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

Options

A. `lambda=(pi A)/4`
B. `lambda=(pi A)/2`
C. `lambda = piA`
D. `lambda =2 pi A`

Answer

B

Explanation

Given, `y=A sin 2pi (vt-x/lambda)`,
Wave velocity `=v lambda` ...(i)
Particle velocity `=(dy)/(dt)=(2 pi v A) cos 2 pi (vt-x/lambda)`
Maximum particle velocity `= 2pi v A` ...(ii)
Given, the maximum particle velocity is equal to four times the wave velocity.
`:. 2 pi v A=4 xx (v lambda)` or `lambda =(pi A)/2`