A longitudinal wave is described by the equation `y = y_(0) sin 2pi (ft - x// lambda)` . The maximum particle velocity is equal to four times the wave velocity if ……….. .

Options

A. `lambda = pi y_(0)//4`
B. `lambda = pi y_0//2`
C. `lambda = 4 pi y_(0)`
D. `lambda = 2 pi y_(0)`

Answer

B

Explanation

Particle velocity ` v= (dy)/(dt) = 2 pi y_(0) cos {2 pi (ft - x// lambda)}`
`v_("max") = 2pi fy_0`
`v_("max") = 2pi f y_(0) = 4 f lambda`
`implies lambda = (pi y_(0))/(2)`