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. (a) `lambda = pi(y_(0))/(4)`
B. (b) `lambda = pi(y_(0))/(2)`
C. ( c ) `lambda = piy_(0)`
D. (d) `lambda = 2piy_(0)`

Answer

B

Explanation

(b) `y = y_(0)sin 2pi[(f_(1) - (x)/(lambda)]`
:. `(dy)/(dt) = [y_(0) cos 2pi((ft - (x)/(lambda))] xx 2pif`
or, `[(dy)/(dt)]_(max) = y_(0) xx 2pif`
Given that the maximum particle velocity is equal to four times the wave velocity `(c = f xx lambda)` :. `lambda = (piy_(0))/(2)`