The coordinates of a particle moving in a plane are given by x (t) = a cos (pt) and y (t) = b sin (pt), where a, b (`lt` a), and p are positive constants of appropriate dimensions. Then:

Options

A. A node occurs at x = 0.15 m
B. An antinode occurs at `x -0.3 m`
C. The speed of wave is `5 ms^(-1)`
D. The wavelength is `0.2 m`

Answer

A, B, C, D

Explanation

`(2pi)/(lamda)=10pi rArrlamda=0.2m`
Node occurs at `x=(lamda)/(4),(3lamda)/(4), (5lamda)/(4)=0.05m`
`0.15 m`
Antinode occurs at `x=(lamda)/(2),lamda,3(lamda)/(2)`....=
`0.1 m,0.2,0.3m`
`v = (50 pi)/(10 pi) = 5 m//s`