Question

find out the resultant displacement of the particle at x at time t.of y1(x,t)= 0.2 sin π (t-2x) and 1(x,y)= 0.2 sin π (t+ 2x)​

Answer 1

Answer:

0.4 sin(t) cos(2x)

Explanation:

1st equation : y1(x,t)= 0.2 sin π (t-2x)

2st equation : Y2(x,t)= 0.2 sin π (t+ 2x)​               ( assume this one corrected)

Y = Y1 + Y2

  = 0.2 sin π (t-2x) + 0.2 sin π (t+ 2x)​          

  = 0.2 ( 2 sin(t)cos(2x) )                             ( sin(a-b) + sin(a+b) = 2sin(a).cos(b) )

  = 0.4 sin(t) cos(2x)  

so given the resultant displacement of the particle at x at time t.of y1 and Y2