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=piy_(0)`
D. `lamda=2piy_(0)`

Answer

B

Explanation

`y=y_0 sin2pi[ft-x/lambda] therefore dy/dt=[y_0cos 2pi(ft-x/lambda)]xx2pi f implies[dy/dt]_max=y_0xx2xf`
Given that maximum particle velocity is equal to four times the wave velocity `(c=lambda)`
`therefore y_0xx2pi f=4 fxxlambda,lambda=(piy_0)/2`