The equation of a wave distrubance is a given as `y= 0.02 sin ((pi)/(2)+50pi t) cos (10 pix)`, where x and y are in metre and t is in second . Choose the correct statement (s).

Options

A. Velocity of medium particle at x=0.12 m at `t=(1)/(5)` sec is zero
B. displacement node occurs at x=0.15 m
C. displacement antinode occurs at x=0.3 m
D. the speed of contrituent waves is 0.2 m/s

Answer

A, B, C, D

Explanation

`v(x,t)=(deltay)/(deltat)=-0.02cos(10pix)sin(50pit)xx50pi`
`implies v(0.012,(1)/(5))=0`
Displacement node occurs at `10pix=(pi)/(2),(3pi)/(2)` etc. `implies x=0.05,0.15` . .
Displacement antinode ocurs at `10pix=0,pi,2pi,3pi implies x=0,0.10.2` . . .
A=0.02 m
`omega=50rad//s" "k=10pi//m" "v=(omega)/(k)=5m//s`.