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 a)/(8)`
B. `lamda = (pi a)/(4)`
C. `lamda = (pi a)/(2)`
D. `lamda = (pi a)/(0.5)`

Answer

C

Explanation

`y = a sin (omega t - (2pi x)/(lamda))`
`:. v = (dy)/(dt) = a omega cos (omega t - (2pi x)/(lamda))`
This is maximum, when `cos (omega t - (2pi x)/(lamda)) = 1`
`:. v_("max") = a omega = 2pi n a` and wave velocity `= n lamda`
`:' 2pi na = 4n lamda = lamda = (pi a)/(2)`