NEET Class neet Answered

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Asked by Prashant DIGHE | 02 Jun, 2020, 10:03: PM

Expert Answer

F o r space d e s c r i b i n g space a s space w a v e space m o t i o n comma space t h e space e x p r e s s i o n space m u s t space s a t i s f y space t h e space f o l l o w i n g space c o n d t i o n comma space fraction numerator partial differential squared y over denominator partial differential t squared end fraction space equals space omega squared over k squared fraction numerator partial differential squared y over denominator partial differential x squared end fraction space... space left parenthesis asterisk times right parenthesis space L e t apostrophe s space c h e c k space e a c h space o p t i o n colon space minus space a right parenthesis space y space equals space cos space k x space sin omega t fraction numerator partial differential y over denominator partial differential t end fraction equals space omega cos space k x space cos omega t fraction numerator partial differential squared y over denominator partial differential t squared end fraction equals space minus omega squared space cos k x space sin omega t space... space left parenthesis 1 right parenthesis fraction numerator partial differential squared y over denominator partial differential x squared end fraction space equals space minus k squared space cos k x space sin omega t space... space left parenthesis 2 right parenthesis space f r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space i t apostrophe s space c l e a r space t h a t space t h e space e q left parenthesis asterisk times right parenthesis space i s space s a t i s f i e d space b right parenthesis space y space equals space k squared x squared space minus space omega squared t squared space fraction numerator partial differential y over denominator partial differential t end fraction space equals space minus 2 space omega squared t fraction numerator partial differential squared y over denominator partial differential t squared end fraction equals negative 2 space omega squared space... space left parenthesis 3 right parenthesis space fraction numerator partial differential squared y over denominator partial differential x squared end fraction space space equals space 2 k squared space... space left parenthesis 4 right parenthesis space O p t i o n space left parenthesis b right parenthesis space d o e s space n o t space s a t i f y space t h e space c o n d i t i o n c right parenthesis space y space equals space cos squared space left parenthesis k x space plus omega t right parenthesis space fraction numerator partial differential squared y over denominator partial differential t squared end fraction space equals space minus 2 omega squared space cos left parenthesis 2 k x space plus space 2 omega t right parenthesis space space... space left parenthesis 5 right parenthesis fraction numerator partial differential squared y over denominator partial differential x squared end fraction space equals space minus 2 k squared space cos left parenthesis 2 k x space plus space 2 omega t right parenthesis... space left parenthesis 6 right parenthesis space O p t i o n space left parenthesis c right parenthesis space s a t i f i e s space t h e space c o n d i t i o n space d right parenthesis space y space equals space cos space left parenthesis k squared x squared space minus space omega squared t squared right parenthesis space fraction numerator partial differential squared y over denominator partial differential t squared end fraction space equals space 2 omega space sin left parenthesis k squared x squared space minus space omega squared t squared right parenthesis space minus space 4 omega squared t squared space space cos space left parenthesis k squared x squared space minus space omega squared t squared right parenthesis space space fraction numerator partial differential squared y over denominator partial differential x squared end fraction space equals space minus 2 k squared space sin space left parenthesis k squared x squared space minus space omega squared t squared right parenthesis space minus space 4 k x space cos left parenthesis k squared x squared space minus space omega squared t squared right parenthesis O p t i o n space left parenthesis d right parenthesis space a l s o space d o space n o t space s t a i s f y space t h e space c o n d i t i o n. space

Thus, correct option will be (a) and (c)

Answered by Shiwani Sawant | 03 Jun, 2020, 11:39: PM

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