MHT CET20226 Aug 2022Evening ShiftPhysicsWaves and SoundActual
A wave travelling along uniform string represented by Y=A ( t-k x) is superimposed on another wave travelling along the same string represented by Y=A ( t+k x) . The resultant is
Options
- AA wave travelling along +x direction.
- BA standing wave having nodes at x= (n+ 1 2 ) 2 , where n=0,1,2,3
- CA wave travelling along -x direction
- DA standing wave having nodes at x= n 2 , where n=0,1,2,3 .
Correct answer
B. A standing wave having nodes at x= (n+ 1 2 ) 2 , where n=0,1,2,3
Step-by-step solution
The equation of the standing wave formed due to superposition of Y=A ( t-k x) and Y=A ( t+k x) is given by, Y=[2 A (k x)] ( t) Location of the nodes is dictated by condition: [2 A (k x)]=0 Therefore, aligned & k x= ( 2 ) x=(2 n+1) 2 & x= (n+ 1 2 ) 2 ; n=0,1,2, . aligned