Two progressive waves Y₁= 2 ( t 0 4 - x 4 ) and Y ₂= 2 ( t 0 4 + x 4 ) superpose to form a standing wave. ' x ' and ' y ' are in SI system. Amplitude of the particle at x=0.5 ~m is [ 45^ = 45^ = 1 2 ]

Step-by-step solution

Y=Y₁+Y₂ array ll & Y= ( 2 t 0.4 - 2 x 4 )+ ( 2 t 0.4 + 2 x 4 ) & (A+B)+ (A-B)=2 A B & Y=2 ( 2 t 0.4 ), ( 2 x 4 ) & Y=R ( 2 t 0.4 ), where R is the amplitude & R=2 ( 2 x 4 ) & at x=0.5 & R=2 ( 2 4 2 )=2 ( 4 )= 2 2 = 2 array