A travelling wave is described by the equation `y = y_(0) sin2 pi ((ft - (x)/lambda))`. The maximum particle velocity is equal to four times the wave velocity if

Options

A. `lamda = (pi y_(0))/(4)`
B. `lamda = (pi y_(0))/(2)`
C. `lamda = pi y_(0)`
D. `lamda = 2 pi y_(0)`

Answer

B

Explanation

`y=y_(0)sin 2pi(ft-(x)/(lamda)),v=y_(0)(2pit)cos2 pi(ft-(x)/(lamda))`
`:. v_(max)=y_(0)2pit,v_("wave")=f lamda`
`v_(max)=4v_("wave")`
`rArr y_(0)(2pif)=4(lamda)=(pi y_(0))/(2)`.