A travelling wave is described by the equation `y = y_(0) sin ((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 2 pi [ft-(x)/(lamda)]`
`:. (dy)/(dt)=[y_(0) cos 2 pi(ft -(x)/(lamda))] xx 2 pi f`
`rArr [(dy)/(dt)]_(max) = y_(0) xx 2pi f`
Given that the maximum particle velocity is equal to four times the wave velocity `(c = f lamda)`
`:. y_(0) xx 2pi f = 4 f xx lamda`
`lamda = (pi y_(0))/(2)`.