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NEET Class neet Answered

please answer this (only part B)
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Asked by Prashant DIGHE | 04 Jun, 2020, 10:13: PM
answered-by-expert Expert Answer
Z1=ACos(kx-wt)
Z2=ACos(kx+wt)
Z3=Acos(ky-wt)
A wave travelling in the direction making an angle of 450
with the positive x and y axis.
Z subscript 1 equals A C o s open parentheses k x minus omega t close parentheses
Z subscript 2 equals A C o s open parentheses k x plus omega t close parentheses
Z subscript 3 equals A C o s open parentheses k y minus omega t close parentheses
O n space l a n a l y sin g space t h e space e q u a t i o n space w e space g e t space t h a t space Z subscript 1 space a n d space Z subscript 2 space a r e space t r a v e l l i n g space i n space o p p o s i t e space d i r e c t i o n space a n f d space h e n c e space s u p e r i m p o s e space t o space p r o d u c e space s tan d i n g space w a v e space
F o r space Z subscript 1 space a n d space Z subscript 3 space t r a v e l l i n g space i n space p o s i t i v e space d i r e c t i o n space o f space space x space a n d space y space a x i s space r e s p e c t i v e l y comma space t h e r e f o r e space m a k e s space t h e space
o n l y space c o m b i n a t i o n space w h i c h space c a n space p r o d u c e space t h e space d e s i r e d space r e s u l t.
T h e space r e s u l tan t space w a v e space w o u l d space b e
Z equals Z subscript 1 plus Z subscript 3
Z equals A C o s open parentheses k x minus omega t close parentheses plus A C o s open parentheses k y minus omega t close parentheses
C o s space C space plus C o s space D equals 2 C o s fraction numerator C plus D over denominator 2 end fraction C o s fraction numerator C minus D over denominator 2 end fraction
Z equals 2 C o s fraction numerator k x plus k y minus 2 omega t over denominator 2 end fraction C o s fraction numerator k x minus k y over denominator 2 end fraction
T h e space r e s u l tan t space w o u l d space b e space z e r o space w h e n

C o s fraction numerator k x minus k y over denominator 2 end fraction equals 0

fraction numerator k x minus k y over denominator 2 end fraction equals open parentheses fraction numerator 2 n plus 1 over denominator 2 end fraction close parentheses straight pi
straight x minus straight y equals open parentheses fraction numerator 2 straight n plus 1 over denominator straight k end fraction close parentheses straight pi
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