a
New ideaNew idea inin
Wiener Hopf technique Wiener Hopf technique in the in the
Strip GeometryStrip Geometry
![Page 67: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/67.jpg)
To understand this, we need to To understand this, we need to have the idea of the half plane and have the idea of the half plane and
the strip geometries. the strip geometries. Lets have a trip to these. Lets have a trip to these.
![Page 68: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/68.jpg)
Half Plane GeometryHalf Plane Geometry
![Page 69: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/69.jpg)
Strip GeometryStrip Geometry
![Page 70: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/70.jpg)
DDiscussioniscussionIf we gradually increase the value of If we gradually increase the value of
the strip length the strip length ll. . PleasePlease
Imagine what will happenImagine what will happen??
![Page 71: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/71.jpg)
DiscussionDiscussion
The Strip geometry supposed to be The Strip geometry supposed to be converted into Half plane geometry.converted into Half plane geometry.
![Page 72: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/72.jpg)
This phenomenon must be This phenomenon must be implemented to check the validity of implemented to check the validity of
the results obtained for the Strip the results obtained for the Strip geometry both Mathematically and geometry both Mathematically and
Graphically.Graphically.
![Page 73: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/73.jpg)
Mathematical VerificationMathematical Verification
![Page 74: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/74.jpg)
![Page 75: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/75.jpg)
Mathematical VerificationMathematical Verification
![Page 76: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/76.jpg)
Graphical VerificationGraphical Verification
![Page 77: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/77.jpg)
Amplitude of the separated field for Amplitude of the separated field for different values of strip frequency for different values of strip frequency for
l 101
![Page 78: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/78.jpg)
Amplitude of the separated field for different values Amplitude of the separated field for different values of strip frequency forof strip frequency for
l 1014
![Page 79: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/79.jpg)
Amplitude of the separated field for different values Amplitude of the separated field for different values of of stripstrip frequency for frequency for l 1022 .
![Page 80: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/80.jpg)
Bashir’s Half Plane resultBashir’s Half Plane result
![Page 81: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/81.jpg)
Amplitude of the diffracted field for different values of Amplitude of the diffracted field for different values of half planehalf plane frequency frequency
![Page 82: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/82.jpg)
Amplitude of the separated field for different
values of Oscillating Strip frequency for l 1022 .
Amplitude of the diffracted field for
different values of Half Plane frequency
![Page 83: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/83.jpg)
![Page 84: Acoustic diffraction by an Oscillating strip. This problem is basically solved by a technique called Wiener Hopf technique](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649f005503460f94c162e9/html5/thumbnails/84.jpg)
Question/AnswerQuestion/Answer
SessionSession